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A hybrid MCDM approach for order distribution in a multiple-supplier supply chain: A case study
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Journal of Industrial Information Integration journal homepage: www.elsevier.com/locate/jii
A hybrid MCDM approach for order distribution in a multiple-supplier supply chain: A case study ⁎
Mostafa Zandieha, , Babak Aslanib a b
Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd St, Norman, OK 73019, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Order distribution Genetic algorithm (GA) Analytical hierarchy process (AHP) Best-Worst method Supply chain management Central coordination system
The ever-increasing challenges in the business markets have intensified the need for cooperation among all parts of a supply chain. Allocating orders to suppliers in order to satisfy different and conflicting criteria has caused the emergence of new mulita-criteria approaches to address these problems more effectively. This paper investigated an order distribution problem in a real case of Iranian's oil and gas industry. In order to overcome the high complexity of the problem, a hybrid approach combining the features of genetic algorithm (GA) and analytical hierarchy process (AHP) is implemented. An improved version of the central coordination system (CCS) is suggested to integrate and process the various input information of the problem. The selected criteria are based on experts’ opinion in the focused section of the industry. In order to obtain the weights of the criteria, a linear model of the Best-Worst method, a recently developed MCDM method, is implemented. Several candidate solutions are obtained from the results of the proposed hybrid method as the first stage of the study. Then, as the second phase, an AHP approach is used to rank the available solutions. Finally, a sensitivity analysis is conducted to test the reliability of the approach. The results indicated the high robustness of the proposed method in dealing with possible changes in the future.
1. Introduction A supply chain consists of several stages. At first, the raw materials are used to produce final products. This phase is related to production planning and inventory control process. Then, the final products should be allocated to the customers. This phase is related to distribution and logistics processes. As a result, a supply chain incorporates these two categories of processes. Since the costs of manufacturing are increasing and the life cycles of products are decreasing, supply chains need collaborative strategies. The effects of this collaboration are fast responsiveness, high flexibility, more enhanced customer service satisfaction, and more retention of customers [38]. Distribution problems are concerned with the allocation of a number of input points to a number of source points, such as material suppliers, manufacturing plants, warehouses, distribution centers, and customers, linked by different transportation facilities to form a supply network [4]. In supply chain management, decision-makers usually are dealing with multi-criteria problems. These criteria include total costs, quality of product, customer service level, inventory level, manufacturing lead times, resources utilization, number of employees, material resources, etc. In the supply chain environment, there are many
⁎
decision criteria that need to be considered. They are highly interrelated and influence each other. Most of the optimization tools that can only optimize one single criterion are not able to be utilized in these situations. A real intelligent distribution algorithm, specially designed for supply chain management, should be capable of considering more than one single factor. Moreover, because of different weights of factors in various structures of the supply chain environment in different situations, consideration of weighting is also critical [3]. An intelligent distribution methodology for orders distribution is a key element in supply chain management which determines the effectiveness of a supply chain. A supply chain network usually consists of more than one supplier, located at different coordination. Also, each supplier has its limitations and characteristics such as capacity, cost, lead-time, etc. These suppliers can be considered as manufacturing plants under a single organization or different organizations under a central coordination system [7]. Collaborating organizations need to establish and commit a set of rules in order to collaborate. These rules may include the determination of the type of information to share, communication media, sharing of financial expenditure from collaboration activities, sharing of benefits gained from collaboration, level of customer satisfaction to offer, the
Corresponding author. E-mail address: [email protected] (M. Zandieh).
https://doi.org/10.1016/j.jii.2019.08.002 Received 3 July 2018; Received in revised form 1 August 2019; Accepted 26 August 2019 2452-414X/ © 2019 Elsevier Inc. All rights reserved.
Please cite this article as: Mostafa Zandieh and Babak Aslani, Journal of Industrial Information Integration, https://doi.org/10.1016/j.jii.2019.08.002
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2. Literature review
procedure to make joint decisions between organizations, penalties, and voting for a coordinator. More importantly, when there is more than one collaborating organization for a customer, the organizations have to set rules about the allocation of the customer's order [5]. The central coordination system collects the customers’ orders to distribute them among available suppliers. Following that, the suppliers deliver the products to the customers. The central coordination system functions as a central coordinator in a supply chain network. It is a demand allocation optimization tool considering a series of specific criteria. The final purpose of a supply chain is to serve the consumers and satisfy their demands [38]. Over the past decades, industries have experienced dramatic changes in their organizational activities. Industry 4.0 as a new concept has emerged as a promising technology framework for integrating and extending manufacturing processes at intra-organizational and interorganizational levels. The developments and the technological advances in this novel notion will provide viable solutions to the growing information-related needs of manufacturing industries. Modern enterprise's operation involves various decision-making activities, requiring a large amount of information and intensive computation. This ever-increasing trend has intensified the need for multiple computing resources such as servers for databases and decision-making units. In recent years, the concept of integration as a core competency of digital transformation, one of the five main features of Industry 4.0, has been widely recognized. This integration includes heterogeneous data sources, processes, applications, platforms and standards. Service-oriented architecture (SOA) is a ubiquitous trend in integrating heterogeneous systems. It has received a great deal of attention from companies that are interested in implementing Industry 4.0. Industry 4.0 creates a cyber-physical manufacturing environment that enables the communication and interaction amongst all the players in the valuecreation chain. In this sense, service-oriented architectures serve as an emerging paradigm for enterprises to coordinate seamlessly in the environment of heterogeneous information systems, enabling the timely sharing of information, and enhancing integration [35]. Industrial Information Integration Engineering (IIIE) is a complex giant system that can advance and integrate the concepts, theory, and methods in each relevant discipline and open up a new discipline for industry information integration purposes [36]. In general, IIIE is a series of fundamental concepts and techniques facilitating the industrial information integration process. In particular, IIIE comprises methods for solving complex problems when developing information technology infrastructure for industrial sectors, especially in the aspect of information integration [6]. Central coordination system can function as an effective integration system in a supply chain. This system can gather the data from different layers of a supply chain to process and provide the required information for making the most crucial decisions such as order distribution. Central coordination system has several functions in a supply chain. Firstly, it has the responsibility of organizing collaborating organizations. This task includes activities such as scheduling collaborating activities, determining demand allocations, monitoring performances, and dealing with changes. Secondly, this entity is a central information database. Basically, two types of required input information are classified as decision-making, and performance. Decision-making information includes the information required for demand allocation, such as product specifications, quantity, due date, etc. On the other hand, the constraints-related category includes information such as available production quantity and capacities, storage capacities, production lead-time, and selling price. The last task of the central coordination system is the optimization of demand allocations. At first, it considers the requirements of orders as well as constraints of collaborating organizations. Then, it allocates the orders to the organizations according to the order distribution rules [5].
Researchers usually have approached the supplier selection and order allocation problem with integrated methods. However, in the current study, the supplier selection phase is not included in the problem. So, the literature review is divided into two separate sections. At first, studies investigated the supplier selection and order allocation problem are presented. However, only the recent studies focusing on hybrid approaches of MCDM and heuristic algorithms are chosen to focus on more relevant studies to the current study. At the second section, the studies considered the order allocation, sometimes also known as order distribution, separately are presented. 2.1. Supplier selection and order allocation Demirtas and Üstün [9] proposed an approach integrating analytic network process (ANP) and multi-objective mixed integer linear programming (MOMILP) to consider supplier selection process. They calculated the priorities for each supplier via ANP. Four different firms in the plastic industry were evaluated according to the obtained results. Finally, the non-dominated solutions were selected by considering the decision maker's preferences and the results obtained by these techniques were compared. Wu et al. [34] proposed an integrated multi-objective decisionmaking method included ANP and mixed integer programming (MIP) to address the supplier selection problem. The criteria were gathered from experts through Delphi method, and were used as inputs of the ANP model. Likewise, the ANP results were implemented in the MIP model to allocate orders to the suppliers. A numerical example was presented and the results indicated the usefulness of the proposed method. Fazlollahtabar et al. [10] proposed an integrated approach of analytical hierarchy process (AHP), the technique for order of preference by similarity to ideal solution (TOPSIS), and multi-objective nonlinear programming for the problem. The priorities were calculated for each supplier by AHP. Then, TOPSIS was implemented for ranking the suppliers. Finally, the optimal quantities of orders to the suppliers were determined in the multi-period horizon. A case study was used to evaluate the validity and efficiency of the proposed model. They conducted a performance analysis to investigate the capability and effectiveness of the results. Liao and Kao [21] implemented integrated fuzzy techniques for TOPSIS and multi-choice goal programming (MCGP) approach for a case study in a watch firm. Ghorbani et al. [11] approached the problem via a two-phase model. At first, suppliers were evaluated using strengths, weaknesses, opportunities, Threats (SWOT) analysis. Having the criteria, Shannon entropy was used to obtain the weight of criteria. Then, the results were used in the integer linear programming (ILP) to allocate orders to suppliers. Kilic [15] implemented an integrated approach including fuzzy Technique for TOPSIS and a mixed integer linear programming model to investigate supplier selection in a multi-supplier environment. Then, the results were used in the mathematical model to assign orders to suppliers. To validate the proposed methodology, a case in air filter section was considered. Arabzad et al. [2] developed a two-phase model. They implemented a SWOT analysis to evaluate the available suppliers considering qualitative and quantitative criteria. In this phase, a fuzzy-TOPSIS method was developed to calculate the weights of the criteria. In the second phase, results from fuzzy-TOPSIS were used an input for linear programming to allocate orders. A case study was used to validate the proposed model. Govindan and Sivakumar [13] investigated recycling and optimized sourcing through a case study in the paper industry. A two-phase hybrid approach was proposed to select the best green suppliers and to allocate the orders among the potential suppliers. The first phase rated the potential suppliers using Fuzzy-TOPSIS methodology. The order allocation phase was addressed by multi-objective linear programming. The results showed a 26.2% reduction of carbon emission by using recycled 2
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system combined with a multi-criteria genetic algorithm. They proposed a modified MCOGA based on the TOPSIS. Compared with the MCOGA, the proposed method had less complexity in the evaluation phase. The numerical example of order distribution demonstrated the efficiency of the proposed method. Recently, Kumar et al. [16] investigated order distribution problem considering all three dimensions of sustainability, including economic, social, and environmental. They used an integrated fuzzy-AHP and fuzzy multi-objective linear programming approach for order distribution problem. A case study of an Indian automobile company was investigated in this study. Liu et al. [22] approached the order allocation problem in a two-echelon supply chain consisting of a logistics service integrator (LSI) and several functional logistics service providers (FLSPs). They proposed a two-stage order allocation model considering demand updating and the FLSPs’ fairness preferences. To find the optimal point, they implemented the ideal point method. They also verified the theoretical perspectives of their method through an empirical study of Tianjin SND Logistics Company. Likewise, Wang and Miao [33] investigated an interdependent order allocation problem in a twoechelon supply chain, including manufacturer echelon and supplier echelon. They developed an agent-based negotiation algorithm to support the order allocation process and the conflicts resolution. They demonstrated the good performance of their algorithm in various supply chain contexts.
