Zero waste strategy for green supply chain management with minimization of energy consumption

Journal Pre-proof Zero waste strategy for green supply chain management with minimization of energy consumption

Muhammad Waqas Iqbal, Yuncheol Kang, Hyun Woo Jeon PII:

S0959-6526(19)33697-2

DOI:

https://doi.org/10.1016/j.jclepro.2019.118827

Reference:

JCLP 118827

To appear in:

Journal of Cleaner Production

Received Date:

09 December 2018

Accepted Date:

09 October 2019

Please cite this article as: Muhammad Waqas Iqbal, Yuncheol Kang, Hyun Woo Jeon, Zero waste strategy for green supply chain management with minimization of energy consumption, Journal of Cleaner Production (2019), https://doi.org/10.1016/j.jclepro.2019.118827

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Zero waste strategy for green supply chain management with minimization of energy consumption Muhammad Waqas Iqbal1), Yuncheol Kang*1), and Hyun Woo Jeon2) 1. Department of Industrial Engineering, Hongik University, Seoul, South Korea 2. Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA, USA

Abstract Conservation of natural resources, reduction of waste, and minimization of energy consumption is now the primary focus of green supply chain management. In order to address the objectives of green supply chain management, this paper suggests a supply chain model to practically eliminate waste from the system while consuming a minimum amount of energy. The target of “zero waste” is achieved by structuring three layers of supply chains, viz., primary supply chain, secondary supply chain, and reverse supply chain. The primary product deteriorates at a specific rate, which creates a substantial amount of waste. The waste disposed of by consumers is categorically segregated into “main product waste” and “packaging waste” at a collection center. The main product waste is converted into a secondary product through a secondary supply chain and the packaging waste is recycled into the same product through a reverse supply chain. The three layers of supply chain are connected at the collection center, which maintains inventory of the collected waste and provides material to the secondary supply chain and the reverse supply chain. In this paper, we propose a model for the centralized supply chain system (i.e., the three layers of supply chain making decisions jointly) by defining a nonlinear mathematical model for minimizing total cost. In particular, the minimum value of the cost is obtained by searching for the optimal period in the planning horizon through an analytical optimization technique. In addition, we minimize the energy consumed for producing the primary and secondary products and recycling the packaging material. Robustness of the model is verified through numerical experiments and sensitivity analysis. The proposed model achieves 98.4% efficiency of waste removal, which is demonstrated through the results of numerical experiments. The obtained optimal length for the planning horizon provides the optimal production time and minimizes the consumption of energy. Keywords: Green supply chain; Zero waste; Secondary and reverse supply chain; Energy consumption

*Corresponding author Dr. Yuncheol Kang Email: [email protected] Phone: +82-2-320-3072

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1. Introduction Management of end-of-life products (or waste products) after their useful lifetime is one of the objectives of green supply chain management (GSCM). The environmental concerns arising from the increasing levels of waste have led to legislations requiring producers and suppliers to deal responsibly with their end-of-life products. Products that deteriorate with time, for example, food products, tend to create more waste in a shorter period of time. Carefully carried out surveys estimate that 1.3 billion tons of food are being wasted each year, which is 33% of the total food produced in the world (Gustavsson et al., 2011). This large amount of waste is polluting the environment which is damaging the health of living beings. Addressing the world’s waste issue is an important step in creating and sustaining a clean environment. As such GSCM calls upon industries to minimize their waste as a means of protecting the environment, and recent research, like the proposed model in this work, is looking for effective ways to reduce waste while still contributing to the economy. In addition to reduce product waste, GSCM involves conservation of energy resources. Increased energy prices and the impact of energy consumption on the environment have led to the need for supply chain managers to minimize their energy consumption. A balance between energy formation and its consumption is mandatory to ensure energy supplies for future generations. Given the limited amount of available energy, there is a need to minimize energy consumption globally as well as devise renewable energy sources. Within the supply chain of a consumer product, energy is consumed while the product is being produced and delivered to the customers. Consumption of energy within such a supply chain can be minimized by following certain dispatching rules and production sequences (Mouzon et al., 2007). A consumer product, for example, a food product, is delivered to customers in a packed form. Practically, the waste of the consumer product contains several components that are mainly categorized into “product waste and packaging waste”. The food waste is organic in nature, which can be decomposed and converted into some secondary product, such as fertilizer, animal feed, or biofuel. Kroger in California, AgriDust in Italy, Greenland in New Zealand, and GasCon in Denmark are some typical examples of the companies that have successfully adopted the food waste conversion practices. Common forms of packaging waste include aluminum, cardboard, foam, glass, paper, and plastic. These packaging materials can be recycled. This way, by transforming the waste into useful products, the system can be cleaned. Moreover, the waste can also be used to extract energy in the form of biofuel, which are a good source of renewable energy. The following definition was adopted by the Zero Waste International Alliance (ZWIA): “Zero waste is the conservation of all resources by means of responsible production, consumption, reuse, and recovery of 2

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products, packaging, and materials without burning, and with no discharges to land, water, or air that threaten the environment or human health.” Given this definition, this study aims at attaining the “zero waste” level within food supply chains by removing food waste and packaging waste through the proposed supply chain model. The “zero waste” level within a supply chain is difficult to achieve by using conventional models of supply chain management. Neither the reverse logistics nor the closed-loop supply chain (CLSC) models provide a solution for attaining “zero waste” for all types of products. These models provide solutions if the product or its components are recyclable, but they are not applicable if the product is not recyclable. In food supply chains, deteriorating products, (i.e., the food products), cannot be recycled for the same consumption purposes. In order to consume the waste of such products, there is a need to introduce a secondary supply chain that works in coordination with the primary supply chain. Then, the waste from the primary product produced by the primary supply chain can be used to produce a secondary product through the secondary supply chain. Moreover, the waste packaging material can be recycled through CLSC such that all types of waste are eliminated from the system. To demonstrate this, the merger of a primary and secondary supply chain (PSSC) with a CLSC is illustrated in this paper. This merger is called a primary, secondary, and closed-loop supply chain (PSCLSC). This innovation helps to eliminate the waste completely from the system, which is proved through the numerical experiments. This paper aims at achieving the “zero waste” level and discusses important parameters of the PSCLSC by suggesting its framework. The framework is sculpted into a mathematical model by calculating the costs involved within the PSCLSC, including the cost of energy consumption. The model is solved through an analytical optimization method to obtain the optimal planning horizon such that the total cost is minimized. Validity of the model is exhibited through numerical experiments by considering practical examples. Results of the experiments are analyzed, which demonstrate complete elimination of waste from the system. Benefits of PSCLSC are threefold. It provides a “zero waste” strategy within supply chain management, minimizes energy consumption, and minimizes total cost. Thus, PSCLSC not only serves to attain the objectives of GSCM but also supports the construction of a more sustainable supply chain system. The structure of the paper is as follows. Section 2 presents the literature review related to the introduced research problem. Section 3 explains the structure of the supply chain by defining the process flow within PSCLSC and the necessary assumptions for the model. Section 4 provides a mathematical model for the described supply chain system. Solution methodology is explained in Section 5. Practical implications of

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the proposed model are discussed in Section 6 with subsequent analyses. Managerial insights are provided in Section 7, and results of the proposed study is summarized in Section 8.

