A review of applications of genetic algorithms in operations management

Engineering Applications of Artificial Intelligence 76 (2018) 1–12

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A review of applications of genetic algorithms in operations management C.K.H. Lee Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong

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Keywords: Operations management Genetic algorithms Review

ABSTRACT Many decisions in operations management (OM) belong to the class of Non-deterministic Polynomial hard problems and thus heuristic search methods have been applied to improve OM decisions. While genetic algorithms (GAs) are promising tools for searching fast and good solutions in diverse OM areas, future research will benefit from a review of the OM problems solved by GAs. The purpose of this paper is to review the literature on OM with GA-based solutions and to suggest possible gaps from the point of view of researchers and practitioners. A total of 119 peer reviewed journal papers published from 2007 to 2017 are reviewed and analysed methodologically. The applications of GAs in OM are categorized into process and product design, operations planning and control, and operations improvement. Observations from the existing literature are presented and future research directions are suggested. Although GAs have been one of the most popular heuristic approaches for optimization, there are OM problems that are yet to be investigated. The findings of this review pave the path for future research to apply GAs to solve OM problems.

1. Introduction Operations management (OM) is the activity of managing the resources that create and deliver services and products (Slack et al., 2013). All organizations need operations to produce some mix of services and products. In any organization, three core functions are the marketing function, product/service development function and operations function. The marketing function is responsible for communicating the services and products to its markets to generate customer requests; the product/service development function is responsible for coming up with new or modified services and products to generate future customers’ requests; the operations function is responsible for creating and delivering services and products based on customer requests. In practice, however, there is not a clear division among these three functions while there exist other support functions enabling the core functions. From a broad perspective, OM has to interact with all other functions of an organization and thus comprises all activities necessary for the day-to-day fulfilment of customer requests. Many decisions in OM can be characterized as complex optimization problems that require a heuristic search method. Therefore, OM is an active research area benefited from the use of artificial intelligence (AI) techniques such as genetic algorithms (GAs) in the search for fast and good solutions to many practical problems. While GAs seem to be promising tools for solving OM related problems, a systematic review of applications of GAs in OM can help researchers to identify potential research areas and future directions.

The aim of the paper is to explore OM using GAs as useful tools, either as a standalone technique or integrated with other suitable techniques. However, for ease of exposition, some developments of GAs in the review are not included. First, though GAs are included in the evolutionary computation (EC) field, other EC methods or Darwinian approaches are not included in this paper. This is because these approaches deserve a separate review. For a detailed literature review of bio-inspired computing algorithms, readers are referred to a recent review by Kar (2016). Second, in line with the focus of this paper, the theoretical developments of the algorithms are not explored. There are many variants of GAs such as variable-length GAs and fuzzy GAs. Details of the modification of the algorithms are not discussed here. Instead, this paper focuses on the applications. Given the growing number of GA applications, a number of papers surveying its applications have been published regularly. Coello (2000) provided a review of GA-based multi-objective optimization techniques. The discussion was at the technical side, and thus the applications of OM were not covered. Aguilar-Rivera et al. (2015) reviewed the GA applications in finance. In addition to GAs, they also reviewed other methods based on Darwinian evolution such as genetic programming, learning classifier systems, multi-objective evolutionary algorithms, coevolutionary optimization schemes and competent evolutionary algorithms. In view of the fact that there are various focused areas in OM, some researchers reviewed applications of data mining and AI in particular areas, such as job-shop scheduling (Cheng et al., 1996),

E-mail address: [email protected]. https://doi.org/10.1016/j.engappai.2018.08.011 Received 2 August 2017; Received in revised form 14 May 2018; Accepted 21 August 2018 0952-1976/© 2018 Elsevier Ltd. All rights reserved.

C.K.H. Lee

Engineering Applications of Artificial Intelligence 76 (2018) 1–12 Table 1 Classification of OM areas. Authors

Classification of OM areas

Mertens and Kanet (1986)

Production planning and control, materials control, purchasing, inventory management, forecasting, manufacturing engineering, industrial engineering, maintenance, quality control

Rao and Lingaraj (1988)

Aggregate planning, forecasting, location decisions, scheduling, capacity planning, layout, process and product design, quality control, job design, inventory control, maintenance and reliability

Partovi et al. (1990)

Forecasting, supplier selection, facility location, choice of technology, product design, plant layout, maintenance frequency selection, choice of logistic carrier

Schroeder (1993)

Quality management and control, process design, capacity planning and scheduling, inventory management, work-force management

Jayaraman and Srivastava (1996)

Process choice, process design, product design, quality planning, facility location, facility layout, project management, long-term capacity planning, job design, aggregate planning, long-term forecasting, short-term capacity planning, distribution, scheduling, quality control, inventory control, maintenance, short-term forecasting, purchasing

Proudlove et al. (1998)

Operations strategy, product design, quality management and control, process design, capacity planning and scheduling, inventory management, work-force management

Aytug et al. (2003)

Production control, facility layout design, line balancing, production planning, supply chain management and design, other

Chaudhry and Luo (2005)

Environment, process choice, process design, product design, quality planning, facility location, facility layout, project management, long-term capacity planning, job design, aggregate planning, long-term forecasting, short-term capacity planning, distribution, scheduling, quality control, inventory control, maintenance, short-term forecasting, purchasing

Kobbacy and Vadera (2011)

Design, scheduling, process planning and control, quality, maintenance and fault diagnosis