products in the production process. Sodenkamp et al. [31] proposed a new meta-approach to support collaborative multi-objective decisions regarding a case study in the agricultural sector. They integrated multicriteria decision analysis and linear programming (LP). Hamdan and Cheaitou [14] proposed a decision-making tool for a multi-period green supplier selection and order allocation problem. They implemented multi-period bi-objective and multi-objective optimization for the problem. The results showed that the two approaches provided very close solutions. However, the bi-objective approach had lower computational time. Recently, Gören [12] proposed a decision framework for sustainable supplier selection and order allocation problem. The framework consisted of integrated fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) approach and Taguchi Loss Functions, and a new bi-objective model considering the issue of lost sales. Later, Park et al. [26] proposed a two-phase integrated approach to effectively reflect the multi-perspectives of global supply chain design for sustainability. They implemented a multi-attribute utility theory in the first phase to identify sustainable supplier regions. In the second phase, a multi-objective integer linear programming model for multiple sourcing and multiple product designs was designed to minimize economic and environmental objectives and find optimal suppliers and their order quantities in the regions selected from the first phase. Lo et al. [23] proposed a novel model integrating the Best–Worst Method (BWM), modified fuzzy-TOPSIS, and fuzzy multi-objective linear programming (FMOLP) to solve the green supplier selection and order allocation problem. They used a case study in an electronics company to test the proposed approach. Mohammed et al. [24] presented an integrated methodology to solve a sustainable two-stage supplier selection and order allocation problem for a meat supply chain. They used fuzzy-AHP, fuzzy-TOPSIS, a multi-objective programming model (MOPM), and a fuzzy MOPM to address the problem. Vahidi et al. [32] suggested a novel bi-objective two-stage mixed possibilistic-stochastic programming model to address sustainable supplier selection and order allocation problem under operational and disruption risks. To select the criteria, they used a hybrid SWOT- Quality Function Deployment (QFD) approach. To validate the approach, they used a number of numerical examples.
3. Problem description The order distribution problem can be considered as a permutation problem in which a series of orders should be assigned to a number of available suppliers in order to optimize several objectives simultaneously. Due to the complicated nature of supply chains, these objectives are usually conflicting with each other or are interconnected. For instance, a supplier offering a lower cost for an order may deliver it in a longer period of time. So, decision-makers should consider these conflicts by an effective holistic approach. The effects of this phase are farreaching to all levels of a supply chain. Customers can have more satisfaction from delivering their orders at a reasonable cost as soon as possible. In addition, suppliers can establish deeper relationships with their customers, too. Hence, considering a supply chain as an interconnected network can benefit all sections in terms of meeting the needs of all layers of a multi-layer supply chain. Order distribution problem can be considered as a specific category of general assignment problems. In order to overcome the complexity of these problems, MCDM techniques are great options. They provide this opportunity for decision-makers to assess different scenarios based on several criteria in an efficient procedure [17,25]. Moreover, as the number of alternatives increases, the order distribution problem becomes more and more complicated. As a result, exact methods are not practical in real-life problems. This feature has led to an increasing trend to heuristic and metaheuristic approaches to deal with this problem more effectively. As a result, in this study, a hybrid approach of MCDM techniques and metaheuristic algorithms is implemented to address the order distribution problem.
2.2. Order distribution Chan et al. [5] investigated vertical and horizontal supply chain collaboration. Their framework contained a multi-criteria genetic optimization feature. The proposed method combined an AHP with genetic algorithms. Chan and Chung [3] developed a multi-criteria genetic optimization approach, precisely designed for solving optimization problems in supply chain management. The proposed method integrated the AHP with genetic algorithms. The numerical results showed the reliability and robustness of the proposed algorithm. Following that, Altiparmak et al. [1] proposed a new approach based on genetic algorithms to find Pareto-optimal solutions for multi-objective supply chain network design problem. A case study of plastic products in Turkey was investigated in two stages. As the first stage of the study, the effects of weight approaches on the performance were investigated. Then, as the second stage, the proposed approach and simulated annealing (SA) were compared in terms of the quality of Pareto-optimal solutions. Chan et al. [4] focused on order due date fulfillment reliability in multi-echelon distribution network problem with uncertainties. They proposed a multi-criteria genetic integrative optimization approach for the problem. The computational results showed the reliability of the proposed algorithm. Later, Chung et al. [7] developed a multi-criteria genetic algorithm for solving distribution problems in supply chain management. The proposed methodology combined AHP with GA. The numerical results showed that the proposed method was reliable and robust. Zhang et al. [38] adopted a framework of a central coordination
3.1. Extended CCS In this research, an extended version of CCS is proposed to address the information integration aspect of the problem. The structure of this information integration system is shown in Fig. 1. The proposed system consists of two separate units, processing and decision-making. 3.2. Processing unit Like the original version of CCS, in the extended version, two types of information also enter the processing unit. These large amounts of data are processed by using specific rules to make a balance between 3
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Fig. 1. Extended version of CCS.
production limitations and customers’ expectations. Integrating these types of information can facilitate the decision-making process greatly. So, the processed information in the processing unit can be used as the input data for the decision-making unit.
2- Supplier rule: The available suppliers should be appraised using certain measures to be considered as an eligible one. This rule can be summarized as follow:
3.2.1. Reasoning machine After integrating the two types of information in the processing unit, a reasoning machine is implemented in order to provide the required decisions for the company. This machine uses three different rules so that analyzes the input information and make the final decisions about orders, suppliers, and criteria. These decisions are made through three rules:
Supplier rule =
If the supplier is qualified ⎧ ⎪ ⎨ → Consider the supplier as a suitable one ⎪ Else → Eliminate from the list ⎩
3- Criteria rule: This rule assess the various types of criteria and select the most influential ones. These criteria can affect the relationship between different parts of the supply chain. This rule can be summarized as follow:
1- Order rule: the placed orders should be assessed based on several criteria such as production capacity and customers’ due dates. This rule can be summarized as follow:
If the criteria is effective → Put it on the list Criteria rule = ⎧ ⎨ ⎩ Else → Eliminate from the list
If the order is practical → Accept the order Order rule = ⎧ → Reject the order Else ⎨ ⎩ 4
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valid upstream documents such as five-year development plans. Considering the position of the Iranian oil industry, the vision of this industry is so important that various goals have been taken into account for this section. The reduction of the country's energy intensity to lower than 0.3 (equivalent to crude oil per thousand dollars of GDP at constant prices in 2000) and maintaining the capacity of the second largest producer of crude oil in OPEC are among the set goals of this industry. Achieving the second position in the natural gas production capacity considering the need for using common reservoirs is another objective in the field of the petroleum industry.
3.2.2. Output The output of this phase consists of three distinct categories: 1- Orders: by assessing the available production capacities and comparing them with the available pool of orders, a series of orders are selected to be allocated to suppliers. 2- Suppliers: a certain number of suppliers are selected based on specific policies of the organization. In this matter, the previous transactions with suppliers are also taken into account. 3- Criteria: In order to compare the available distribution schemes, a series of criteria should be provided to decision makers. These criteria are the input information for the hybrid MCDM approach, too.
4.1.3. Upstream and downstream industries The upstream industry in the oil industry refers to the search, exploration, drilling, and production of crude oil and natural gas, and sometimes also is known as exploration and production. The upstream industry includes searching for potential underground or submarine fields, drilling and exploration of wells, and ultimately activities related to wells that extract crude oil as well as natural gas. The downstream industry in the oil industry is a phrase commonly used to refer to crude oil refining, the sale and distribution of natural gas and crude oil products. Operations such as the sale and distribution of natural gas and products derived from crude oil such as liquid gas (LPG), gasoline, jet fuel, diesel fuel, oils, and asphalt are classified in this section.
3.3. Decision-making unit This unit is responsible for allocating the orders to available suppliers in the most efficient way. To do so, after receiving the experts’ opinion about the different criteria, the weights are calculated in a predefined procedure. Then, the candidate solutions from GA-AHP process should be ranked by another AHP process. The best solutions can be considered as the output of the decision-making unit. In addition, feedback from this unit is sent to the processing section. This feedback includes the performance of suppliers, the relative importance of different criteria, mutual cooperation with suppliers, and so on. The processing unit can use this information in future processing cycles. Moreover, the data can be stored in separate records (or clouding systems) for each customer and supplier for future decisions. Therefore, the orders of customers will be allocated to the most suitable supplier considering the details of previous mutual collaborations.