2. Literature review The models considering waste reduction through recycling of end-of-life products are classified into two main categories: the models on reverse logistics and those on CLSC. Among the first attempts to provide insight into reverse logistics and emphasize its importance is the work of Barry et al. (1993). The authors discussed how industries in Europe became more focused at the start of 1990s on redesigning their products to increase recyclability and reduce waste. The ability of a manufacturer to recycle its product in order to reduce environmental pollution affords companies a competitive edge as does on-time delivery of a quality product. A comprehensive survey of the literature quantitative models for reverse logistics and CLSC has been conducted by Fleischmann et al. (1997). Later, the research in this area expanded, and practitioners started manufacturing products that after their useful lifetime could be disassembled and remanufactured. These products were named eco-designed products. Lee (2012) suggested that the waste of a mainstream product could be converted into a valuable byproduct. He named this process byproduct synergy (BPS). The model proposed in our study extends this research by combining BPS with recycling of packaging material; thus giving a threefold benefit: (a) converting waste products into new products, (b) recycling packaging material, and (c) removing all waste. This innovation in our study is referred to as PSCLSC. The literature on eco-design greatly informs efforts to reduce the waste of end-of-life products, such as how to efficiently disassemble a product to acquire the correct components and remanufacture the product with minimum cost. Several eco-design methods have been discussed by Pigosso et al. (2010), and the authors provided strategies for remanufacturing end-of-life products within CLSCs. The authors suggested that consideration of eco-design during product development is a proactive approach to eliminate environmental pollution due to product waste. Rashid et al. (2013) concluded that consumption of a product over several lifecycles could be made possible by improving product design and development. The authors introduced resource conservative manufacturing to conserve material and energy, eliminate waste, and protect the environment. The purpose of resource conservative manufacturing is to minimize the waste created from expired products. Several efforts have been carried out to minimize the waste within supply chains. The idea of attaining zero waste within a supply chain has been proposed by Song et al. (2015), who recognized the need to develop a robust waste management system. The authors emphasized the significant role of the waste management system in resource conservation and its lasting impact on future generations. They discussed several 4

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challenges that demand immediate attention and resolution, including completely eliminating waste from the supply chain of consumer products. Thyberg and Tonjes (2016) specifically investigated the drivers of food waste generation. The authors examined the impact of food system industrialization, urbanization, globalization, and economic growth on food waste generation. They explored people’s changing perspectives on food waste in different regions of the world and based on socio-demographics, culture, politics, and economics. The waste of food/biodegradable products is largely created due to deterioration, which reduces the quality as well as quantity of these products. The effect of depreciation in value of other products with time is similar to the decrease in quality of food products due to deterioration. The concept of outdated electronic products as deteriorated ones has been proposed by Yang et al. (2010). The authors suggested that the waste due to deterioration could be controlled by recycling the outdated products. Chung and Wee (2011) suggested that green product design is necessary for recycling and to avoid the negative impact of waste on the environment. Papargyropoulou et al. (2014) classified food waste into “avoidable food waste” and “unavoidable food waste.” Realizing the need for recycling and for industries to adopt recycling practices, Hong et al. (2014) explored the effects of government subsidies on consumption of recycled products and found they improved the rate of return of end-of-life products and reduced the amount of waste. Later, the economic and environmental benefits of adopting reverse operations of end-of-life products were exhibited by Kumar Mishra (2016). A sustainable supply chain design has been proposed by Xu et al. (2017) and the authors introduced a global reverse supply chain, emphasizing its necessity for environmental protection, conservation of resources, and creation of jobs. The authors discussed the major challenges of uncertainty in waste collection, transportation, and currency exchange rates associated with designing a global reverse supply chain. Calmon and Graves (2017) proposed an inventory management model within a CLSC for new and remanufactured products having short lifetime. The price of these products decreases with time, which is modeled similar to the deterioration of food products. In addition, our study considers the remanufacturing of packaging materials and extends this idea by incorporating a secondary supply chain for expired food products. Reduction of waste of end-of-life products through recycling depends on return policies adopted by the manufacturers. To collect end-of-life products, most of the reverse supply chains lease the services of a third party while others encourage customers to return end-of-life products back to retailers by introducing return incentives. Huang et al. (2013) concluded that a dual channel return policy (in which retailers and third parties both collect the end-of-life products) is better than a single channel collection policy. Later, Modak et al. (2018) provided models for a three channel (retailer, manufacturer, and third party) collection 5

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policy. The authors concluded that both the manufacturer and the retailer served as an effective collection center, depending on the threshold value of collection efforts. The dependence of effectiveness of a reverse supply chain on returns has been empirically studied by Shaharudin et al. (2017). The authors concluded that higher rates of return of end-of-life products encourage manufacturers to adopt the route of CLSC. The problem of uncertain rates of return has been solved by Cui et al. (2017), which provided an effective optimal policy within a CLSC. Emphasizing the importance of adopting reverse logistics operations for waste reduction, Polo et al. (2018) found that implementation of reverse operations for conversion of used products was economically beneficial and offered a competitive edge to modern industries. The increased cost of energy due to increasing demand and limited availability has resulted in increasing production and transportation costs, which increase the overall cost of a supply chain. In response to this, Shrouf et al. (2014) suggested a production model to minimize energy consumption cost by optimizing the length of the production cycle. Similarly, Nilakantan et al. (2015) proposed an assembly line model to minimize energy consumption by optimizing production cycle time. Inspired by increased energy costs, depleted energy resources, and climate change, Zhou et al. (2016) summarized the models related to energy efficiency and presented a comprehensive literature review to point to new research avenues in this field. Later, Zhang et al. (2016) developed a nonlinear planning process that allowed for selecting the right process and the right machine for minimum consumption of energy. Li et al. (2017) suggested that machine scheduling was a decisive variable in determining the amount of energy consumption. The authors suggested an effective algorithm to minimize energy consumption. Further, Wang et al. (2018) minimized total energy consumption for the identical parallel machine scheduling problem. As proposed by Song et al. (2015) regarding zero waste strategies, modern methods and strategies are required to overcome the challenges of increasing waste within modern societies. Based on the literature related to strategies and methods for protecting the environment by controlling unavoidable food waste, this paper suggests a novel idea to completely eliminate unavoidable food waste within the food supply chain. This research proposes joining three layers of supply chain together to achieve the objective of zero waste. Moreover, the provided model integrates the cost of energy consumption, as suggested by Jeon et al. (2015), with the total cost of the supply chain. Total cost is minimized by determining and utilizing the optimal value of the planning horizon, which is an important parameter for energy consumption as informed by Li et al. (2017).