Wong and Lai (2011)

Environment, process choice, process design, product design, quality planning, facility location, facility layout, project management, long-term capacity planning, aggregate planning, short-term capacity planning, distribution, scheduling, quality control, inventory control, maintenance, short-term forecasting, purchasing

Subramanian and Ramanathan (2012)

Operations strategy, process and product design, planning and scheduling resources, project management, managing the supply chain

supplier evaluation and selection (Ho et al., 2010), and quality improvement (Köksal et al., 2011). Ho et al. (2010) concluded that GA applications in supplier evaluation and selection were limited while Köksal et al. (2011) identified that GAs were frequently used for parameter optimization for quality improvement. There are a number of reviews in OM areas and different researchers classified them in different ways. Rao and Lingaraj (1988) classified OM applications into strategically and tactically oriented applications. They identified eleven areas: aggregate planning, forecasting, location decisions, scheduling, capacity planning, layout, process and product design, quality control, job design, inventory control, and maintenance and reliability. Aytug et al. (2003) classified OM areas into six categories: production control (e.g. loading and scheduling), facility layout design, line balancing, production planning, supply chain management and design, and other. Jayaraman and Srivastava (1996) identified nineteen areas under two board categories of strategic and operational decisions. Chaudhry and Luo (2005) adopted Jayaraman and Srivastava’s (1996) classification scheme but added environment as an additional area to be considered under strategic decisions. Based on Chaudhry and Luo (2005) and Wong and Lai (2011) classified OM into eighteen areas for reviewing the applications of fuzzy set theory in production and OM. Kobbacy and Vadera (2011) reviewed AI in OM categorized into four areas: design, scheduling, process planning and control, and quality, maintenance and fault diagnosis. Subramanian and Ramanathan (2012) categorized OM into five broad themes: operations strategy, process and product design, planning and scheduling resources, project management, and managing the supply chain. The classification of OM areas by researchers is summarized in Table 1. To the best of our knowledge, there has not been a study that has reviewed GA applications in specific areas of OM, with the exception of a review by Chaudhry and Luo (2005), who presented

a review of GA-related research published from 1990 to 2001. They did not discuss GA applications in specific OM areas individually in detail, but provided a journal-wise appearance of GA-related papers. This is considered a significant gap in the literature and this paper aims to provide an up-to-date review of GA applications in specific OM areas to fill the gap. The rest of the paper is organized as follows. Section 2 describes the framework of the classification of GA applications in this paper. Section 3 presents a detailed review of GA applications in OM. Section 4 discusses the observations from the review and provides suggestions for future work. Section 5 concludes the paper. 2. A framework for classification Based on Table 1, the applications of GAs in OM in this paper are categorized into three broad themes, namely (i) process and product design, (ii) operations planning and control, and (iii) operations improvement. (i) Process and product design is a theme comprising design activities for satisfying customers’ requirements through shaping or configuring products, services and processes. Activities in this theme determine the resources required for the creation of services and products. At the most strategic level, process and product design means shaping the networks of operations that supply products and services. At a more operational level, it means the arrangement of the processes and resources that constitute operations processes. (ii) Operations planning and control is a theme dealing with the delivery of products and services. The key to an operation’s ability to deliver is the way it plans its activities and controls them so that customer demand is satisfied. This theme covers activities related to planning and controlling resources which are capable of satisfying 2

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Engineering Applications of Artificial Intelligence 76 (2018) 1–12

Table 2 Key decision areas in OM themes. OM theme

Decision areas

Process and product design

Facility layout design Supply network design Job design and work Forecasting

Operations planning and control

Capacity planning Inventory control Scheduling

Operations improvement

Maintenance Risk management

and then the determination of the need of re-designing the layout in the next period (Mazinani et al., 2013; Kia et al., 2014; Vitayasak et al., 2016). Depending on the nature of jobs to be performed, different departments may have different desired areas. Therefore, in OM, the unequalarea facility layout problem (UA-FLP) is another practical problem to be solved by GAs. Commonly used representations in GAs when solving unequal-area static facility layout problem (UA-SFLP) and unequal-area dynamic facility layout problem (UA-DFLP) are the slicing structure (Aiello et al., 2012) and flexible bay structure (FBS) (Mazinani et al., 2013; Palomo-Romero et al., 2017). On the other hand, GAs have been applied in solving stochastic UA-DFLP and the results were compared with Backtracking Search Algorithm (BSA) and modified BSA (Vitayasak et al., 2016). The experimental results indicated that the GA’s performance was better than the conventional BSA in terms of minimizing total cost. FLP of cellular manufacturing (CM) has also been solved by GAs. In this context, hierarchical GAs were useful in concurrently determining cell formulation (CF), group layout (GL) and group scheduling (GS) decisions (Wu et al., 2007a, b). In addition to material handling costs, the total costs of intra-cell, inter-cell and inter-floor in CM systems were taken into account (Kia et al., 2014).