4.2. The investigated case study In this study, a facility in the downstream section of the oil and gas industry is investigated. The facility has a number of orders, all of which are outsourced to external suppliers. As a result, this case is a suitable example of order distribution problem with which we are dealing in this study. In order to have a clearer image of the process of assigning orders to suppliers, 3 experts in this sector of the industry are selected. Having the opinions of these experts, the most important criteria for the order distribution problem are organized as follow: Cost: Like every other similar part of a supply chain, a major contributing factor in this decision are monetary aspects. While total cost includes order, production, and transportation elements, the transportation item is much more influential. However, all components are considered as a whole cost category in the order distribution problem. The closer suppliers are more desired since they impose fewer transportation costs, though. Another part of the differences among costs is because of business schemes presented by different suppliers and the special discounts based on mutual contracts. Quality: The organizational policy indicates that the required parts should be delivered at the highest level of quality. So, the suppliers assuring more quality are more desirable for assigning orders. In fact, following the ISO regulations have made the quality among the most important factors in this facility. Delivery: The assigned orders to each supplier are delivered within a specified timeframe. However, this factor is not as much important as total cost due to the nature of the business and orders of the focused industry. Utility: In order to make the situation more competitive, the policy of industry dictates that orders should be distributed among all existing suppliers. The mentioned policy is intended to assure a fair business interaction between all parts of the supply chain. The utility of a solution is calculated through the following steps:
4. Case study In this section, firstly, an overview of the oil and gas industry in Iran is presented. Following that, the investigated case study is explained in terms of the scope and the position in the industry. The detailed information of the first part is gathered from the official site of the national Iranian's oil company.1 4.1. The overview of the oil and gas industry Iran has the second largest production in Organization of the Petroleum Exporting Countries (OPEC) and the fifth largest in the world. Iran produced more than 3.7 million barrels a day in 2010. The National Iranian Oil Company (NIOC) has held crude production between 3.8 and 4.0 million barrels a day for in the last decade. Iran has also the second largest gas reserves in the world. Iran's gas production growth has gone up by 10% on average. 4.1.1. Main mission NIOC is a national symbol of independence and has a key role in the protection of Iran's oil and gas as the main components of Iran's economic production. The production of crude oil and natural gas and liquid hydrocarbons, transportation, marketing and sale of it as part of national wealth, as well as the safeguarding of this public asset, is the main assignment of the NIOC. To do so, equipping and designing industrial and production complexes and training local staff to maximize the use of national capabilities is considered as one of the most important missions and duties of the NIOC. 4.1.2. Goals and organizational strategy The goals and policies of the NIOC are part of the policies of the Islamic Republic of Iran. Accordingly, the vision of the NIOC is founded within the framework of the national macroeconomic strategies and the 1
1- Calculate the frequency of all n suppliers (n is the number of suppliers) in the solution (ui) 2- Find the average frequency (u¯ ) 3- Calculate the standard deviation of obtained frequencies using the following formula:
www.nioc.ir 5
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Fig. 2. Chromosome representation of GA.
utility =
1 n
attempts to find better solutions along with preserving the best current individuals in the population. The possible solutions should be coded in the form of chromosomes and be decoded at the end of the process to actual numbers. Due to the high speed of the algorithm and high quality of solutions to complicated and hard problems, GA has become a popular method in different fields, including industrial optimization. In addition, the evolutionary theory and coding strategy of GA, has eliminated the full consideration given to the complex mathematical characteristics of real problems and no restrictions imposed on objective functions [18]. More specifically, GA can be implemented in generic assignment problems, one of which is allocating orders among a set of suppliers [20].
n
∑ (ui − u¯)2 i=1
(1)
Environmental: Since the selected facility is related to the downstream section of the petroleum industry, the environmental regulations are very vital to abide by. To meet these requirements, suppliers with better performance are considered more suitable than others. Following ISO 14001, indicate clear guidelines for the facility in the environmental section. As this criterion is a qualitative one, it is defined as a number between 1 and 5 based on a series of specific assessments. The factory policy clearly states that suppliers with a factor below 1 should be excluded from all possible interactions. As a result, this criterion is among the most important factors. The considered timeframe included 480 orders and 22 suppliers to distribute orders among them. All data related to the chosen criteria for each supplier are available before running the proposed method for the order distribution process.
5.2.1. Representation of chromosome Each chromosome shows a potential optimal solution for the problem. In this specific problem, the values of the genes represent the suppliers, and their locations represent the orders. Consider we have 5 suppliers as potential candidates to process 10 orders in the investigated horizon. The chromosome for this example is shown in Fig. 2.
5. Methodology 5.2.2. Fitness To compare the strength of the members of a population in GA, a value known as fitness value is assigned to them. In addition, the selection process is dependent on this value, too. This value can be calculated using several methods. However, since in the current study several objectives should be assessed simultaneously, the fitness value is calculated by using an AHP method.
5.1. Best-Worst method This method is introduced by Rezaei [27] in order to overcome the disadvantages of other MCDM methods. In this method, the best and the worst criteria are selected by the decision maker(s) and a pairwise comparison is conducted between other criteria and the chosen ones. The problem can be formulated as a min-max problem to obtain final weights of all criteria. Like AHP, an inconsistency rate is calculated to assess the comparisons between criteria. This recently proposed method has some advantages over other MCDM methods. First of all, it needs fewer pairwise comparisons compared to other similar procedures such as AHP. Second of all, the results are more reliable and more robust. Finally, the accuracy of comparisons can be assessed in a more efficient way, too [27].
5.2.3. Selection process This stage has a key role in the performance of GA since a good strategy can help the algorithm to move to more promising areas of solution space. To do so, a roulette wheel selection procedure is used in this research to give more chance to better individuals to participate in crossover and mutation phases. In this selection method, the probability of selection of individual x is computed as follows:
5.2. Genetic algorithm
p (x i ) =
Evolutionary computation is an area of computer science that uses ideas from biological evolution to solve computational problems. Searching a vast solution space is the common feature of these problems. An adaptive system capable of coping with changes is another requirement for solving these problems. Biological evolution can also be seen as a method for adapting to changing environments. In nature, species evolve by means of random variation (mutation, recombination, and other operators), followed by natural selection in which the fittest members tend to survive and reproduce. These apparently simple rules also guarantee that the best features are transferred to future generations, too. Genetic algorithm (GA) is one of the most effective approaches which is inspired by biological evolution strategies [19]. GA was introduced by Holland and DeJong [8] in 1975. The algorithm begins with an initial generation of possible solutions. Then, by implementing crossover and mutation operators, the algorithm
fitness (x i ) n ∑i = 1 fitness (x i )
(2)
As a result, more powerful individuals have more chance to enter the mating pool. This strategy guarantees more promising populations in the next generations of GA [30]. 5.2.4. Crossover Crossover operator uses the individuals in the current generation as parents, and through some changes creates two offspring. In the current study, a two-point crossover is implemented as a powerful procedure to achieve more suitable offspring in the next iterations. However, the length of the selected string should be large enough to be effective. Fig. 3 shows the used method for a sample chromosome. 5.2.5. Mutation This operator is used to maintain the diversification of the 6
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Fig. 3. Two-point crossover of GA. Fig. 4. Mutation operator of GA.
5.5. Relative values
algorithm. Hence, a more radical process is implemented in this section. At first, a sub-string is chosen randomly from a parent. Then, the order of suppliers is reversed inside the selected string. This can assure that the algorithm will search previously uninvestigated regions of the problem, too. Fig. 4 demonstrates the mentioned method in a sample chromosome.
As a critical step of AHP, the alternatives should be compared in each criterion. Consequently, relative values are calculated based on the nature of the criterion for all alternatives. In this section, the comprehensive method for obtaining these values for each criterion is presented. Cost: Since a lower cost for assigning an order to a supplier is more suitable, the relative values for two alternatives are calculated as follows:
5.3. AHP AHP is a multi-criteria approach introduced by Saaty [29] for the first time in 1980. This method is developed based on pairwise comparisons between criteria and alternatives. The AHP has been implemented in various decision-making problems due to its clear procedure as well as its usefulness in real life problems. AHP is a multicriteria method that can be used to evaluate the importance of each component of a problem. The AHP hierarchy model consists of a top layer that is the goal, the second layer that is the criteria level, and the third layer that is the alternative level. The data are collected by using a set of pairwise comparisons conducted by experts in the respected field. These comparisons show the relative preference of the decision criteria and the relative preference of the alternatives in each decision criterion. An inconsistency rate is calculated to assess the reliability of comparisons [37]. AHP is helpful in dealing with several available options in terms of finding the most suitable alternative. This feature of AHP makes it a useful tool to evaluate the fitness of a population in GA. Considering several objectives in an optimization problem intensifies the need for AHP in the evaluation phase of GA. The assigned weights to criteria mirroring the human knowledge can be used to find better solutions among available alternatives. The salient characteristic of the AHP is organizing a complex problem into a structured hierarchy. As a result, it integrates all the criteria into a hierarchy of weightings.
Relative Cost (i,j) =
Cost j Costi
(3)
Quality: This criterion is presented using qualitative numbers. So, if the accumulated quality of a solution is higher than the other one, the first one is more favorable.
Qualityi Qualityj
Relative Quality (i,j) =
(4)
Delivery: Naturally, the facility is looking for faster deliveries. Hence, a solution with a lower total delivery time is more suitable than a solution with a higher one.
Relative Delivery (i,j) =
Deliveryi Deliveryj
(5)
Utility: The lower degrees of utility indicates the more equitable distribution of orders among available suppliers. Therefore, in order to compare two solutions in terms of utility, the reversed fraction is an acceptable method.
Relative Utility (i,j) =
Utilityj Utilityi
(6)
5.4. Proposed method Environmental: The higher ranks of environmental factor represent the conformity of environmental regulations by the selected supplier. Thus, the solutions with a higher total value in this criterion are more desirable for the company.
Since the investigated problem is essentially a multi-objective problem, AHP is used in the evaluation phase of the proposed GA. Fig. 5 shows the pseudo-code of the proposed method. 7
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Fig. 5. Pseudo-code of the proposed method.
case the opinions of 3 experts are gathered, the average numbers are used in the final assessment.
Table 1 GA parameters. Parameter
Value
Max Iteration Population Size Crossover rate Mutation rate
600 400 0.6 0.1
Relative Environmental (i,j) =
Environmentali Environmental j
AB = (1, 2, 5, 7, 3) AB = (1, 6, 5, 9, 1) AB = (1, 3, 4, 8, 7)
Average
⇒
AB = (1, 4, 5, 8, 4)
Step 4: Assign a number between 1 and 9 as the preference of all the criteria over the worst criterion. Like the best criterion, in the worst criterion vector, average numbers are also used in the final assessment.