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3. Problem formulation In this section, the proposed research problem is defined by illustrating the process flow within PSCLSC. The notations and assumptions to construct the mathematical model are provided in this section. 3.1. Problem Definition This paper considers three layers of supply chain, (i.e., primary, secondary, and closed-loop), which are connected through a collection center. A deteriorating product (e.g., food product) is supplied in nondeteriorating packaging (e.g., plastic bags) through the primary supply chain. A substantial amount of the product, due to deterioration and consumption habits, is wasted by consumers, which creates environmental pollution. This waste affects the health of living beings and creates landfills. In order to avoid these environmental problems and obtain some value, the created waste is handled properly. The end-of-use/endof-life/deteriorated primary products are collected at a collection center, where the main product and the packaging materials are segregated and their inventories are maintained separately. Two different routes are adopted: one for the waste of the main product and another for the packaging material. The waste of the main product is converted into a secondary product and is supplied through a secondary supply chain. The waste of the packaging material is recycled through a recycling plant/remanufacturer and is used within the primary supply chain, thus making a closed-loop for packaging materials. By consuming the waste of primary product, the created waste is completely eliminated from the system. A primary supply chain consists of a primary manufacturer and a primary retailer. The primary product is prepared at the primary manufacturer and is vended at the primary retailer. This product is deteriorating in nature and the rate of deterioration depends on its lifetime. Similarly, a secondary supply chain is constructed by including an additional manufacturer and retailer. Typically, the secondary product is prepared from the waste of the primary product. Therefore, outside material is generally not required for its preparation. Secondary products commonly include animal feed, biofuel, and fertilizer, which have negligible rates of deterioration. These products are supplied through the secondary supply chain. In a reverse supply chain, a remanufacturer recycles the packaging material of the primary product. The recycled packaging material is considered to be the same quality as the original packaging material and their inventories are maintained together at the primary manufacturer. The collection center, a concurrent point of primary, secondary, and reverse supply chain, separately maintains the inventories of waste from the primary product and its packaging material. The three layers of supply chain are synchronized. Thus, the length of their planning horizon is considered to be the same. The flow of products and materials within the primary, secondary, and closed-loop supply chain (PSCLSC) is illustrated in Figure (1). 7

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Primary supply chain

Material supplier

Primary manufacturer

Customers

Primary retailer

Closed-loop supply chain

Collection center

Recycling plant Packing waste

Customers

Secondary retailer

Secondary manufacturer

Food waste

Secondary supply chain Fig. 1. Process flow within PSCLSC 3.2. Notations The notations used to describe the mathematical model are provided in this subsection. Indices

i

i  1, 2 , where 1 represents the primary and 2 the secondary supply chains

R

represents retailer

M

represents manufacturer

Variable

T

cycle time (time units)

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Retailers’ parameters

d Ri

customer’s demand per unit time at retailer of supply chain i (units/unit time)

DRi

customer’s demand per cycle at retailer of supply chain i (units/cycle)

Li

maximum lifetime of the product i (time units)

i

rate of deterioration of the product of supply chain i

N Di

number of deteriorated items per cycle at retailer of supply chain i (units/cycle)

o I Ri  t  on-hand inventory at retailer of supply chain i at any time t , 0  t  T (units)

I Ri

total inventory at retailer of supply chain i for one cycle (units/cycle)

ARi

ordering cost per order at retailer of supply chain i ($/order)

hRi

inventory carrying cost per unit per unit time at retailer of supply chain i ($/unit/unit time)

TCRi

total cost per unit time at retailer of supply chain i ($/unit time)

Manufacturers’ parameters

d Mi

demand per unit time at manufacturer of supply chain i (units/unit time)

DMi

demand per cycle at manufacturer of supply chain i (units/cycle)

Pi

rate of production at manufacturer of supply chain i (units/unit time)

ki

scaling parameter between production and demand at manufacturer of supply chain i

a I Mi  t  on-hand inventory at manufacturer of supply chain i at any time t , 0  t  ti (units) b I Mi  t  on-hand inventory at manufacturer of supply chain i at any time t , ti  t  T (units)

I Mi

total inventory at manufacturer of supply chain i for one cycle (units/cycle)

N Pi

at manufacturer of supply chain i , the number of items produced per cycle (units/cycle)

CE

cost of energy consumption per unit of energy ($/kWh)

H

conversion factor of time unit into hours

CSETi

setup cost per cycle of manufacturer of supply chain i ($/cycle)

a CMT 1

material cost per unit of main product at primary manufacturer ($/unit)

b CMT 1

material cost per unit of packaging at primary manufacturer ($/unit)

CPa1

production cost per unit of main product at primary manufacturer ($/unit)

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CPb1

production cost per unit of packaging at primary manufacturer ($/unit)

CMT 2

material cost per unit of secondary product ($/unit)

CP 2

production cost per unit at secondary manufacturer ($/unit)

Crem

remanufacturing cost per unit at recycling plant ($/unit)

hMi

inventory holding cost per unit per unit time at manufacturer of supply chain i ($/unit/unit time)

TCMi

total cost per unit time at manufacturer of supply chain i ($/unit time)

Collection center’s parameters

CSETc

setup cost per cycle of the collection center ($/cycle)



rate of return of the product of primary supply chain

Cc

cost of collection per unit ($/unit)

Nc

number of collected items per cycle at collection center (units/cycle)

I ca1  t  on-hand inventory of packaging material at collection center at any time t , 0  t  t1 (units) I cb1  t  on-hand inventory of packaging material at collection center at any time t , t1  t  T (units)

I c1

total inventory of packaging material at collection center per cycle (units/cycle)

hc1

inventory holding cost per unit of packing per unit time at collection center ($/unit/unit time)

I ca2  t  on-hand inventory of main product at collection center at any time t , 0  t  t2 (units) I cb2  t  on-hand inventory of main product at collection center at any time t , t2  t  T (units)

Ic2

total inventory of main product at collection center per cycle (units/cycle)

hc 2

inventory holding cost per unit of main product per unit time at collection center ($/unit/unit time)

TCc

total cost per unit time at collection center ($/unit time)