customer demand on a day-to-day basis and ensuring the availability of resources. (iii) Operations improvement is viewed as making the operations perform better and stopping them from failure. Activities in this theme play a critical role in maintaining competitiveness because the operations’ competitors will also be improving. The above themes can be further divided into more detailed operations decision areas as listed in Table 2. Applications of GAs in each area are reviewed in Section 3. This review is based on published literature of international journal papers from 2007 to 2017 related to the applications of GAs in OM. The search of published OM with GA applications journal papers was performed using three online databases that were Science Direct, Emerald Insight and Google Scholar. For each journal paper, the OM decision areas and the term ‘‘genetic algorithm’’ were searched in the title, subject and keyword fields. Papers were examined in terms of their relevance to this study and only those that are relevant were selected for detailed analysis and classification into appropriate OM decision areas. The classification for most of the journal papers was quite simple and straightforward. However, there existed some papers relevant to more than one decision areas. For instance, some papers integrated inventory control with capacity planning, or addressed scheduling problems with maintenance activities. In this case, the papers would be placed into an OM decision area that was more appropriately in line with the major purposes of the papers. A total of 119 peer reviewed journal papers were reviewed and analysed methodologically. While the majority of the papers were selected from specialist journals in the area of OM, some papers from other journals that are not viewed as mainstream OM journals were also reviewed if they featured GA applications that fall within the context of OM.

3.1.2. Supply network design Supply network problems can be classified into two categories in terms of capacity limitation: those with unlimited capacity and those with limited capacity. The first attempt to go beyond the traditional mathematical modelling and to investigate the efficiency of GAs to solve supply network design problems was by Zhou et al. (2002) in which facilities having unlimited capacity were assumed. However, such an assumption might not reflect the realistic situations. The majority of the papers impose capacity constraints on facilities and consider multiple echelons so as to correspond to the actual situations (Nachiappan and Jawahar, 2007; Farahani and Elahipanah, 2008; Altiparmak et al., 2009; Sharma and Jana, 2009; Sourirajan et al., 2009; Chang, 2010; Costa et al., 2010; Dai and Zheng, 2015; Soleimani and Kannan, 2015; Afrouzy et al., 2016; Diabat and Deskoores, 2016; Amirtaheri et al., 2017; Shi et al., 2017a; Soleimani et al., 2017). In the reviewed work, the demand was modelled as being deterministic, except that the demand in Dai and Zheng (2015) was described as a fuzzy variable. Dai and Zheng (2015) developed a Monte Carlo simulation embedded hybrid GA to solve CLSN and used a fuzzy programming and chance-constrained programming to deal with the uncertainties. In a similar vein, supply network design problems were also solved by GAs with fuzzy objectives (Sharma and Jana, 2009; Soleimani et al., 2017). The complexity of the supply networks increase when the problems involve multi-product, multi-period, and/or close-loop supply chains (CLSNs). Solution algorithms include steady-state genetic algorithm (ssGA) (Altiparmak et al., 2009), Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Shi et al., 2017a), and hybridizing GAs with other algorithms such as particle swarm optimization (PSO) (Soleimani and Kannan, 2015). On the other hand, the majority of the GA applications in supply network design attempt to optimize the economic factors, for example, minimizing costs and maximize profits. Shi et al. (2017b) made the first attempt to consider carbon emissions in a multi-objective CLSN design problem. Other multi-objective genetic algorithm (MOGA) studies on supply network design include Farahani and Elahipanah (2008).

3. Applications of GA in OM 3.1. Process and product design Key decision areas addressed by the researchers in the areas of process and product design include facility layout design, supply network design, job design and work, and forecasting. Table 3 provides information about some important papers in various decision areas related to process and product design. 3.1.1. Facility layout design Most organizations aim to design facility layouts that allow jobs to be performed in a cost-effective manner. Material handling costs could incur when materials or any sorts of objects are transferred from one area to another. From the cost perspective, facility layout problem (FLP) is viewed as a static facility layout problem (SFLP) if the costs remain unchanged with time. This review found that the most typical objective in GAs for solving SFLP was to minimize the total material handling costs between facilities (Datta et al., 2011; Sadrzadeh, 2012; Palomo-Romero et al., 2017). When the material-handling requirements are dynamic and redesign of layout is needed, FLP is viewed a dynamic facility layout problem (DFLP), involving the selection of a static layout for each period

3.1.3. Job design and work OM involves determining the number of types of human resources that are needed to manage, run and develop the organization so that it meets its objectives. Activities related to job design and work include allocation of work times, work design, and division of labour. While some scholars used GAs to maximize the resource utilization (Puente 3

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Engineering Applications of Artificial Intelligence 76 (2018) 1–12

Table 3 GA studies on process and product design. Decision area

Problem solved

Solution(s)

Reference(s)

Facility layout design

SFLP SFLP, CM UA-SFLP

GA Hierarchical GA MOGA Parallel GA, island model GA GA GA, backtracking search algorithm

Datta et al. (2011) and Sadrzadeh (2012) Wu et al. (2007a) and Wu et al. (2007b) Aiello et al. (2012) Palomo-Romero et al. (2017) Kia et al. (2014) Mazinani et al. (2013) Vitayasak et al. (2016)

GA GA, fuzzy goal programming GA, PSO NSGA-II Co-evolutionary constraint GA ssGA MOGA GA, fuzzy set theory GA, fuzzy set theory GA, PSO Simulation-based GA, fuzzy set theory

Nachiappan and Jawahar (2007), Sourirajan et al. (2009), Costa et al. (2010) and Diabat and Deskoores (2016) Sharma and Jana (2009) Amirtaheri et al. (2017) Shi et al. (2017b) Chang (2010) Altiparmak et al. (2009) Farahani and Elahipanah (2008) Afrouzy et al. (2016) Soleimani et al. (2017) Soleimani and Kannan (2015) Dai and Zheng (2015)