(7)
Aw = (7, 6, 5, 1, 4) Aw = (9, 7, 3, 1, 6) Aw = (8, 7, 5, 1, 5)
6. Computational results
Average
⇒
Aw = (8, 7, 5, 1, 5)
6.1. Weight calculation Step5: Find the optimal weights. Since there are more than 3 criteria in our problem, a linear model of BWM can result in a unique solution with a low inconsistency rate. As Rezaei [28] stated, to obtain a more consistent and unique result for the problems with more than 3 criteria, a linear model is a more suitable choice. The linear model can be shown through the following sets of equations:
In order to find the weights of the criteria, a linear Best-Worst method is used in this study. To create the model, the following steps should be followed: Step 1: select the criteria: The selected criteria are based on experts’ opinion, including cost, quality, delivery, utility, and environmental. Step 2: select the best and the worst criteria: Considering all the contributing factors, experts asserted that the cost and the utility are the best and the worst criteria, respectively. Step3: Assign a number between 1 and 9 as the preference of the best criterion over all the other criteria. Since in the investigated 8
Minσ
(8)
s. t: wB − aBj wj ≤ σ , ∀ j
(9)
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∑ wj = 1
Table 2 Detailed output of the proposed GA-AHP.
(11)
j
No. of run
Criteria Cost
Quality
Delivery
Utility
Environmental
Weight of AHP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
251,149 251,854 251,382 250,603 251,476 252,597 249,638 252,219 252,806 251,649 251,983 251,788 250,285 250,885 253,223 252,043 251,281 252,492 252,389 251,742 251,818 252,420 251,191 251,903 250,535 250,889 251,257 253,078 251,394 251,511 253,590 251,056 251,254 251,508 251,516 251,820 250,516 251,152 250,802 251,624
1446 1519 1468 1418 1467 1461 1450 1428 1480 1490 1444 1432 1409 41,431 1422 1433 1491 1488 1491 1430 1426 1447 1437 1490 1427 1461 1427 1444 1555 1515 1434 1434 1449 1481 1483 1451 1427 1479 1448 1356
16,570 16,721 16,574 16,631 16,635 16,912 16,935 16,470 17,006 16,656 16,722 16,631 16,965 16,768 16,844 16,493 16,457 16,642 16,634 16,893 16,455 16,278 16,446 16,708 16,641 16,689 16,897 16,639 17,029 16,915 17,111 16,524 16,628 16,836 16,900 16,560 16,583 17,075 16,621 16,821
0.0014 0.0011 0.0008 0.0012 0.0011 0.0035 0.0016 0.0006 0.0008 0.0012 0.0012 0.0029 0.0012 0.0014 0.0029 0.0033 0.0011 0.0012 0.0012 0.0018 0.0012 0.0011 0.0012 0.0012 0.0014 0.0008 0.0008 0.0004 0.0008 0.0020 0.0011 0.0035 0.0012 0.0011 0.0011 0.0011 0.0011 0.0011 0.0018 0.0012
1418 1491 1443 1376 1390 1424 1457 1485 1438 1461 1382 1471 1378 1411 1509 1435 1485 1397 1457 1483 1467 1434 1438 1449 1460 1384 1477 1409 1447 1405 1390 1460 1409 1491 1467 1472 1440 1456 1465 1453
0.0253 0.0260 0.0263 0.0253 0.0256 0.0246 0.0253 0.0270 0.0262 0.0257 0.0254 0.0248 0.0253 0.0253 0.0248 0.0246 0.0260 0.0255 0.0257 0.0251 0.0256 0.0257 0.0256 0.0257 0.0254 0.0262 0.0263 0.0281 0.0265 0.0251 0.0253 0.0247 0.0255 0.0259 0.0258 0.0258 0.0257 0.0258 0.0252 0.0253
wj ≥ 0, ∀ j
wj − ajw ww ≤ σ , ∀ j
(12)
Considering the AB and AW vectors, the obtained optimum result from solving the model by LINGO presenting the weights of criteria as follow:
Cost Quality FW = Delivery Utility Environmental
⎛ 0.502 ⎞ ⎜ 0.162 ⎟ ⎜ 0.130 ⎟ ⎜ 0.044 ⎟ ⎝ 0.162 ⎠
Since the calculated inconsistency rate, 0.147, is very close to 0, the asserted comparisons among different criteria are reliable enough to use them in the proposed method. 6.2. GA-AHP approach Due to the stochastic nature of GA, the proposed GA-AHP algorithm ran 40 times using the same parameters. Table 1 shows the implemented parameters of GA algorithm. The exhaustive results of the proposed GA-AHP are demonstrated in Table 2. 6.3. Best solution selection strategy In order to find the best solutions among all runs, we are facing several alternatives with different values in each criterion. So, essentially we are dealing with a MCDM problem. In this stage, an AHP method is implemented to rank the solutions in different runs of the proposed algorithm in an efficient way. The structure of this procedure is depicted in Fig. 6. The 3 best solutions based on the results of AHP process are indicated in the bold format in Table 2. The following diagrams show the obtained solutions in each criterion separately. The highlighted triangles indicate the chosen best solutions in AHP process, while the line indicates the average value of the criterion. From the mentioned diagrams we can infer some conclusions. First of all, two of the chosen solutions have a total cost higher than the average value. Interestingly, solutions 8 and 28 have a total
(10)
Fig. 6. AHP structure for the evaluation phase. 9
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Fig. 7. Cost criterion of evaluated alternatives.
Fig. 8. Quality criterion of evaluated alternatives.
Fig. 9. Delivery criterion of evaluated alternatives.
6.4. Sensitivity analysis
quality lower than the average quality value, too. These two mentioned solutions have a better delivery time compared to the other one that is solution 29. However, all three solutions have the lowest figures in the utility criterion. Considering the environmental criterion, two solutions are below the average line. So, in order to select better solutions, a trade-off should be considered in which solutions with higher values than average values are chosen to satisfy other influential criteria. (Figs. 7–11)
Since the obtained results are directly affected by human judgment, they are prone to possible changes. For example, external factors such as transportation costs or taxation policies can affect the weights of the criteria. As a result, in this section, a sensitivity analysis is conducted to evaluate the robustness of the ranking procedure. To achieve this goal, 4 scenarios are defined and the ranking is conducted considering the new weights. Since the cost criterion is stated as the most influential 10
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Fig. 10. Utility criterion of evaluated alternatives.
Fig. 11. Environmental criterion of evaluated alternatives.
Fig. 12. Current scenario.
Fig. 13. Scenario 1.
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Fig. 14. Scenario 2.
Fig. 15. Scenario 3.
Fig. 16. Scenario 4.
hybrid GA-AHP was proposed. To have a number of best scenarios, the proposed algorithm executed 40 times. Having the results of the previous phase, an AHP was conducted to rank the possible alternatives. Following that, in order to maintain the flexibility of the managers and the decision makers, three of the best answers were chosen in this phase. Finally, a sensitivity analysis was implemented in order to assess the effects of possible changes in the weights of the criteria on the ranks of the best solutions. The results indicated that the AHP is reliable and the ranks are immune from possible alterations in the weights of the criteria. Due to the complex nature of the investigated problem, developing new hybrid MCDM methods and evolutionary algorithms is the most promising path for researchers. In addition, considering the effects of uncertainty in some criteria such as delivery time on the proposed method is another fruitful area to study.
criterion, we focused on it in this section. The weight of cost criterion is increased about 20% (from 50.2% to 60.2) in the first two scenarios, while in the two other scenarios this number declined 20% (from 50.2% to 40%). The results are shown in the following graphs where the left ones demonstrate the weights of criteria in percent, whereas the right ones show the three top solutions in each scenario along with their weights. Fig. 12 shows the current investigated scenario with current weights, though. (Figs. 13–16) As the presented figures show, the ranks of three top solutions are the same in the all devised scenarios. So, the results of the conducted AHP process are reliable enough to apply to a real situation since ± 20% changes in the weight of cost criteria, the most important one, does not have a tangible effect on the output of the method. 7. Conclusion and future research
Declaration of Competing Interest
In this paper, the order distribution problem in a real case from the oil and gas industry in Iran was investigated. An improved version of CCS was proposed to collect and integrate information from different sectors of the problem. The outputs of the processing unit of CCS were used as the input information for the proposed hybrid MCDM method in the decision-making unit. The most influential criteria in assigning orders to suppliers were organized based on experts’ opinion in the industry. In order to address the multi-objective problem effectively, a
The authors declare that there is no conflict of interest. References [1] F. Altiparmak, M. Gen, L. Lin, T. Paksoy, A genetic algorithm approach for multiobjective optimization of supply chain networks, Comput. Ind. Eng. 51 (1) (2006) 196–215.