3.3. Assumptions The model provided in this research is established on the basis of some assumptions, all of which are described below. 1. A waste elimination system of three layers of supply chain is considered, which is referred to as a primary, secondary, and closed-loop supply chain (PSCLSC) system. Primary product waste is eliminated by consuming it through secondary and closed-loop/reverse supply chains. 10

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2. For the smooth working of the system, synchronization among these three layers of supply chain is made possible by considering their cycle time to be of equal length. Integration of the supply chain players is achieved through synchronization of their planning horizon, which is required to keep the materials and products balanced and flowing between them. Integration of all the players of the supply chain leads to a more accurate, reliable, and controllable plan (Özceylan et al., 2014). 3. The products under consideration deteriorate at variable rates i , which depend on their lifetime. The rate of deterioration of the primary product is high, which is a major cause of waste, while that of the secondary product is negligible. Moreover, these products do not deteriorate at the manufacturer but start deteriorating after delivery to the retailers. 4. All the waste created from the end-of-life/deteriorated primary products is returned to the collection center. The collection center serves as a material supplier for the secondary supply chain and the reverse supply chain. The amount of returned product is  d R1 , which is a fraction of the demand/sale of the primary products. The rate of return remains constant over time. 5. The rate of production at the respective manufacturers depends on the rate of demand (Qin and Liu, 2014) (i.e., Pi  ki d Mi ). In order to avoid shortages at the manufacturers, the rate of production is kept higher than the rate of demand. The value of the scaling parameter is decided based on the properties of the system such that the total cost remains as low as possible. 6. The requirements for producing packaging materials for the primary product are fulfilled from freshmanufactured as well as recycled packaging materials. 7. The amount of energy consumed during manufacturing depends on the power of the machine and its time of utilization, as proposed by Jeon et al. (2015). 8. In order to fulfill service-level requirements, shortages at the retailers are not allowed. Thus, demand at the retailers is fulfilled during the planning horizon by replenishing the amount of product that will fulfill this demand and compensate for the effects of deterioration. 9. Decision-making at the three layers of supply chain are carried out centrally to obtain globally optimal solutions and performance.

4. Mathematical model In general, a product with a longer lifetime deteriorates at a slower rate. For example, the rate of deterioration of dry grains is lower than that of fresh fruits and vegetables. Lifetime is a primary parameter for predicting a product’s deterioration rate. Therefore, we consider the rate of deterioration as a function of the lifetime of a product. Different products have different rates of deterioration. Comparing rates of 11

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deterioration for several different products, the product with the longest lifetime will have the slowest rate of deterioration. Thus,



 1 L

,   1,

(2)

where  is the scaling parameter and is known as the degree of vulnerability to deterioration, which depends on the ambient conditions where the product is warehoused and their effect on the product’s degradation. 4.1. Model for primary supply chain In our model, we assume that the primary supply chain is comprised of a manufacturer and a retailer. The models for the manufacturer and retailer are as follows. Primary retailer The retailer in the primary supply chain receives a specific quantity of finished primary product from its manufacturer at the start of the planning horizon. As soon as the product is replenished at the retailer, the level of inventory starts depleting due to demand and deterioration. The inventory depletes at a specific rate, which is provided in the equation below. dI Ro1  t  dt

  d R1  1 I Ro1 , 0  t  T

(3)

In order to obtain the value of on-hand inventory at any time t , boundary inventory condition (i.e.,

I Ro1  t   0 at t  T ) is used. The value of on-hand inventory at the primary retailer can be calculated by using the following expression: I Ro1  t  

d R1

1

e 

1 T t 



1 , 0  t  T

(4)

The retailer is responsible for ordering the required quantity of the product for the planned cycle and maintaining its inventory. The costs incurred at the primary retailer include the ordering cost and inventory holding cost. For the replenishment of fresh inventory, several activities, such as preparation of purchasing orders, arrangement of transportation and warehouse operations, inspection of the product, and product storage,

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are performed. The cost to perform these activities is known as the ordering cost. Ordering cost per cycle of the retailer is expressed below; Ordering cost per cycle  AR1

(5)

Inventory stock is maintained by the retailer to fulfill the demand of its customers. An out-of-stock situation is avoided by replenishing the calculated amount of product based on its demand during the planning horizon. The cost acquired to maintain the inventory is the inventory holding cost, which is calculated by using the total inventory carried during the cycle and the cost of keeping one unit of the product hR1 per unit time. The inventory carried during the cycle is computed by using on-hand inventory and integrating it for the complete cycle; T

I R1  I Ro1  t  dt 

 0

d R1

12

e

1T



 1T  1

(6)

This expression is used to calculate inventory holding cost per cycle, which is provided below; Inventory holding cost per cycle  hR1 I R1

(7)

Total cost to the retailer is obtained by adding its ordering cost and inventory holding cost. The following equation provides the expression of total cost per unit time at the retailer for the primary supply chain; Total cost TCR1  

1  AR1  hR1I R1  T

(8)

Primary manufacturer Primary products are prepared at the primary manufacturer and delivered to the retailer. The product at the retailer depletes due to customer demand as well as deterioration. The proposed model considers a good service level and avoids any kind of out-of-stock situation. Therefore, the production quantity is decided in such a way that it fulfills customer demand at the retailer by compensating for deteriorated quantity. The demand at the manufacturer is computed by adding the demand at the retailer and the quantity that would deteriorate during the planning horizon. The demand at the manufacturer for the primary supply chain per cycle is expressed below; Manufacturer’s demand per cycle  DM 1   DR1  N D1

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(9)

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where DR1 is the demand per cycle at the retailer and N D1 is the number of items of the primary product that would deteriorate at the retailer during one cycle. Both of these quantities are exhibited below; T



DR1  d R1dt  d R1T

(10)

0

T

N D1  1 I Ro1  t  dt 



d R1

0

1

e

1T



 1T  1

(11)

Both the players (the retailer and the manufacturer) of the primary supply chain can be synchronized by considering an equal length for their cycle time (i.e., T ). The rate of demand at the manufacturer is computed by using total demand per cycle and the cycle time, which is expressed in the following equation; 𝑑𝑀1 =

𝐷𝑀1 𝑇

=

𝐷𝑅1 + 𝑁𝐷1 𝑇

(12)

The demand per cycle is the total number of items demanded by the customers during the planning horizon/cycle time, while demand per unit time is the number of units demanded during one unit of time (in this study we consider a month as time unit). The rate of production for the manufacturer is considered dependent on the rate of demand, which is a common phenomenon for food production units (Qin and Liu, 2014);

P1  k1d M 1  k1

DR1  N D1 T

(13)