GA MOGA NSGA-II GA GA, fuzzy goal programming Simulation-based GA GA GA, fuzzy set theory

Puente et al. (2009) and Lau et al. (2010) Lin and Gen (2008) Hu (2015) Perkgoz et al. (2007) Cheshmehgaz et al. (2012) Tiacci (2015) Kaya and Engin (2007) Engin et al. (2008)

GA GA, SVR GA, fuzzy time series Chaotic GA, SVR Adaptive GA, SVR Chaotic GA, NN GA, grey system method, regression GA, NN

Núñez Letamendia (2007) Sermpinis et al. (2015) Sakhuja et al. (2016) Hong et al. (2011) Chen et al. (2015) Yu and Xu (2014) He and Chang (2014) Jiang et al. (2017)

DFLP, CM UA-DFLP Supply network design

Single-product, single-period

Single-product, single-period, close-loop Multi-product, single-period Multi-product, multi-period Multi-product, multi-period, close-loop

Job design and work

Human resource allocation Berth allocation Lead time control Assembly line balancing Attribute control chart

Forecasting

Financial trading Tourism demand

Natural gas loading Logistics demand Healthcare service demand

the weights of different single models and then developed a combined forecasting model to predict regional logistics demand. Besides, GAs have been commonly used in non-linear forecasting, for example, when dealing with the non-linearity of tourist arrival patterns (Hong et al., 2011; Chen et al., 2015; Sakhuja et al., 2016). Techniques integrated with GA in this area include support vector regression (SVR) (Sermpinis et al., 2015; Hong et al., 2011; Chen et al., 2015), fuzzy set theory (Sakhuja et al., 2016); and neural network (NN) (Yu and Xu, 2014; Jiang et al., 2017). In addition to the non-linearity of demand, the seasonality characteristics were considered in Chen et al. (2015). Chen et al. (2015) forecasted holiday daily tourist flow by hybridizing SVR with adaptive GA and seasonal index adjustment. There are also research works focusing on the forecasting tasks in the financial markets (Núñez Letamendia, 2007; Sermpinis et al., 2015). The role of GAs in this context was to optimize the controlling parameters used in trading to improve the forecasting ability.

et al., 2009; Lau et al., 2010), some claimed that job design and work problems usually involve multiple objectives. Nevertheless, the optimization objectives are usually to minimize the cost and maximize the efficiency, which could be conflicting in nature. Perkgoz et al. (2007) considered a multi-stage assembly system involving four conflicting objective functions in order to optimize the lead time. They applied GA to solve the problem using goal attainment formulation. Lin and Gen (2008) and Hu (2015) developed MOGA approaches to solve multi-criteria human resource allocation problems and berth allocation problems in maritime terminals, respectively. Regarding work design, some scholars used GAs to design quality control tasks in which the sample size and the acceptance number in attribute control charts are important for determining whether the lot is deemed acceptable or has to be examined entirely. To define the sample size, known defective item rates were assumed in the GA model (Kaya and Engin, 2007). However, in real situations, parameters could be changed dynamically due to material, human factors or operating faults. This problem could be solved by evaluating parameters such as ratios of defective item as fuzzy before the attempted problem was solved by GAs (Engin et al., 2008). On the other hand, when jobs were performed by workers, human factors, such as physical overload (Cheshmehgaz et al., 2012), and dispersion of completion times for each worker (Tiacci, 2015) were considered in GAs. In this survey, if the objective is to determine the sequence of jobs at the workplace, the problem is considered a scheduling problem to be discussed in Section 3.2.3.

3.2. Operations planning and control Key decision areas addressed by the researchers in the areas of operations planning and control include capacity planning, inventory control, and scheduling. Table 4 provides information about some important papers in various decision areas related to operations planning and control. 3.2.1. Capacity planning Due to Non-deterministic Polynomial hard (NP-hard) class of aggregate production planning (APP), GAs, as a standalone tool or integrated with other AI or mathematical tools, have been implemented to solve the problem (Aliev et al., 2007; Chen et al., 2016). An APP model for twophase production systems was considered in Ramezanian et al. (2012). In their work, the quality of solutions obtained by GA was better than

3.1.4. Forecasting A well-performed forecasting can provide essential information for operations planning and control. The majority of studies in this area showed that a combinative model can improve forecast accuracy compared to a single model. He and Chang (2014) used GAs to determine 4

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Table 4 GA studies on operations planning and control. Decision area

Problem solved

Capacity planning APP Resource portfolio planning AOPP Capacity expansion Capacity loading APDP Multi-generational product plan Technology replacement capacity plan Inventory control Inventory

Inventory-routing Location-inventory-routing Lot sizing

Scheduling

Solution(s)

References

GA Modified GA GA GA, stochastic sampling GA GA, Primal-Dual algorithm GA GA, fuzzy programming GA, Taguchi Pattern search-GA

Ramezanian et al. (2012) Musharavati and Hamouda (2011) Wang et al. (2007a, b), Wang et al. (2008) and Wang and Wang (2013) Wang and Shih (2011) Zhang (2007) Abazari et al. (2012) and Chen et al. (2016) Aliev et al. (2007) Hu et al. (2017) Wang and Nguyen (2017)

GA GA, fuzzy set theory GA, support vector machine GA GA, Taguchi GA GA TGA NSGA-II