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[21] C.N. Liao, H.P. Kao, An integrated fuzzy TOPSIS and MCGP approach to supplier selection in supply chain management, Expert Syst. Appl. 38 (9) (2011) 10803–10811. [22] W. Liu, S. Wang, D. Zhu, D. Wang, X. Shen, Order allocation of logistics service supply chain with fairness concern and demand updating: model analysis and empirical examination, Ann. Oper. Res. , 268 , 1 (–2) (2017) 1–37. [23] H.W. Lo, J.J. Liou, H.S. Wang, Y.S. Tsai, An integrated model for solving problems in green supplier selection and order allocation, J. Clean. Prod. 190 (2018) 339–352. [24] A. Mohammed, R. Setchi, M. Filip, I. Harris, X. Li, An integrated methodology for a sustainable two-stage supplier selection and order allocation problem, J. Clean. Prod. 192 (2018) 99–114. [25] L.A. Ocampo, Fuzzy analytic network process (FANP) approach in formulating infrastructural decisions of sustainable manufacturing strategy, J. Manag. Anal. 3 (3) (2016) 266–284. [26] K. Park, G.E.O. Kremer, J. Ma, A regional information-based multi-attribute and multi-objective decision-making approach for sustainable supplier selection and order allocation, J. Clean. Prod. 187 (2018) 590–604. [27] J. Rezaei, Best-worst multi-criteria decision-making method, Omega 53 (2015) 49–57. [28] J. Rezaei, Best-worst multi-criteria decision-making method: some properties and a linear model, Omega 64 (2016) 126–130. [29] R.W. Saaty, The analytic hierarchy process—what it is and how it is used, Math. Modell. 9 (3–5) (1987) 161–176. [30] A. Shukla, H.M. Pandey, D. Mehrotra, Comparative review of selection techniques in genetic algorithm, International Conference on Futuristic Trends on Computational Analysis and Knowledge Management (ABLAZE), 2015, pp. 515–519. [31] M.A. Sodenkamp, M. Tavana, D. Di Caprio, Modeling synergies in multi-criteria supplier selection and order allocation: an application to commodity trading, Eur. J. Oper. Res. 254 (3) (2016) 859–874. [32] F. Vahidi, S.A. Torabi, M.J. Ramezankhani, Sustainable supplier selection and order allocation under operational and disruption risks, J. Clean. Prod. 174 (2018) 1351–1365. [33] J. Wang, H. Miao, Interdependent order allocation in the two-echelon supply chain using agent-based negotiation, 2017 36th Chinese Control Conference (CCC), July, IEEE, 2017, pp. 7516–7521. [34] W.Y. Wu, B.M. Sukoco, C.Y. Li, S.H. Chen, An integrated multi-objective decisionmaking process for supplier selection with bundling problem, Expert Syst. Appl. 36 (2) (2009) 2327–2337. [35] L.D. Xu, E.L. Xu, L. Li, Industry 4.0: state of the art and future trends, Int. J. Prod. Res. 56 (8) (2018) 2941–2962. [36] L. Xu, Enterprise Integration and Information Architectures, CRC Press, Taylor & Francis, 2015 ISBN: 978-1-4398-5024-4. [37] S. Xu, L. Da Xu, X. Chen, Determining optimum edible films for kiwifruits using an analytical hierarchy process, Comput. Oper. Res. 30 (6) (2003) 877–886. [38] H. Zhang, Y. Deng, F.T. Chan, X. Zhang, A modified multi-criterion optimization genetic algorithm for order distribution in collaborative supply chain, Appl. Math. Model. 37 (14–15) (2013) 7855–7864.
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Contents lists available at ScienceDirect
Journal of Industrial Information Integration journal homepage: www.elsevier.com/locate/jii
A hybrid MCDM approach for order distribution in a multiple-supplier supply chain: A case study ⁎
Mostafa Zandieha, , Babak Aslanib a b
Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd St, Norman, OK 73019, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Order distribution Genetic algorithm (GA) Analytical hierarchy process (AHP) Best-Worst method Supply chain management Central coordination system
The ever-increasing challenges in the business markets have intensified the need for cooperation among all parts of a supply chain. Allocating orders to suppliers in order to satisfy different and conflicting criteria has caused the emergence of new mulita-criteria approaches to address these problems more effectively. This paper investigated an order distribution problem in a real case of Iranian's oil and gas industry. In order to overcome the high complexity of the problem, a hybrid approach combining the features of genetic algorithm (GA) and analytical hierarchy process (AHP) is implemented. An improved version of the central coordination system (CCS) is suggested to integrate and process the various input information of the problem. The selected criteria are based on experts’ opinion in the focused section of the industry. In order to obtain the weights of the criteria, a linear model of the Best-Worst method, a recently developed MCDM method, is implemented. Several candidate solutions are obtained from the results of the proposed hybrid method as the first stage of the study. Then, as the second phase, an AHP approach is used to rank the available solutions. Finally, a sensitivity analysis is conducted to test the reliability of the approach. The results indicated the high robustness of the proposed method in dealing with possible changes in the future.
1. Introduction A supply chain consists of several stages. At first, the raw materials are used to produce final products. This phase is related to production planning and inventory control process. Then, the final products should be allocated to the customers. This phase is related to distribution and logistics processes. As a result, a supply chain incorporates these two categories of processes. Since the costs of manufacturing are increasing and the life cycles of products are decreasing, supply chains need collaborative strategies. The effects of this collaboration are fast responsiveness, high flexibility, more enhanced customer service satisfaction, and more retention of customers [38]. Distribution problems are concerned with the allocation of a number of input points to a number of source points, such as material suppliers, manufacturing plants, warehouses, distribution centers, and customers, linked by different transportation facilities to form a supply network [4]. In supply chain management, decision-makers usually are dealing with multi-criteria problems. These criteria include total costs, quality of product, customer service level, inventory level, manufacturing lead times, resources utilization, number of employees, material resources, etc. In the supply chain environment, there are many
⁎
decision criteria that need to be considered. They are highly interrelated and influence each other. Most of the optimization tools that can only optimize one single criterion are not able to be utilized in these situations. A real intelligent distribution algorithm, specially designed for supply chain management, should be capable of considering more than one single factor. Moreover, because of different weights of factors in various structures of the supply chain environment in different situations, consideration of weighting is also critical [3]. An intelligent distribution methodology for orders distribution is a key element in supply chain management which determines the effectiveness of a supply chain. A supply chain network usually consists of more than one supplier, located at different coordination. Also, each supplier has its limitations and characteristics such as capacity, cost, lead-time, etc. These suppliers can be considered as manufacturing plants under a single organization or different organizations under a central coordination system [7]. Collaborating organizations need to establish and commit a set of rules in order to collaborate. These rules may include the determination of the type of information to share, communication media, sharing of financial expenditure from collaboration activities, sharing of benefits gained from collaboration, level of customer satisfaction to offer, the
Corresponding author. E-mail address: [email protected] (M. Zandieh).
https://doi.org/10.1016/j.jii.2019.08.002 Received 3 July 2018; Received in revised form 1 August 2019; Accepted 26 August 2019 2452-414X/ © 2019 Elsevier Inc. All rights reserved.
Please cite this article as: Mostafa Zandieh and Babak Aslani, Journal of Industrial Information Integration, https://doi.org/10.1016/j.jii.2019.08.002
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2. Literature review
procedure to make joint decisions between organizations, penalties, and voting for a coordinator. More importantly, when there is more than one collaborating organization for a customer, the organizations have to set rules about the allocation of the customer's order [5]. The central coordination system collects the customers’ orders to distribute them among available suppliers. Following that, the suppliers deliver the products to the customers. The central coordination system functions as a central coordinator in a supply chain network. It is a demand allocation optimization tool considering a series of specific criteria. The final purpose of a supply chain is to serve the consumers and satisfy their demands [38]. Over the past decades, industries have experienced dramatic changes in their organizational activities. Industry 4.0 as a new concept has emerged as a promising technology framework for integrating and extending manufacturing processes at intra-organizational and interorganizational levels. The developments and the technological advances in this novel notion will provide viable solutions to the growing information-related needs of manufacturing industries. Modern enterprise's operation involves various decision-making activities, requiring a large amount of information and intensive computation. This ever-increasing trend has intensified the need for multiple computing resources such as servers for databases and decision-making units. In recent years, the concept of integration as a core competency of digital transformation, one of the five main features of Industry 4.0, has been widely recognized. This integration includes heterogeneous data sources, processes, applications, platforms and standards. Service-oriented architecture (SOA) is a ubiquitous trend in integrating heterogeneous systems. It has received a great deal of attention from companies that are interested in implementing Industry 4.0. Industry 4.0 creates a cyber-physical manufacturing environment that enables the communication and interaction amongst all the players in the valuecreation chain. In this sense, service-oriented architectures serve as an emerging paradigm for enterprises to coordinate seamlessly in the environment of heterogeneous information systems, enabling the timely sharing of information, and enhancing integration [35]. Industrial Information Integration Engineering (IIIE) is a complex giant system that can advance and integrate the concepts, theory, and methods in each relevant discipline and open up a new discipline for industry information integration purposes [36]. In general, IIIE is a series of fundamental concepts and techniques facilitating the industrial information integration process. In particular, IIIE comprises methods for solving complex problems when developing information technology infrastructure for industrial sectors, especially in the aspect of information integration [6]. Central coordination system can function as an effective integration system in a supply chain. This system can gather the data from different layers of a supply chain to process and provide the required information for making the most crucial decisions such as order distribution. Central coordination system has several functions in a supply chain. Firstly, it has the responsibility of organizing collaborating organizations. This task includes activities such as scheduling collaborating activities, determining demand allocations, monitoring performances, and dealing with changes. Secondly, this entity is a central information database. Basically, two types of required input information are classified as decision-making, and performance. Decision-making information includes the information required for demand allocation, such as product specifications, quantity, due date, etc. On the other hand, the constraints-related category includes information such as available production quantity and capacities, storage capacities, production lead-time, and selling price. The last task of the central coordination system is the optimization of demand allocations. At first, it considers the requirements of orders as well as constraints of collaborating organizations. Then, it allocates the orders to the organizations according to the order distribution rules [5].