The production rate is kept higher than the demand rate to avoid shortages at the manufacturer. The production setup works from 0 to t1 , while the retailer’s order is fulfilled until the end of the planning horizon. The level of inventory I Ma 1 increases during the production cycle and it amount I Mb 1 starts depleting after the production is completed at time t1 . The inventory is completely depleted at the end of planning horizon T . From 0 to t1 , the rate of inventory replenishment is P1  d M 1 , while from t1 to T , the rate of inventory depletion is  d M 1 . Figure (2) explains the behavior of the inventory level during a complete cycle at the manufacturer. The differential equations governing the inventory level at the manufacturer are expressed as follows; 𝑑𝐼𝑎𝑀1(𝑡) 𝑑𝑡

= 𝑃1 ― 𝑑𝑀1 = (𝑘1 ― 1)𝑑𝑀1, 0 ≤ 𝑡 ≤ 𝑡1

𝑑𝐼𝑏𝑀1(𝑡) 𝑑𝑡

= ― 𝑑𝑀1, 𝑡1 ≤ 𝑡 ≤ 𝑇

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On-hand inventory at the manufacturer is calculated by using the given boundary conditions;

I Ma 1  t   0 at t  0

Inventory Level

I Mb 1  t   0 at t  T I Ma 1  t    k1  1 d M 1t , 0  t  t1

(16)

I Mb 1  t   d M 1 T  t  , t1  t  T

(17)

𝑃1 ― 𝑑𝑀1

―𝑑𝑀1

Production and delivery Only delivery 𝑡1

0 Time

𝑇

Fig. 2. Behavior of the inventory level at the primary manufacturer As observed from Figure (2), for an instant, the level of inventory is the same when t  t1 . Thus, equating the on-hand inventory equations at the point t1 , we get;

 k1  1 d M 1t1  d M 1 T  t1  

t1 

T k1

Hence, the value for production time t1 depends on the value for the planning horizon T and that of the scaling parameter k1 for the production rate. The primary manufacturer prepares the production facility for producing the primary product. Production of the primary product involves production of the main product and the packaging material (freshmanufactured and recycled). The manufacturer prepares production setup for each operation separately. The cost to prepare the production facility is called setup cost, which is exhibited as follows; Setup cost per cycle of primary manufacturer  CSET 1 15

(18)

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Material for the primary product is classified into two categories: material for main product and material for packaging. The quantity of material purchased for the main product is proportionate to the number of items being produced. In the case of packaging, some of the material requirements are fulfilled from a recycled packaging. By using the material cost per unit for the main product CMT 1 and for the packaging b

material CMT 1 , the total cost of material is calculated and provided in the following expression; a b Material purchasing cost per cycle of primary manufacturer  CMT 1 N P1  CMT 1  N P1   DR1 

(19)

where the number of items of primary product produced per cycle is N P1 , while the number of recycled packaging items per cycle is  DR1 . The value of N p1 is calculated below; t1



N P1  P1dt  DR1  N D1

(20)

0

The production activities at the primary manufacturer are classified into two categories, production of the main product and preparation of packaging. The required quantity of the main product is obtained at only one type of machine. However, the required quantity of packaging is obtained by using production machines for fresh packaging and recycling machines. The number of items required per cycle of the primary product is N P1 . Therefore production quantity of the main product is N P1 . However, the production quantity of fresh packaging is N P1   DR1 and the remaining quantity  DR1 is obtained through recycling machines. a b Since CP1 and CP1 represent the cost of production per unit of the main product and the cost of packaging

per unit, respectively, the total cost of production of the primary product is exhibited below; Production cost per cycle at primary manufacturer  CPa1 N P1  CPb1  N P1   D R1 

(21)

The finished primary product is stocked at the manufacturer in preparation for fulfilling retailer demand. Several activities are performed to maintain the inventory stock, which incur some cost. The inventory of the primary product carried by the manufacturer for one cycle is calculated and expressed in the equation below; t1

T

I M 1  I Ma 1  t  dt  I Mb 1  t  dt 

 0

 t1

16

 k1  1 d M 1T 2 2k1

(22)

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The inventory holding cost is calculated by using the above expression and the holding cost per unit of the product hM 1 per unit time, which is provided below; Inventory holding cost per cycle at primary manufacturer  hM 1 I M 1

(23)

Total cost at the primary manufacturer is calculated by using the costs explained and calculated above. The expression for total cost per unit time is provided below;

TCM 1 





1 a b a b CSET 1  CMT 1 N P1  CMT 1  N P1   DR1   C P1 N P1  C P1  N P1   D R1   hM 1 I M 1 (24) T

4.2. Model for the secondary and closed-loop supply chains The model for the secondary and closed-loop supply chains is comprised of a collection center, a recycling plant/remanufacturer of the packaging material, a manufacturer of the secondary product, and a retailer. The functions and costs at each of these players are explained next. Collection center The secondary and CLSC are connected to the primary supply chain at a collection center. The collection center is responsible for collecting the end-of-life/end-of-use/deteriorated/waste primary product and maintaining the smooth supply of raw material to the secondary and reverse supply chains. The purpose of setting up the collection center is twofold. It not only removes waste from the system but also helps to save the cost of material for the secondary and reverse supply chains. There is an initial investment to set up a warehouse at the collection center, which is called its setup cost and is provided below; Setup cost per cycle  CSETc

(25)

Incentive policies encourage customers to return the waste to the collection center. At the collection center, the returned waste is classified into main product waste and packaging waste. The activities involved in collecting and segregating the waste are called waste collection operations, and the cost incurred to perform these operations is called the waste collection cost. The total cost of collection per cycle depends on the cost of collection per unit Cc and the total number of items collected per cycle N c ; Waste collection cost per cycle  Cc N c where the value of N c is calculated by using the following quation;

17

(26)

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T



T



N c  Rdt   d R1dt  d R1T 0

(27)

0

The inventories of both types of waste, the main product waste and the packaging waste, are maintained separately and material is supplied to the secondary and reverse supply chains. At the start of each cycle, the level of inventory of both types of waste depletes because the inventory is transported to the respective production plants. When the production is complete at the secondary manufacturer and at the recycling plant, inventory of both types of waste is replenished due to constant rates of return. The differential equations governing the behavior of the inventory level of the main product’s waste are expressed below;

dI ca2   d R1  k2 d R 2 , 0  t  t2 dt dI cb2  t  dt

(28)

  d R1 , t2  t  T

(29)

The above differential equations are solved by using the following inventory conditions;

I ca2  t   0 at t  t2 I cb2  t   0 at t  t2 By using the above conditions, the value of on-hand inventory of the main product at any time t at the collection center is calculated in the following equation; T  I ca2  t    k2 d R 2   d R1    t  , 0  t  t2  k2 