Pasandideh et al. (2011a, b) and Ongkunaruk et al. (2016) Lin et al. (2010), Maiti (2011) and Taleizadeh et al. (2013) Chi et al. (2007) Moin et al. (2011) and Park et al. (2016) Azadeh et al. (2017) Hiassat et al. (2017) Li et al. (2007) and Çelebi (2015) Bhunia et al. (2009) Rezaei and Davoodi (2011)

Airline flight scheduling

GA, simulation MOGA, simulation Flexible manufacturing system scheduling GA JSP GA NSGA-II MOGA, fuzzy set theory, dispatching rules FJSP GA GA, TS Hierarchical GA, distributed GA DFJSP GA Flow-shop scheduling GA, TS Hybrid flow shop scheduling GA No-wait flow shop scheduling GA GA, local search IPPS GA

Dynamic IPPS Parallel machine scheduling Supply chain scheduling

Project scheduling

Resource-sharing and scheduling Single machine scheduling Vehicle routing scheduling

GA, multi-agent system Simulation-based MOGA GA, variable neighborhood search GA, fuzzy set theory GA, constructive heuristics algorithm Gendered GA

Abdelghany et al. (2017) Lee et al. (2007) Prakash et al. (2011) Yang et al. (2012) Zhang et al. (2013), Liu et al. (2016) and Guido and Conforti (2017) Huang and Süer (2015) Al-Hinai and ElMekkawy (2011) Li and Gao (2016) Ishikawa et al. (2015) De Giovanni and Pezzella (2010) Tseng and Lin (2010a) and Sukkerd and Wuttipornpun (2016) Engin et al. (2011) Pang (2013) Tseng and Lin (2010b) Shao et al. (2009), Li et al. (2012), Zhang and Wong (2015) and Zhang et al. (2016) Li et al. (2010) Zhang et al. (2015) Xia et al. (2016) Mok et al. (2007), Engin and Gözen (2009) and Balin (2011) Naso et al. (2007) Zegordi et al. (2010)

GA Sampling GA, variable-length GA GA, local search GA, branch-and-bound algorithm GA, bees algorithm GA GA, fuzzy set theory, stochastic simulation GA, local search

Gonçalves et al. (2008) and Palencia and Delgadillo (2012) Yassine et al. (2017) Lova et al. (2009) Pinto et al. (2009) Yuce et al. (2017) Razali (2015) Shi et al. (2017a) Arakaki and Usberti (2018)

the tabu search (TS) results for small-sized problems. For larger-sized instances, the quality of solutions obtained by GA was better than the TS results, but the computational times were greater than that in TS. Wang and Shih (2011) developed an advanced overlapping production planning (AOPP) model which considered multi-site process selection, sequential constraints, and capacity constraints in a manufacturing supply chain environment. GAs were applied to determine the capacity plan and order margin allocation for each site and machine and to provide the capacity information for a production planner to adjust the production strategies of overloading resources. Aliev et al. (2007) applied GA to solve an aggregate production–distribution planning (APDP) model under a fuzzy environment. A number of papers relate capacity planning to other OM issues such as resource allocation (Wang et al., 2007b), technology replacement (Wang and Nguyen, 2017) and multi-generation product diffusion (Hu et al., 2017). Due to the high complexity of problems, it could be time consuming to parameterize a GA implementation. There is a possibility of premature convergence in the genetic search process. Some researchers focused more on modified GAs that are more competent than the simple GAs (Musharavati and Hamouda2011) or combining GA

with other algorithms such as Primal–Dual algorithm (Zhang, 2007). Specifically, GA was used to optimize the capacity decision variables while the Primal–Dual method was used to solve a product-mix decision problem with quadratic constraints. 3.2.2. Inventory control Many industries are required to improve supply chain operations by sharing inventory or demand information with suppliers and customers. When there is not sufficient inventory or production capacity, shortage occurs. There are two strategies to deal with shortages: backordering (Pasandideh et al., 2011a) and lost sales (Park et al., 2016). When evaluating the fitness of solutions using either strategy, a larger penalty was given to a more infeasible solution, and hence a zero-penalty for a feasible chromosome. Both backordering and lost sales scenarios would have different impacts to the organizations. GAs were applied to optimize inventory control and results were compared based on these two scenarios (Rezaei and Davoodi, 2011). Partial backlogged shortages with a deterioration rate of items was investigated and solved by a hybrid tournament genetic algorithm (TGA) (Bhunia et al., 2009). Some researchers addressed routing issues when dealing with inventory 5

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control (Park et al., 2016; Moin et al., 2011). Azadeh et al. (2017) was the first study that incorporated perishability of the products into inventory routing problem with transshipment. Hiassat et al. (2017) addressed a location–inventory-routing model for perishable products. They added a strategic-level component in their model by using GA to determine the number and location of required warehouses. In the existing literature, various assumptions and constraints have been designed to better match the actual inventory control environments. Nevertheless, traditional models of inventory control seldom took into account the multiple uses of products and it was important to integrate product recovery management into planning (Li et al., 2007).