Researchers usually have approached the supplier selection and order allocation problem with integrated methods. However, in the current study, the supplier selection phase is not included in the problem. So, the literature review is divided into two separate sections. At first, studies investigated the supplier selection and order allocation problem are presented. However, only the recent studies focusing on hybrid approaches of MCDM and heuristic algorithms are chosen to focus on more relevant studies to the current study. At the second section, the studies considered the order allocation, sometimes also known as order distribution, separately are presented. 2.1. Supplier selection and order allocation Demirtas and Üstün [9] proposed an approach integrating analytic network process (ANP) and multi-objective mixed integer linear programming (MOMILP) to consider supplier selection process. They calculated the priorities for each supplier via ANP. Four different firms in the plastic industry were evaluated according to the obtained results. Finally, the non-dominated solutions were selected by considering the decision maker's preferences and the results obtained by these techniques were compared. Wu et al. [34] proposed an integrated multi-objective decisionmaking method included ANP and mixed integer programming (MIP) to address the supplier selection problem. The criteria were gathered from experts through Delphi method, and were used as inputs of the ANP model. Likewise, the ANP results were implemented in the MIP model to allocate orders to the suppliers. A numerical example was presented and the results indicated the usefulness of the proposed method. Fazlollahtabar et al. [10] proposed an integrated approach of analytical hierarchy process (AHP), the technique for order of preference by similarity to ideal solution (TOPSIS), and multi-objective nonlinear programming for the problem. The priorities were calculated for each supplier by AHP. Then, TOPSIS was implemented for ranking the suppliers. Finally, the optimal quantities of orders to the suppliers were determined in the multi-period horizon. A case study was used to evaluate the validity and efficiency of the proposed model. They conducted a performance analysis to investigate the capability and effectiveness of the results. Liao and Kao [21] implemented integrated fuzzy techniques for TOPSIS and multi-choice goal programming (MCGP) approach for a case study in a watch firm. Ghorbani et al. [11] approached the problem via a two-phase model. At first, suppliers were evaluated using strengths, weaknesses, opportunities, Threats (SWOT) analysis. Having the criteria, Shannon entropy was used to obtain the weight of criteria. Then, the results were used in the integer linear programming (ILP) to allocate orders to suppliers. Kilic [15] implemented an integrated approach including fuzzy Technique for TOPSIS and a mixed integer linear programming model to investigate supplier selection in a multi-supplier environment. Then, the results were used in the mathematical model to assign orders to suppliers. To validate the proposed methodology, a case in air filter section was considered. Arabzad et al. [2] developed a two-phase model. They implemented a SWOT analysis to evaluate the available suppliers considering qualitative and quantitative criteria. In this phase, a fuzzy-TOPSIS method was developed to calculate the weights of the criteria. In the second phase, results from fuzzy-TOPSIS were used an input for linear programming to allocate orders. A case study was used to validate the proposed model. Govindan and Sivakumar [13] investigated recycling and optimized sourcing through a case study in the paper industry. A two-phase hybrid approach was proposed to select the best green suppliers and to allocate the orders among the potential suppliers. The first phase rated the potential suppliers using Fuzzy-TOPSIS methodology. The order allocation phase was addressed by multi-objective linear programming. The results showed a 26.2% reduction of carbon emission by using recycled 2
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system combined with a multi-criteria genetic algorithm. They proposed a modified MCOGA based on the TOPSIS. Compared with the MCOGA, the proposed method had less complexity in the evaluation phase. The numerical example of order distribution demonstrated the efficiency of the proposed method. Recently, Kumar et al. [16] investigated order distribution problem considering all three dimensions of sustainability, including economic, social, and environmental. They used an integrated fuzzy-AHP and fuzzy multi-objective linear programming approach for order distribution problem. A case study of an Indian automobile company was investigated in this study. Liu et al. [22] approached the order allocation problem in a two-echelon supply chain consisting of a logistics service integrator (LSI) and several functional logistics service providers (FLSPs). They proposed a two-stage order allocation model considering demand updating and the FLSPs’ fairness preferences. To find the optimal point, they implemented the ideal point method. They also verified the theoretical perspectives of their method through an empirical study of Tianjin SND Logistics Company. Likewise, Wang and Miao [33] investigated an interdependent order allocation problem in a twoechelon supply chain, including manufacturer echelon and supplier echelon. They developed an agent-based negotiation algorithm to support the order allocation process and the conflicts resolution. They demonstrated the good performance of their algorithm in various supply chain contexts.
products in the production process. Sodenkamp et al. [31] proposed a new meta-approach to support collaborative multi-objective decisions regarding a case study in the agricultural sector. They integrated multicriteria decision analysis and linear programming (LP). Hamdan and Cheaitou [14] proposed a decision-making tool for a multi-period green supplier selection and order allocation problem. They implemented multi-period bi-objective and multi-objective optimization for the problem. The results showed that the two approaches provided very close solutions. However, the bi-objective approach had lower computational time. Recently, Gören [12] proposed a decision framework for sustainable supplier selection and order allocation problem. The framework consisted of integrated fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) approach and Taguchi Loss Functions, and a new bi-objective model considering the issue of lost sales. Later, Park et al. [26] proposed a two-phase integrated approach to effectively reflect the multi-perspectives of global supply chain design for sustainability. They implemented a multi-attribute utility theory in the first phase to identify sustainable supplier regions. In the second phase, a multi-objective integer linear programming model for multiple sourcing and multiple product designs was designed to minimize economic and environmental objectives and find optimal suppliers and their order quantities in the regions selected from the first phase. Lo et al. [23] proposed a novel model integrating the Best–Worst Method (BWM), modified fuzzy-TOPSIS, and fuzzy multi-objective linear programming (FMOLP) to solve the green supplier selection and order allocation problem. They used a case study in an electronics company to test the proposed approach. Mohammed et al. [24] presented an integrated methodology to solve a sustainable two-stage supplier selection and order allocation problem for a meat supply chain. They used fuzzy-AHP, fuzzy-TOPSIS, a multi-objective programming model (MOPM), and a fuzzy MOPM to address the problem. Vahidi et al. [32] suggested a novel bi-objective two-stage mixed possibilistic-stochastic programming model to address sustainable supplier selection and order allocation problem under operational and disruption risks. To select the criteria, they used a hybrid SWOT- Quality Function Deployment (QFD) approach. To validate the approach, they used a number of numerical examples.
3. Problem description The order distribution problem can be considered as a permutation problem in which a series of orders should be assigned to a number of available suppliers in order to optimize several objectives simultaneously. Due to the complicated nature of supply chains, these objectives are usually conflicting with each other or are interconnected. For instance, a supplier offering a lower cost for an order may deliver it in a longer period of time. So, decision-makers should consider these conflicts by an effective holistic approach. The effects of this phase are farreaching to all levels of a supply chain. Customers can have more satisfaction from delivering their orders at a reasonable cost as soon as possible. In addition, suppliers can establish deeper relationships with their customers, too. Hence, considering a supply chain as an interconnected network can benefit all sections in terms of meeting the needs of all layers of a multi-layer supply chain. Order distribution problem can be considered as a specific category of general assignment problems. In order to overcome the complexity of these problems, MCDM techniques are great options. They provide this opportunity for decision-makers to assess different scenarios based on several criteria in an efficient procedure [17,25]. Moreover, as the number of alternatives increases, the order distribution problem becomes more and more complicated. As a result, exact methods are not practical in real-life problems. This feature has led to an increasing trend to heuristic and metaheuristic approaches to deal with this problem more effectively. As a result, in this study, a hybrid approach of MCDM techniques and metaheuristic algorithms is implemented to address the order distribution problem.
2.2. Order distribution Chan et al. [5] investigated vertical and horizontal supply chain collaboration. Their framework contained a multi-criteria genetic optimization feature. The proposed method combined an AHP with genetic algorithms. Chan and Chung [3] developed a multi-criteria genetic optimization approach, precisely designed for solving optimization problems in supply chain management. The proposed method integrated the AHP with genetic algorithms. The numerical results showed the reliability and robustness of the proposed algorithm. Following that, Altiparmak et al. [1] proposed a new approach based on genetic algorithms to find Pareto-optimal solutions for multi-objective supply chain network design problem. A case study of plastic products in Turkey was investigated in two stages. As the first stage of the study, the effects of weight approaches on the performance were investigated. Then, as the second stage, the proposed approach and simulated annealing (SA) were compared in terms of the quality of Pareto-optimal solutions. Chan et al. [4] focused on order due date fulfillment reliability in multi-echelon distribution network problem with uncertainties. They proposed a multi-criteria genetic integrative optimization approach for the problem. The computational results showed the reliability of the proposed algorithm. Later, Chung et al. [7] developed a multi-criteria genetic algorithm for solving distribution problems in supply chain management. The proposed methodology combined AHP with GA. The numerical results showed that the proposed method was reliable and robust. Zhang et al. [38] adopted a framework of a central coordination
3.1. Extended CCS In this research, an extended version of CCS is proposed to address the information integration aspect of the problem. The structure of this information integration system is shown in Fig. 1. The proposed system consists of two separate units, processing and decision-making. 3.2. Processing unit Like the original version of CCS, in the extended version, two types of information also enter the processing unit. These large amounts of data are processed by using specific rules to make a balance between 3
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Fig. 1. Extended version of CCS.
production limitations and customers’ expectations. Integrating these types of information can facilitate the decision-making process greatly. So, the processed information in the processing unit can be used as the input data for the decision-making unit.
2- Supplier rule: The available suppliers should be appraised using certain measures to be considered as an eligible one. This rule can be summarized as follow:
3.2.1. Reasoning machine After integrating the two types of information in the processing unit, a reasoning machine is implemented in order to provide the required decisions for the company. This machine uses three different rules so that analyzes the input information and make the final decisions about orders, suppliers, and criteria. These decisions are made through three rules:
Supplier rule =
If the supplier is qualified ⎧ ⎪ ⎨ → Consider the supplier as a suitable one ⎪ Else → Eliminate from the list ⎩
3- Criteria rule: This rule assess the various types of criteria and select the most influential ones. These criteria can affect the relationship between different parts of the supply chain. This rule can be summarized as follow:
1- Order rule: the placed orders should be assessed based on several criteria such as production capacity and customers’ due dates. This rule can be summarized as follow:
If the criteria is effective → Put it on the list Criteria rule = ⎧ ⎨ ⎩ Else → Eliminate from the list
If the order is practical → Accept the order Order rule = ⎧ → Reject the order Else ⎨ ⎩ 4
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valid upstream documents such as five-year development plans. Considering the position of the Iranian oil industry, the vision of this industry is so important that various goals have been taken into account for this section. The reduction of the country's energy intensity to lower than 0.3 (equivalent to crude oil per thousand dollars of GDP at constant prices in 2000) and maintaining the capacity of the second largest producer of crude oil in OPEC are among the set goals of this industry. Achieving the second position in the natural gas production capacity considering the need for using common reservoirs is another objective in the field of the petroleum industry.
3.2.2. Output The output of this phase consists of three distinct categories: 1- Orders: by assessing the available production capacities and comparing them with the available pool of orders, a series of orders are selected to be allocated to suppliers. 2- Suppliers: a certain number of suppliers are selected based on specific policies of the organization. In this matter, the previous transactions with suppliers are also taken into account. 3- Criteria: In order to compare the available distribution schemes, a series of criteria should be provided to decision makers. These criteria are the input information for the hybrid MCDM approach, too.
4.1.3. Upstream and downstream industries The upstream industry in the oil industry refers to the search, exploration, drilling, and production of crude oil and natural gas, and sometimes also is known as exploration and production. The upstream industry includes searching for potential underground or submarine fields, drilling and exploration of wells, and ultimately activities related to wells that extract crude oil as well as natural gas. The downstream industry in the oil industry is a phrase commonly used to refer to crude oil refining, the sale and distribution of natural gas and crude oil products. Operations such as the sale and distribution of natural gas and products derived from crude oil such as liquid gas (LPG), gasoline, jet fuel, diesel fuel, oils, and asphalt are classified in this section.