(30)

I cb2  t     d R1  t2  t  , t2  t  T

(31)

The stock of inventory of the main product that is carried at the collection center during one cycle  0,T  , is exhibited in the following equation; t2

Ic2 

T

  t  dt    t  dt   k d I ca2

0

I cb2

t2

2 R2

T 2  d R1T 2  k2  1    d R1  2    2  k2  2k2

2

(32)

Using the above expression and the inventory holding cost hc 2 per unit per unit time, the inventory holding cost per cycle of the main product at the collection center is calculated in the following equation;

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hc 2 I c 2

2  T 2  d R1T 2  k2  1    hc 2  k2 d R 2   d R1  2     2  k2   2k2  

(33)

The inventory holding cost of the waste packaging material at the collection center is calculated similarly. The final expression of inventory holding cost per cycle of packaging waste at the collection center is provided below; 2  T 2  d R1T 2  k1  1   hc1 I c1  hc1  k1d R1   d R1  2     2  k1   2k1  

(34)

Total cost per cycle of holding inventory of collected waste at the collection center is computed by using the inventory holding cost of both components of waste, which is expressed below; Total inventory holding cost per cycle at collection center  hc1 I c1  hc 2 I c 2 Total cost of the collection center per unit time is computed in the following equation;

TCc 

1  CSETc  Cc N c  hc1I c1  hc 2 I c 2  T

(35)

Recycling plant (Remanufacturer) Recycling of the waste packaging material is performed by using recycling plants. All the collected quantity

 D R1 of the packaging waste is recycled and the quality of the recycled packaging is equivalent to that of the freshly manufactured packaging due to investing in the remanufacturing process. At the remanufacturer, only recycling activities are performed, and the recycled packaging is sent to the manufacturer for storage. Employing the cost of recycling one unit of waste Crem and the total number of recycled items per cycle, the total cost of remanufacturing per cycle is calculated, which is provided below; Total remanufacturing cost  Crem  D R1

(36)

The rate of recycling the packaging waste is equal to that of the fresh counterpart, such that the supply of packaging remains synchronized with the supply of the main product.

Secondary retailer

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The secondary product is sold at the secondary retailer. As mentioned earlier, the secondary product (e.g., fertilizer) has a longer lifetime than does the primary product. Therefore, the rate of deterioration of the secondary product is very low. The secondary product is replenished at its retailer at the start of the inventory cycle. With the passage of time, inventory depletes due to customer demand and product deterioration. The rate of inventory depletion at the secondary retailer is provided below; dI Ro 2  t  dt

  d R 2   2 I Ro 2 , 0  t  T

(37)

The value of on-hand inventory is calculated by using the inventory condition I Ro 2  t   0 at t  T ; I Ro 2  t  

dR2

2

e

 2 T t 



1 , 0  t  T

(38)

Like the primary retailer, the secondary retailer orders the required quantity once during the cycle. The ordering cost is exhibited in the following expression; Ordering cost per cycle  AR 2

(39)

Inventory holding cost of the secondary product depends on the holding cost per unit per unit time hR 2 and the total inventory per cycle I R 2 . The total inventory per cycle is calculated by using on-hand inventory; T

I R 2  I Ro 2  t  dt 

 0

dR2



2 2

e

 2T



  2T  1

(40)

Thus, the inventory holding cost at the secondary retailer is provided in the following expression; Inventory holding cost per cycle  hR 2 I R 2

(41)

Total cost per unit time incurred at the secondary retailer is provided below; Total cost TCR 2  

1  AR 2  hR 2 I R 2  T

(42)

Secondary manufacturer Today, secondary supply chains generally produce biofuel, animal feed, and fertilizer. The manufacturing setup within a secondary supply chain is entirely different from the setup for the primary supply chain. Anaerobic digesters are installed at the secondary manufacturer to transform the recyclable food waste into

20

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fertilizer and biofuel. The production quantity of the secondary product is decided based on its demand and calculated using the formula below; Manufacturer’s demand per cycle  DM 2   DR 2  N D 2

(43),

where T



DR 2  d R 2 dt  d R 2T

(44)

0

and T

N D 2   2 I Ro 2  t  dt 



dR2

0

2

e

 2T



  2T  1

(45)

The rate of demand for the secondary product at its manufacturer is provided below;

dM 2 

DM 2 DR 2  N D 2  T T

(46)

Similar to production at the primary manufacturer, the rate of production at the secondary manufacturer is expressed in the following equation;

P2  k2 d M 2  k2

DR 2  N D 2 T

(47)

As soon as the production starts at the secondary manufacturer, the inventory starts building and demand by the retailer is fulfilled from the inventory. The required quantity is produced within the time t2 , which is supplied to the retailer during complete cycle T . The level of inventory at the secondary manufacturer increases during production  0,t2  due to the rate of production P2 being higher than the demand rate d M 2 . It depletes during the time t2 , T  due to constant delivery of the product to the retailer at rate d M 2 . The differential equations governing the behavior of inventory at the secondary manufacturer are expressed below; dI Ma 2  t  dt

 P2  d M 2   k2  1 d M 2 , 0  t  t2

dI Mb 2  t  dt

  d M 2 , t2  t  T

The value of on-hand inventory, at any time t , is calculated by using the given inventory conditions;

21

(48)

(49)

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I Ma 2  t   0 at t  0 I Mb 2  t   0 at t  T I Ma 2  t    k2  1 d M 2t , 0  t  t2

(50)

I Mb 2  t   d M 2 T  t  , t2  t  T

(51)

The value of inventory during both intervals is equal at the period when t  t2 . Therefore, using the above equations, the following results are obtained;

 k2  1 d M 2t2  d M 2 T  t2  

t2 

T k2

The costs incurred at the secondary manufacturer include the setup cost, material cost, production cost, and cost of inventory holding. The production setup activities include preparing the plant, testing for the required energy and nutrition in the food waste, and preparing the warehouse to store the finished product. The acquired cost to set up the production plant is called the setup cost, which is expressed as follows; Setup cost per cycle of secondary manufacturer  CSET 2

(52)

The secondary product is produced from the end-of-life deteriorated primary product. Generally, material other than that from the primary product is not required to produce the secondary product. However, if demand for the secondary product outpaces production, additional material could be purchased to meet this demand. To avoid shortages, the excess required material is purchased from external suppliers. External suppliers of organic waste are generally municipal organizations that collect and dispose of residential and commercial garbage. The manufacturer bears a cost per unit CMT 2 for the additional organic waste. Practically, one unit of the primary product may not produce exactly one unit of the secondary product. Therefore, we assume that one unit of the waste primary product produces  number of units of the secondary product. The raw material quantity N o to be purchased per cycle to produce the secondary product is calculated by the conditional expression provided below;