3.3.1. Maintenance Corrective maintenance and preventive maintenance are often carried out together to improve the reliability and availability of operations. Many GA studies on maintenance focus on the integration optimization of production scheduling and preventive maintenance. The majority of the work aimed to minimize the system unavailability or disruption (Aghaie et al., 2013; Compare et al., 2015; Wang and Liu, 2015) or optimize costs (Chen et al., 2013; Piasson et al., 2016). GA and PSO were hybridized for long-term generator maintenance scheduling and results were compared with other techniques (Samuel and Rajan, 2015). Interestingly, it was found that there were other techniques generating better results than their hybrid GA. The uncertainty in a maintenance environment was handled by incorporating GA and fuzzy set concepts (Touat et al., 2017) or optimizing both robustness and stability simultaneously (Lu et al., 2015). Nevertheless, while most of the reviewed work considered single type of resources (i.e. machines), a more responsive GA model should be able to deal with multiple types of resources. Wang and Liu (2015) investigated a multi-objective integrated optimization method with NSGA-II to solve a parallel machine scheduling problem with flexible preventive maintenance activities on two kinds of resources which were machine and moulds.

3.2.3. Scheduling GA has demonstrated considerable success in providing good solutions in scheduling problems, including job-shop scheduling problem (JSP), flexible job-shop scheduling problem (FJSP), distributed and flexible job shop scheduling problem (DFJSP), no-wait flowshop scheduling, and integrated process planning and scheduling (IPPS). There are extensive literature solving scheduling problems with maintenance. In this survey, scheduling with maintenance is categorized into operations improvement in Section 3.3.1. This is because maintenance is viewed as an important area for improving the reliability and availability of the operations. It has been observed that the objective functions in most studies include measures on production efficiency (e.g. makespan, tardiness, and due date related performance) (Al-Hinai and ElMekkawy, 2011; Ishikawa et al., 2015). Yet, in some industries, firms are also concerned with the minimization of production costs (Naso et al., 2007; Zhang et al., 2013; Guido and Conforti, 2017; Shi et al., 2017a) and energy consumption (Liu et al., 2016; Zhang et al., 2016). In addition, a considerable amount of OM studies has been devoted to DFJSP, no-wait flowshop scheduling, and IPPS. To improve the optimization performance in these areas, a number of efficient genetic representation and operator schemes were developed (Shao et al., 2009; Li et al., 2010, 2012; Pang, 2013; Zhang and Wong, 2015; Zhang et al., 2015) or hybridizing GA with various search methods (De Giovanni and Pezzella, 2010; Tseng and Lin, 2010b; Engin et al., 2011; Xia et al., 2016). Some researchers used fuzzy set theory to deal with uncertainties in scheduling problems. While GA was used to minimize the makespan, demand or the standard operation times were fuzzified so as to incorporate uncertainty in terms of job-specific and human related factors (Mok et al., 2007; Engin and Gözen, 2009; Balin, 2011; Shi et al., 2017a). Regarding vehicle scheduling, conventional GA procedure with an order-based representation might generate invalid candidate solutions when precedence constraints are involved. To obtain feasible solutions which do not violate precedence constraints, an earliest position based topological sort technique was proposed (Razali, 2015). This method was compared with a priority-based topological sort technique and was found that it performed better in terms of the quality of solutions and convergence time. Furthermore, an open capacitated routing problem was solved by a hybrid GA with local search method (Arakaki and Usberti, 2018). The important feature of this problem, which distinguishes it from the traditional capacitated routing problem, is that the vehicle is not required to return to the depot, and thus the vehicle routes are not closed paths but open ones.

3.3.2. Risk management Surprisingly there have not been many GA studies on risk management. In the reviewed work, there were one study using GAs to deal with fire risks, two studies to deal with the financial risks, and two studies to deal with project risks. GAs have been combined with fuzzy multiobjective programming to optimize fire station locations taken into account carious fire risk categories (Yang et al., 2007). NSGA-II was found useful in managing risks in the financial industry. However, when the optimization of mean-capital requirement portfolio was highly complex, non-differentiable and non-convex, NSGA-II cannot be executed on a single processor within a reasonable time frame. To solve this problem, a GA framework allowing parallel execution was encouraged (Drenovak et al., 2017). On the other hand, investor information has to be considered during portfolio optimization. Nevertheless, few studies have developed investment strategy based on investor information. Cluster analysis was suggested by Cheong et al. (2017) for selecting stocks for specific types of investors, followed by GA to optimize their weights for each selected stock with the objective to minimize risk. Regarding risk mitigation in projects, while the objectives were usually to minimize makespan and minimize costs (Kılıç et al., 2008), Pfeifer et al. (2015) maximized project delay subject to particular stochastic task disruptions and introduced GA to identify the critical tasks which lead to the maximum risk of project delay. It is noted that when the fitness function is not deterministic but based on the random completion time of each task, its value does not allow the determination when the GA has converged. Therefore, the number of iterations, instead of convergence, should be chosen to be the stopping criterion. 4. Discussion 4.1. Observations Fig. 1 shows the distribution of GA studies in the nine OM areas. Scheduling is the most popular area where GAs have been vigorously applied, followed by inventory control. The third most popular areas is supply network design. The three least popular areas are forecasting, maintenance, and risk management. Fig. 2 shows the distribution of reviewed GA studies in the three OM themes. It can be seen that the majority of the reviewed work focused on operations planning and control. This is not surprising because the decision areas covered in this theme, which are capacity planning, inventory control, and scheduling, are the top four areas as shown in Fig. 1. On the other hand, operations improvement is the least popular OM theme where GAs have been

3.3. Operations improvement Key decision areas addressed by the researchers in the areas of operations improvement include maintenance, and risk management. Table 5 provides information about some important papers in various decision areas related to operations improvement. 6

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Table 5 GA studies on operations improvement. Decision area

Problem solved

Solution(s)