3.3. Decision-making unit This unit is responsible for allocating the orders to available suppliers in the most efficient way. To do so, after receiving the experts’ opinion about the different criteria, the weights are calculated in a predefined procedure. Then, the candidate solutions from GA-AHP process should be ranked by another AHP process. The best solutions can be considered as the output of the decision-making unit. In addition, feedback from this unit is sent to the processing section. This feedback includes the performance of suppliers, the relative importance of different criteria, mutual cooperation with suppliers, and so on. The processing unit can use this information in future processing cycles. Moreover, the data can be stored in separate records (or clouding systems) for each customer and supplier for future decisions. Therefore, the orders of customers will be allocated to the most suitable supplier considering the details of previous mutual collaborations.
4.2. The investigated case study In this study, a facility in the downstream section of the oil and gas industry is investigated. The facility has a number of orders, all of which are outsourced to external suppliers. As a result, this case is a suitable example of order distribution problem with which we are dealing in this study. In order to have a clearer image of the process of assigning orders to suppliers, 3 experts in this sector of the industry are selected. Having the opinions of these experts, the most important criteria for the order distribution problem are organized as follow: Cost: Like every other similar part of a supply chain, a major contributing factor in this decision are monetary aspects. While total cost includes order, production, and transportation elements, the transportation item is much more influential. However, all components are considered as a whole cost category in the order distribution problem. The closer suppliers are more desired since they impose fewer transportation costs, though. Another part of the differences among costs is because of business schemes presented by different suppliers and the special discounts based on mutual contracts. Quality: The organizational policy indicates that the required parts should be delivered at the highest level of quality. So, the suppliers assuring more quality are more desirable for assigning orders. In fact, following the ISO regulations have made the quality among the most important factors in this facility. Delivery: The assigned orders to each supplier are delivered within a specified timeframe. However, this factor is not as much important as total cost due to the nature of the business and orders of the focused industry. Utility: In order to make the situation more competitive, the policy of industry dictates that orders should be distributed among all existing suppliers. The mentioned policy is intended to assure a fair business interaction between all parts of the supply chain. The utility of a solution is calculated through the following steps:
4. Case study In this section, firstly, an overview of the oil and gas industry in Iran is presented. Following that, the investigated case study is explained in terms of the scope and the position in the industry. The detailed information of the first part is gathered from the official site of the national Iranian's oil company.1 4.1. The overview of the oil and gas industry Iran has the second largest production in Organization of the Petroleum Exporting Countries (OPEC) and the fifth largest in the world. Iran produced more than 3.7 million barrels a day in 2010. The National Iranian Oil Company (NIOC) has held crude production between 3.8 and 4.0 million barrels a day for in the last decade. Iran has also the second largest gas reserves in the world. Iran's gas production growth has gone up by 10% on average. 4.1.1. Main mission NIOC is a national symbol of independence and has a key role in the protection of Iran's oil and gas as the main components of Iran's economic production. The production of crude oil and natural gas and liquid hydrocarbons, transportation, marketing and sale of it as part of national wealth, as well as the safeguarding of this public asset, is the main assignment of the NIOC. To do so, equipping and designing industrial and production complexes and training local staff to maximize the use of national capabilities is considered as one of the most important missions and duties of the NIOC. 4.1.2. Goals and organizational strategy The goals and policies of the NIOC are part of the policies of the Islamic Republic of Iran. Accordingly, the vision of the NIOC is founded within the framework of the national macroeconomic strategies and the 1
1- Calculate the frequency of all n suppliers (n is the number of suppliers) in the solution (ui) 2- Find the average frequency (u¯ ) 3- Calculate the standard deviation of obtained frequencies using the following formula:
www.nioc.ir 5
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Fig. 2. Chromosome representation of GA.
utility =
1 n
attempts to find better solutions along with preserving the best current individuals in the population. The possible solutions should be coded in the form of chromosomes and be decoded at the end of the process to actual numbers. Due to the high speed of the algorithm and high quality of solutions to complicated and hard problems, GA has become a popular method in different fields, including industrial optimization. In addition, the evolutionary theory and coding strategy of GA, has eliminated the full consideration given to the complex mathematical characteristics of real problems and no restrictions imposed on objective functions [18]. More specifically, GA can be implemented in generic assignment problems, one of which is allocating orders among a set of suppliers [20].
n
∑ (ui − u¯)2 i=1
(1)
Environmental: Since the selected facility is related to the downstream section of the petroleum industry, the environmental regulations are very vital to abide by. To meet these requirements, suppliers with better performance are considered more suitable than others. Following ISO 14001, indicate clear guidelines for the facility in the environmental section. As this criterion is a qualitative one, it is defined as a number between 1 and 5 based on a series of specific assessments. The factory policy clearly states that suppliers with a factor below 1 should be excluded from all possible interactions. As a result, this criterion is among the most important factors. The considered timeframe included 480 orders and 22 suppliers to distribute orders among them. All data related to the chosen criteria for each supplier are available before running the proposed method for the order distribution process.
5.2.1. Representation of chromosome Each chromosome shows a potential optimal solution for the problem. In this specific problem, the values of the genes represent the suppliers, and their locations represent the orders. Consider we have 5 suppliers as potential candidates to process 10 orders in the investigated horizon. The chromosome for this example is shown in Fig. 2.
5. Methodology 5.2.2. Fitness To compare the strength of the members of a population in GA, a value known as fitness value is assigned to them. In addition, the selection process is dependent on this value, too. This value can be calculated using several methods. However, since in the current study several objectives should be assessed simultaneously, the fitness value is calculated by using an AHP method.
5.1. Best-Worst method This method is introduced by Rezaei [27] in order to overcome the disadvantages of other MCDM methods. In this method, the best and the worst criteria are selected by the decision maker(s) and a pairwise comparison is conducted between other criteria and the chosen ones. The problem can be formulated as a min-max problem to obtain final weights of all criteria. Like AHP, an inconsistency rate is calculated to assess the comparisons between criteria. This recently proposed method has some advantages over other MCDM methods. First of all, it needs fewer pairwise comparisons compared to other similar procedures such as AHP. Second of all, the results are more reliable and more robust. Finally, the accuracy of comparisons can be assessed in a more efficient way, too [27].
5.2.3. Selection process This stage has a key role in the performance of GA since a good strategy can help the algorithm to move to more promising areas of solution space. To do so, a roulette wheel selection procedure is used in this research to give more chance to better individuals to participate in crossover and mutation phases. In this selection method, the probability of selection of individual x is computed as follows:
5.2. Genetic algorithm
p (x i ) =
Evolutionary computation is an area of computer science that uses ideas from biological evolution to solve computational problems. Searching a vast solution space is the common feature of these problems. An adaptive system capable of coping with changes is another requirement for solving these problems. Biological evolution can also be seen as a method for adapting to changing environments. In nature, species evolve by means of random variation (mutation, recombination, and other operators), followed by natural selection in which the fittest members tend to survive and reproduce. These apparently simple rules also guarantee that the best features are transferred to future generations, too. Genetic algorithm (GA) is one of the most effective approaches which is inspired by biological evolution strategies [19]. GA was introduced by Holland and DeJong [8] in 1975. The algorithm begins with an initial generation of possible solutions. Then, by implementing crossover and mutation operators, the algorithm
fitness (x i ) n ∑i = 1 fitness (x i )
(2)
As a result, more powerful individuals have more chance to enter the mating pool. This strategy guarantees more promising populations in the next generations of GA [30]. 5.2.4. Crossover Crossover operator uses the individuals in the current generation as parents, and through some changes creates two offspring. In the current study, a two-point crossover is implemented as a powerful procedure to achieve more suitable offspring in the next iterations. However, the length of the selected string should be large enough to be effective. Fig. 3 shows the used method for a sample chromosome. 5.2.5. Mutation This operator is used to maintain the diversification of the 6
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Fig. 3. Two-point crossover of GA. Fig. 4. Mutation operator of GA.
5.5. Relative values
algorithm. Hence, a more radical process is implemented in this section. At first, a sub-string is chosen randomly from a parent. Then, the order of suppliers is reversed inside the selected string. This can assure that the algorithm will search previously uninvestigated regions of the problem, too. Fig. 4 demonstrates the mentioned method in a sample chromosome.
As a critical step of AHP, the alternatives should be compared in each criterion. Consequently, relative values are calculated based on the nature of the criterion for all alternatives. In this section, the comprehensive method for obtaining these values for each criterion is presented. Cost: Since a lower cost for assigning an order to a supplier is more suitable, the relative values for two alternatives are calculated as follows:
5.3. AHP AHP is a multi-criteria approach introduced by Saaty [29] for the first time in 1980. This method is developed based on pairwise comparisons between criteria and alternatives. The AHP has been implemented in various decision-making problems due to its clear procedure as well as its usefulness in real life problems. AHP is a multicriteria method that can be used to evaluate the importance of each component of a problem. The AHP hierarchy model consists of a top layer that is the goal, the second layer that is the criteria level, and the third layer that is the alternative level. The data are collected by using a set of pairwise comparisons conducted by experts in the respected field. These comparisons show the relative preference of the decision criteria and the relative preference of the alternatives in each decision criterion. An inconsistency rate is calculated to assess the reliability of comparisons [37]. AHP is helpful in dealing with several available options in terms of finding the most suitable alternative. This feature of AHP makes it a useful tool to evaluate the fitness of a population in GA. Considering several objectives in an optimization problem intensifies the need for AHP in the evaluation phase of GA. The assigned weights to criteria mirroring the human knowledge can be used to find better solutions among available alternatives. The salient characteristic of the AHP is organizing a complex problem into a structured hierarchy. As a result, it integrates all the criteria into a hierarchy of weightings.
Relative Cost (i,j) =
Cost j Costi
(3)
Quality: This criterion is presented using qualitative numbers. So, if the accumulated quality of a solution is higher than the other one, the first one is more favorable.