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1  If N c   DM 2  No   Otherwise 

    1 N o  DM 2  N c    No  0

(53)

Hence, the cost of material for the secondary product is expressed below; Material purchasing cost of secondary product cost per cycle  CMT 2 N o

(54)

The production process of the secondary product is different compared to production of the primary product. The secondary manufacturer uses anaerobic digesters, mixing tanks, and condensers to convert the food waste into biofuel or fertilizer. The waste of the primary product is mixed with enzymes and catalysts within anaerobic digesters. The produced biogas is condensed and stored in cylinders. The cost to carry out these processes for one unit is the production cost per unit C p 2 . Total cost of production is calculated below by using per unit cost of production and the total number of produced units N p 2 ; Production cost per cycle at the secondary manufacturer  CP 2 N P 2

(55)

where t2



N P 2  P2 dt  DR 2  N D 2

(56)

0

The cylinders filled with biofuel are stored under proper inventory conditions. The required number of units of the secondary product is supplied to the retailer during the planning horizon. The inventory carried by the secondary manufacturer during complete cycle I M 2 is calculated below; t2

T

0

t2

I M 2  I Ma 2  t  dt  I Mb 2  t  dt 





 k2  1 d M 2T 2

(57)

2k2

Hence, the inventory holding cost per cycle at the secondary manufacturer is calculated by using the holding cost of one unit per unit time hM 2 and the total inventory carried during the cycle I M 2 ; Inventory holding cost per cycle at secondary manufacturer  hM 2 I M 2

(58)

Total cost at the secondary manufacturer is the sum of its setup cost, production cost, material cost, and inventory holding cost. The total cost per unit time is exhibited below; Secondary manufacturer’s total cost per unit time TCM 2   23



1 CSET 2  CMT 2 N o  CP 2 N P 2  hM 2 I M 2 T



(59)

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Energy consumption In managing a supply chain, energy is consumed during production, delivery, maintenance of inventory conditions, and other operations. However, the consumption of energy is higher during the production process as compared to other supply chain processes. Consumption of energy during production operations mainly depends on the power of machine and the time of utilization. As proposed by Jeon et al. (2015), machine use during production can be divided into different states, with each state associated with a different level of power consumption. Accordingly, the total power of a machine during the production process is calculated by determining the power of the machine during each state and the time period of that state, as provided in the following expression; Energy consumption 

N

 Power x Time i

i

i 1

However, for this paper we modified this formula for the proposed problem. In this paper " i " represents the different types of machines, which are used for all types of production processes. In our model, there are three types of manufacturing machines (i.e., the machine that produces the primary product, the machine that produces the packaging for the primary product, and the machine that produces the secondary product). The power (in kW) required by these machines is PPr , PPk , and PSc , while the time (in months) of their utilization is tPr , t Pk , and tSc , respectively. The time of utilization of these machines is expressed below; tPr  t Pk  t1  tSc  t2 

T k1

T k2

By using the time of utilization for all three types of machines and their power, total energy consumption is calculated in the following expression;  T T Total energy consumption per cycle (kWh)  H  PPr  PPk   PSc  k1 k2  

(60)

The cost of energy consumption during one cycle is provided below;  T T Cost of energy consumption per cycle  CE H  PPr  PPk   PSc  k1 k2  

(61)

where CE is the cost of energy consumptions per unit (kWh) and H is the conversion factor of time units into hours.

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Total cost per unit time of the PSCLSC Total cost of PSCLSC is calculated by adding the cost expended by all of the players (i.e., primary retailer, primary manufacturer, collection center, remanufacturer, secondary retailer, and secondary manufacturer) as expressed respectively in Equations (07, 23, 34, 35, 41, 58). The cost of total energy consumption at all the manufacturers, as provided in Equation (60), is also added within the total cost function. The following expression provides the total cost per unit time of the PSCLSC with energy consumption cost;

    d R1  T d R 1T a a e  1T  1    AR1  CSET 1  hR1 2 e 1  1T  1  CP1  CMT 1 d RT  1 1      1T  k1  1 e  1 Td R1    d R 1T  b b   CP1  CMT 1 1    d RT   e  1T  1   hM 1  2k11 1         d R 2 2T d R 2 2T e   2T  1    AR 2  CSET 2  hR 2 2 e   2T  1  CP 2 d R 2T   2 2     1  TC   k2  1 e2T  1 Td R 2  T o  Crem  d R1T  CMT 2 N  hM 2  2k2 2   2   2 2    d R1T  k1  1   T  C   C  d T  h k d   d       c R1 c1  1 R1 R1 2  SETc  2 k 2 k  1   1      2 2 2     h  k d   d  T   d R1T  k2  1    C H  P  P  T  P T   Pr     R1 E Pk Sc  c2  2 R2 2  k2   k1 k2   2k22      





 









2











 where 1  1 ,  2   2 , and N o    1 L 1 L 1













If N c 

1



No  0

DM 2 ,

Otherwise, 

No 



d R 2 ˆ2T 1 e d R 2T 



2

(62)

       2T  1    d R1T   



This study aims to minimize the total cost and energy consumption within a PSCLSC by searching the optimal value of the cycle time. Mathematically, the objective of the proposed study is defined in the following expression; Minimize TC T 

5. Solution methodology The classical optimization technique was used to optimize the objective function. This technique is very useful in obtaining the optimal solution to problems involving continuous and differentiable functions. This is an analytical technique that is used to obtain maximum and minimum points for unconstrained and constrained continuous objective functions. The model presented in this study is an unconstrained, 25

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continuous, nonlinear model, which is differentiable with respect to the given decision variable. Therefore, the classical optimization technique is employed to obtain the optimal solution. The total cost function is differentiated with respect to the cycle time T in the following expression;

TP 0 T  P  PPk PSc  CE H  Pr   k2   k1  h k  1 e1T 1  e1T  1 d R1  M 1  1   2k11T  2k e1T h  C a  C a  C b  C b    C b  C b  h R1 P1 MT 1 P1 MT 1 1 1 P1 MT 1 R1  1

 

 

 

 