Reference(s)

Maintenance

Preventive maintenance

GA GA, fuzzy set theory GA, PSO NSGA-II NSGA-II GA NSGA-II, fuzzy set theory

Chen et al. (2013) and Lu et al. (2015) Touat et al. (2017) Samuel and Rajan (2015) Wang and Liu (2015) Compare et al. (2015) Aghaie et al. (2013) Piasson et al. (2016)

GA, fuzzy multi-objective programming GA, clustering NSGA-II MOGA GA

Yang et al. (2007) Cheong et al. (2017) Drenovak et al. (2017) Kılıç et al. (2008) Pfeifer et al. (2015)

Condition-based maintenance Reliability-centered maintenance Risk management

Fire risk Financial risk Project risk

Fig. 1. Distribution of GA studies in the nine OM areas.

Fig. 2. Distribution of GA studies in OM.

applied. This is because there are only two decision areas covered in the theme and GA studies on risk management are rather limited. Figs. 3–5 show the distributions of the studies in different decision areas in each theme. In process and product design, the decision area where GAs have been applied the most is supply network design. It has been observed that most GA studies on supply network design attempted to solve different types of design problems. All the supply chain design problems reviewed were capacitated and most of them were solved by singleobjective GAs. The complexity of the problems increases when the networks involve multi-product, multi-period, and CLSNs. In most of the reviewed work, however, the demand was modelled as being deterministic. Job design and work is the second popular decision area. Its popularity is less than that of supply network design is that job design and work problems could be to determine the sequence of

jobs at the workplace. In this paper, such optimization problems are classified as scheduling problems. Besides, job design and work may involve qualitative information such as ergonomic issues which may not be NP-hard problems to be solved by GAs. The third most popular area is the facility layout design. The distributions of SFLP and DFLP are comparable. While most of the models were single-objective, the typical objective was to minimize the costs. The least popular area is forecasting. It has been found that most of the applications in this area integrated GAs with other techniques such as SVR, NN, chaotic mapping, fuzzy theory, and feature selection. The typical objective was to minimize the forecast error. In operations planning and control, slightly more than half of the GA applications are on scheduling. It has been observed that IPPS and JSP were the common scheduling problems to be addressed by GAs. Researchers also extended JSP into different problems such as 7

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Fig. 3. Distribution of GA studies in process and product design.

Fig. 4. Distribution of GA studies in operations planning and control.

Fig. 5. Distribution of GA studies in operations improvement.

FJSP and DFJSP. Because of the large variety of scheduling problems which are NP-hard problems, GA-based approaches have already been applied in solving different scheduling problems. There might not be much contribution or practical insights if GAs are used as a standalone technique for scheduling. Instead, in the recent published literature, when solving scheduling problems, GAs have always been hybridized with other techniques such as TS, and fuzzy set theory. The second most popular area is inventory control. The dominant models using GAs to solve inventory control problems determined tactical- and operationallevels decisions such as order quantity, inventory level, reorder point and so on. Yet, a few models took into account the strategic-level decisions such as the locations of storage facilities. Though the least popular area in operations planning and control is capacity planning, the percentage of GA studies in this area is only slightly less than that in inventory control. Capacity planning is a decision area that is highly related to production demand. Most reviewed capacity planning models considered deterministic demands. Besides, some researchers focused on the constraint-based GAs in order to correspond to actual production situations. In this survey, there are only two decision areas in operations improvement. For most operations, maintenance can be generally classified into corrective maintenance and preventive maintenance. While corrective maintenance is performed after failure, preventive maintenance includes a well-defined set of tasks. In this survey, almost all of the maintenance strategies determined by GAs were preventive and integrated with production scheduling. On the other hand, regarding GA studies on risk management, the existing work was limited to addressing fire risks, project risks and financial risks.

4.2. Future research directions In this section, future research directions in each decision area in OM are suggested. ∙ It has been observed that many researchers described FLP as an optimization problem. This was achieved by collecting quantitative information, for instance, material flows between departments and material handling costs per unit. Future research directions include solving FLP as a design problem. In a design problem, in addition to quantitative data, how qualitative data are collected should be discussed. For example, how the adjacencies of departments are weighed should be considered and then adopted as a measure in the objective function. Furthermore, as far as recent trends in facility layout design are concerned, there is a marked tendency toward integrating FBS, as performed in the works of Aiello et al. (2012), Mazinani et al. (2013), and Palomo-Romero et al. (2017). To go even further, dynamic plan environments based on FBS solved by MOGAs should be considered. In a DFLP, it is suggested that stochastic demand should be assumed to correspond to the actual situations. ∙ In supply network design, future research directions are twofold. First, GA applications in CLSN incorporating uncertainties need more investigations. In recent years, people have begun to pay attention to environmental issues, and thus there is an increasing interest in the investigation of CLSNs that involve the collection and recovery of used products. Besides, one of the important issues in supply network design is to deal with uncertainties. In 8