Qualityi Qualityj
Relative Quality (i,j) =
(4)
Delivery: Naturally, the facility is looking for faster deliveries. Hence, a solution with a lower total delivery time is more suitable than a solution with a higher one.
Relative Delivery (i,j) =
Deliveryi Deliveryj
(5)
Utility: The lower degrees of utility indicates the more equitable distribution of orders among available suppliers. Therefore, in order to compare two solutions in terms of utility, the reversed fraction is an acceptable method.
Relative Utility (i,j) =
Utilityj Utilityi
(6)
5.4. Proposed method Environmental: The higher ranks of environmental factor represent the conformity of environmental regulations by the selected supplier. Thus, the solutions with a higher total value in this criterion are more desirable for the company.
Since the investigated problem is essentially a multi-objective problem, AHP is used in the evaluation phase of the proposed GA. Fig. 5 shows the pseudo-code of the proposed method. 7
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Fig. 5. Pseudo-code of the proposed method.
case the opinions of 3 experts are gathered, the average numbers are used in the final assessment.
Table 1 GA parameters. Parameter
Value
Max Iteration Population Size Crossover rate Mutation rate
600 400 0.6 0.1
Relative Environmental (i,j) =
Environmentali Environmental j
AB = (1, 2, 5, 7, 3) AB = (1, 6, 5, 9, 1) AB = (1, 3, 4, 8, 7)
Average
⇒
AB = (1, 4, 5, 8, 4)
Step 4: Assign a number between 1 and 9 as the preference of all the criteria over the worst criterion. Like the best criterion, in the worst criterion vector, average numbers are also used in the final assessment.
(7)
Aw = (7, 6, 5, 1, 4) Aw = (9, 7, 3, 1, 6) Aw = (8, 7, 5, 1, 5)
6. Computational results
Average
⇒
Aw = (8, 7, 5, 1, 5)
6.1. Weight calculation Step5: Find the optimal weights. Since there are more than 3 criteria in our problem, a linear model of BWM can result in a unique solution with a low inconsistency rate. As Rezaei [28] stated, to obtain a more consistent and unique result for the problems with more than 3 criteria, a linear model is a more suitable choice. The linear model can be shown through the following sets of equations:
In order to find the weights of the criteria, a linear Best-Worst method is used in this study. To create the model, the following steps should be followed: Step 1: select the criteria: The selected criteria are based on experts’ opinion, including cost, quality, delivery, utility, and environmental. Step 2: select the best and the worst criteria: Considering all the contributing factors, experts asserted that the cost and the utility are the best and the worst criteria, respectively. Step3: Assign a number between 1 and 9 as the preference of the best criterion over all the other criteria. Since in the investigated 8
Minσ
(8)
s. t: wB − aBj wj ≤ σ , ∀ j
(9)
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∑ wj = 1
Table 2 Detailed output of the proposed GA-AHP.
(11)
j
No. of run
Criteria Cost
Quality
Delivery
Utility
Environmental
Weight of AHP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
251,149 251,854 251,382 250,603 251,476 252,597 249,638 252,219 252,806 251,649 251,983 251,788 250,285 250,885 253,223 252,043 251,281 252,492 252,389 251,742 251,818 252,420 251,191 251,903 250,535 250,889 251,257 253,078 251,394 251,511 253,590 251,056 251,254 251,508 251,516 251,820 250,516 251,152 250,802 251,624
1446 1519 1468 1418 1467 1461 1450 1428 1480 1490 1444 1432 1409 41,431 1422 1433 1491 1488 1491 1430 1426 1447 1437 1490 1427 1461 1427 1444 1555 1515 1434 1434 1449 1481 1483 1451 1427 1479 1448 1356
16,570 16,721 16,574 16,631 16,635 16,912 16,935 16,470 17,006 16,656 16,722 16,631 16,965 16,768 16,844 16,493 16,457 16,642 16,634 16,893 16,455 16,278 16,446 16,708 16,641 16,689 16,897 16,639 17,029 16,915 17,111 16,524 16,628 16,836 16,900 16,560 16,583 17,075 16,621 16,821
0.0014 0.0011 0.0008 0.0012 0.0011 0.0035 0.0016 0.0006 0.0008 0.0012 0.0012 0.0029 0.0012 0.0014 0.0029 0.0033 0.0011 0.0012 0.0012 0.0018 0.0012 0.0011 0.0012 0.0012 0.0014 0.0008 0.0008 0.0004 0.0008 0.0020 0.0011 0.0035 0.0012 0.0011 0.0011 0.0011 0.0011 0.0011 0.0018 0.0012
1418 1491 1443 1376 1390 1424 1457 1485 1438 1461 1382 1471 1378 1411 1509 1435 1485 1397 1457 1483 1467 1434 1438 1449 1460 1384 1477 1409 1447 1405 1390 1460 1409 1491 1467 1472 1440 1456 1465 1453
0.0253 0.0260 0.0263 0.0253 0.0256 0.0246 0.0253 0.0270 0.0262 0.0257 0.0254 0.0248 0.0253 0.0253 0.0248 0.0246 0.0260 0.0255 0.0257 0.0251 0.0256 0.0257 0.0256 0.0257 0.0254 0.0262 0.0263 0.0281 0.0265 0.0251 0.0253 0.0247 0.0255 0.0259 0.0258 0.0258 0.0257 0.0258 0.0252 0.0253
wj ≥ 0, ∀ j
wj − ajw ww ≤ σ , ∀ j
(12)
Considering the AB and AW vectors, the obtained optimum result from solving the model by LINGO presenting the weights of criteria as follow:
Cost Quality FW = Delivery Utility Environmental
⎛ 0.502 ⎞ ⎜ 0.162 ⎟ ⎜ 0.130 ⎟ ⎜ 0.044 ⎟ ⎝ 0.162 ⎠
Since the calculated inconsistency rate, 0.147, is very close to 0, the asserted comparisons among different criteria are reliable enough to use them in the proposed method. 6.2. GA-AHP approach Due to the stochastic nature of GA, the proposed GA-AHP algorithm ran 40 times using the same parameters. Table 1 shows the implemented parameters of GA algorithm. The exhaustive results of the proposed GA-AHP are demonstrated in Table 2. 6.3. Best solution selection strategy In order to find the best solutions among all runs, we are facing several alternatives with different values in each criterion. So, essentially we are dealing with a MCDM problem. In this stage, an AHP method is implemented to rank the solutions in different runs of the proposed algorithm in an efficient way. The structure of this procedure is depicted in Fig. 6. The 3 best solutions based on the results of AHP process are indicated in the bold format in Table 2. The following diagrams show the obtained solutions in each criterion separately. The highlighted triangles indicate the chosen best solutions in AHP process, while the line indicates the average value of the criterion. From the mentioned diagrams we can infer some conclusions. First of all, two of the chosen solutions have a total cost higher than the average value. Interestingly, solutions 8 and 28 have a total
(10)
Fig. 6. AHP structure for the evaluation phase. 9
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Fig. 7. Cost criterion of evaluated alternatives.
Fig. 8. Quality criterion of evaluated alternatives.
Fig. 9. Delivery criterion of evaluated alternatives.
6.4. Sensitivity analysis
quality lower than the average quality value, too. These two mentioned solutions have a better delivery time compared to the other one that is solution 29. However, all three solutions have the lowest figures in the utility criterion. Considering the environmental criterion, two solutions are below the average line. So, in order to select better solutions, a trade-off should be considered in which solutions with higher values than average values are chosen to satisfy other influential criteria. (Figs. 7–11)
Since the obtained results are directly affected by human judgment, they are prone to possible changes. For example, external factors such as transportation costs or taxation policies can affect the weights of the criteria. As a result, in this section, a sensitivity analysis is conducted to evaluate the robustness of the ranking procedure. To achieve this goal, 4 scenarios are defined and the ranking is conducted considering the new weights. Since the cost criterion is stated as the most influential 10
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Fig. 10. Utility criterion of evaluated alternatives.
Fig. 11. Environmental criterion of evaluated alternatives.
Fig. 12. Current scenario.
Fig. 13. Scenario 1.
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Fig. 14. Scenario 2.
Fig. 15. Scenario 3.
Fig. 16. Scenario 4.
hybrid GA-AHP was proposed. To have a number of best scenarios, the proposed algorithm executed 40 times. Having the results of the previous phase, an AHP was conducted to rank the possible alternatives. Following that, in order to maintain the flexibility of the managers and the decision makers, three of the best answers were chosen in this phase. Finally, a sensitivity analysis was implemented in order to assess the effects of possible changes in the weights of the criteria on the ranks of the best solutions. The results indicated that the AHP is reliable and the ranks are immune from possible alterations in the weights of the criteria. Due to the complex nature of the investigated problem, developing new hybrid MCDM methods and evolutionary algorithms is the most promising path for researchers. In addition, considering the effects of uncertainty in some criteria such as delivery time on the proposed method is another fruitful area to study.
criterion, we focused on it in this section. The weight of cost criterion is increased about 20% (from 50.2% to 60.2) in the first two scenarios, while in the two other scenarios this number declined 20% (from 50.2% to 40%). The results are shown in the following graphs where the left ones demonstrate the weights of criteria in percent, whereas the right ones show the three top solutions in each scenario along with their weights. Fig. 12 shows the current investigated scenario with current weights, though. (Figs. 13–16) As the presented figures show, the ranks of three top solutions are the same in the all devised scenarios. So, the results of the conducted AHP process are reliable enough to apply to a real situation since ± 20% changes in the weight of cost criteria, the most important one, does not have a tangible effect on the output of the method. 7. Conclusion and future research
Declaration of Competing Interest
In this paper, the order distribution problem in a real case from the oil and gas industry in Iran was investigated. An improved version of CCS was proposed to collect and integrate information from different sectors of the problem. The outputs of the processing unit of CCS were used as the input information for the proposed hybrid MCDM method in the decision-making unit. The most influential criteria in assigning orders to suppliers were organized based on experts’ opinion in the industry. In order to address the multi-objective problem effectively, a
The authors declare that there is no conflict of interest. References [1] F. Altiparmak, M. Gen, L. Lin, T. Paksoy, A genetic algorithm approach for multiobjective optimization of supply chain networks, Comput. Ind. Eng. 51 (1) (2006) 196–215.
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