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∙

∙

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approaches could be an appropriate methodology for finding the nearly optimal solutions. To deal with the uncertainties and imprecision, other suitable techniques such as fuzzy set theory could be incorporated with GAs. ∙ The vast majority of GA research addressing scheduling problems include measures on production efficiency in the objective functions. It should be noted that, however, some industries might have other concerns, for example, environmental issues. Therefore, more practical considerations should be included in the objective functions and/or constraints in the future research. For instance, the minimization of energy consumption and nowait constraints could be taken into account. Besides, there might not be much contribution or practical insights if GAs are used as a standalone technique for solving scheduling problems. Future studies in this area could focus on how to parameterize a GA implementation and avoid the possibility of premature convergence in the genetic search process for scheduling. ∙ In the area of maintenance, the majority of the papers describe preventive maintenance. However, no papers seem to exist on the failure limit, repair limit and repair number counting policy. Besides, it is found that integrating maintenance strategies with production scheduling took a great interest in the academia since the last decade. Coupling GAs with different failure probability distributions on machines could be an interesting field for further research. While finding optimal maintenance strategies is important for improving the reliability of a system, the measures of system robustness and stabilities in the GA objective function need more investigations. ∙ Risk management and maintenance are closely related. Maintenance is how companies try to avoid failure by taking care of their physical facilities. Risk management is about things going wrong and what operations can do to stop things going wrong. While there exist different GA studies on maintenance, a research gap exists in applying GAs for risk management. It is suggested that risk management can be integrated with other OM areas when solved by GAs. This is because decisions such as lowering inventories, and changing facility layouts, can all serve as a means to make the operational failure greater. In this sense, the GA objectives can take into account the associated risk levels during optimization. Future GA studies can also focus on optimizing the resource allocations plans such that resources would be available when required.

CLSNs, the uncertain problem is more serious due to the inherent uncertainty of reverse logistics networks, which can be caused by, for example, the quantity and quality of the used products (Pishvaee et al., 2011). Therefore, the issues of uncertainties in CLSNs should be addressed. To know more about CLSNs and the uncertainty in supply chain network design, readers are referred to three recent reviews by Aravendan and Panneerselvam (2014) and Govindan et al. (2015, 2017). Second, designing humanitarian supply networks needs more investigations. The past decade has witnessed major natural and man-made disasters worldwide. Practitioners have recognized that strategic locations of depots and pre-positioning of inventory greatly facilitate the speed and efficiency of evacuation and/or delivering supplies in the crucial days immediately after a disaster strikes. Suggested future GA studies in this area can be done with respect to different disaster types and the integration of location and routing decisions. In job design and work, the majority of information can be qualitative, for instance, how a person interfaces with physical aspects of the working areas (i.e. ergonomics issues). Hence, it is not surprising that GAs are not widely applied in job design and work. In this survey, if the objective is to determine the sequence of jobs at the workplace, the problem is considered as a scheduling problem. When designing individuals’ and groups’ jobs, there are a number of possible solutions for grouping resources within an organization. Most organizational structures are blends of two or more pure types such as the U-form, the M-form, matrix forms, and the N-form. To fill the research gaps in the area of job design and work, researchers are suggested to apply GAs for organization designs and investigate how to group parts of the organization together. In forecasting, most studies designed the forecasting models for a particular operation or party in a supply chain, such as the natural gas supply system, a hotel, and a hospital. From a broader perspective, however, the accuracy of one party’s forecast is important for not only itself but also the other parties, because the quality of its forecast often affects the performance of the entire supply chain. In line with this view, future research in forecasting lies in the directions of supply chain forecasting. According to Syntetos et al. (2016), supply chain forecasting goes beyond the operational task of extrapolating demand requirements at one echelon. It involves complex issues such as supply chain coordination and sharing of information between multiple stakeholders. From the review, it has been observed that there were potential gains in forecast accuracy achieved by hybridization of GAs with other intelligent methods such as neural network. More investigations on applications of hybrid GAs in supply chain forecasting are thus encouraged. Initial capacity planning models mainly consider deterministic demands. Since the recent decades, there has been a growing interest in considering uncertain demands. Future research should be continued in the direction of further extension of existing aggregate planning models under stochastic demands. Additional sources of uncertainty such as lead-time, market price, supplier reliability should be taken into account to determine more comprehensive and practical solutions. Furthermore, optimization of capacity planning with multi-objective needs more investigations. Applications of hybrid GA-based models for capacity planning in more different industries, and the coordination of inter-firm and the sharing of inter-firm resources could also be a subject of further investigations. A research gap in inventory control exists in applying GAs for joint maintenance and inventory optimization systems under uncertainties. In fact, companies keep inventory of spare parts is to perform maintenance in order to restore the system as quickly as possible. As a consequence of the complexity and the stochastic nature of such a joint optimization problem, GA-based

5. Conclusion This paper made an attempt to review the applications of GAs in OM in the last decade. The reviewed literature from 2007 to 2017 was categorized into three themes, namely process and product design, operations planning and control, and operations improvement. The three themes contain nine different decision areas in total, which are facility layout design, supply network design, job design and work, forecasting, capacity planning, inventory control, scheduling, maintenance, and risk management. A total of 119 papers were reviewed methodologically, each of which was categorized into a particular decision area for analysis. Based on the review, important gaps in the applications of GAs were highlighted. A GA-related research and application agenda for further work in OM was also provided. Nevertheless, this review has some limitations. First, it is expected that a different definition of the problem domain might result in a different sample of papers and a different structure of the thematic analysis. Second, reviewed work is limited to English and peer reviewed publications. However, nonpeer reviewed journals, books and non-English journals might contain important GA applications that fall within the scope of this review. While it is hoped that this review will motivate interesting development and use of GAs in OM fields and facilitate more constructive and practical solutions in diverse industries, reviewing works that were excluded from this review could lead to additional insights. 9

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