   

  k1  1 e1T  1 Td R1    d R 1T a CSET 1  hM 1  CPa1  CMT d T  e   T  1   1  R 1 2k11 1 1      2  T    d R1 1T d R 1T b b   AR1  hR1  2 e  1T  1  CP1  CMT 1 1    d RT   e  1T  1  1   1  2   k  1  h  k  1 e2T Td R 2  T Cc  d R1  Crem  d R1   k1d R1   d R1  2   d R1T  1   M 2 2  2k2 k1    k1     2T 2   k2  1 e  1 d R 2   k2  1   1 T    hc 2  k2 d R 2   d R1  2   d R1T      hM 2 T 2k2 2 k2  k2         dR2 dR2    2T  2T   hR 2  2  2 e   2  CP 2 d R 2    2 e   2T   2   2   2  2   d R1T 2  k1  1    AR 2  CSET 2  CSETc  Cc  d R1T  hc1  k1d R1   d R1  T     2  k1    2k12     2    k2  1 e2T  1 Td R 2  1 T 2  d R1T 2  k2  1    2   hc 2  k2 d R 2   d R1  2   h 0    M2  2  k2   2k2 2 T  2k2         d R 2 2T d R 2 2T e   2T  1   Crem  d R1T  hR 2 2 e   2T  1  CP 2 d R 2T   2 2      









 





























(63)





As Equation (62) is not explicit in terms of the value of T , the optimal point can not be located in a closed

 

form. Therefore, an iterative method is used to locate the optimal point T * , which gives the minimum





value of the total cost TC * . The value of T that satisfies the above equation is estimated, which is the optimal value for the cycle time. Putting this value of T in the cost function provides the minimum cost. 26

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In order to estimate the value of T that gives minimum cost, NMinimize function of the Mathematica 9 was employed, which used global optimization algorithm. The NMinimize always attempts to find global minimum value of the objective function (i.e., TC ) with respect to the given variable (i.e., T ).

6. Numerical experiments Practical insights of the provided model are demonstrated through numerical experiments. The optimal length of the planning horizon is obtained, which minimizes the total cost. By using the optimal value of the cycle time, the minimum amount of energy consumption and the cost of energy consumption are computed. Moreover, the complete elimination of primary product waste is demonstrated through numerical analysis. For the optimal solution of PSCLSC, optimal values of retailers’ purchase quantities and optimal production time of manufacturers are obtained. For the calculations and graphical illustrations of the obtained results, Mathematica 9 was used. 6.1. Input parameters The values of relevant input parameters are taken in suitable units, which are provided in Table 1. Some of the cost parameters related to setup and inventory holding costs are taken from Alamri (2011) because they presented a closed-loop supply chain model for deteriorating products that is closely related to this study. The parameters related to cost of material and production cost within the primary supply chain are based on dry food items. The parameters related to the secondary supply chain are based on the production and delivery of bio-fuel and fertilizer. Table 1 Values of input parameters

AR1  $300/cycle

hR1  $0.8/unit/month

CPa1  $4/unit

k1  4

AR 2  $100/cycle

hR 2  $0.6/unit/month

CPb1  $0.2/unit

k2  3.5

CSET 1  $2400/cycle

hM 1  $0.5/unit/month

Crem  $0.1/unit

  0.33

CSET 2  $1600/cycle

hM 2  $0.4/unit/month

CP 2  $2/unit

 2

CSETc  $1200/cycle

a CMT 1  $10/unit

L1  1.5 months

PPr  2 KW

hc1  $0.1/unit/month

b CMT 1  $0.5/unit

L2  12 months

PPk  1 KW

hc 2  $0.2/unit/month

d R1  2000 units/month

1  0.1

PSc  1.5 KW

Cc  $1/unit

d R 2  650 units/month

1  0.0001

CE  $0.5 / KWH

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The time unit is considered to be 1 month. Therefore, H  720 . 6.2. Results and discussion The obtained experimental results are discussed in this section. Several analyses of the solutions and their practical implications are provided to explain the practical insights of the suggested model. By using the provided solution methodology, the optimal length of the planning horizon T is calculated. The obtained optimal value for the cycle time is used to evaluate the minimum value for the cost of PSCLSC. Moreover, optimal energy consumption, cost of energy consumption, optimal production time, and optimal purchase quantities are calculated. The obtained results are exhibited below. Important results Optimal value of cycle time T   1.46 months Minimum value of total cost TC   $38,598/cycle Minimum value of energy consumption per cycle  1, 235.65 kWh/cycle Minimum value of cost of energy consumption  $617.82 / cycle Optimal production time of primary manufacturer  t1   0.364 months  262 hours/cycle Optimal production time of secondary manufacturer  t2   0.416 months  300 hours/cycle Optimal purchasing quantity of primary retailer  2,912 units/cycle Optimal purchasing quantity of secondary retailer  947 units/cycle Discussion Excessive product purchasing by a retailer is due in large part to product deterioration. In order to avoid shortages at the retailer, the ordered amount of the product is more than the demand per cycle such that the purchased quantity fulfills customer demand while compensating for the effects of deterioration. The longer a food product is stored as inventory, the greater the likelihood that product will deteriorate, which would make the system less profitable. The decision about the length of the cycle time is made by considering the rate of deterioration as well as the total cost, such that both these remain minimized. Very long intervals of inventory may save some cost but it causes more deterioration. Conversely, short intervals of inventory may reduce deterioration but increase the total cost. Therefore, the planning horizon/inventory cycle is optimized to reduce product deterioration and total cost. The production time of the secondary manufacturer is greater than that of the primary manufacturer because the production rate is slower at the secondary 28

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manufacturer. This slower production rate is due to the time necessary for anaerobic digestion of waste food to occur. The cost of energy consumption can be further reduced by increasing energy efficiency of the production machines. Graphical illustration of the results The convexity of the obtained solution is proved through the graphical illustration, where the optimal value of cycle time T gives the minimum value of total cost. The total cost is higher for any point of time other than its optimal value T * . Figure (3) illustrates how variation in the cycle time affects the total cost. The optimal length of cycle time T * gives the minimum value of the cost. The total cost increases for any cycle time above or below the optimal cycle time. As the product is deteriorating in nature, the rate of deterioration increases with increases in cycle time. Hence, cost increases due to loss of product by deterioration over time. Conversely, the cost per unit time increases with reduction of cycle time below its optimal value due to smaller sales volume.

Total cost per unit time

Optimal Point (1.46 months) with Minimum Cost

Cycle time Fig. 3. Variation in total cost with respect to cycle time

Waste elimination The objectives of GSCM are obtained by consuming all of the waste of a primary product within secondary and reverse supply chains. The proposed system of PSCLSC is feasible when it cleans the environment by consuming maximum amount of the generated waste. For the suggested model, the amount of waste created

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and the amount of waste consumed are estimated to calculate the waste removal efficiency WR , as is exhibited in the following expression; Efficiency of waste removal WR  

waste consumed x100 waste created

The system of waste collection is assumed to be perfect at the collection center (i.e., the amount of waste created is all collected). Thus, Amount of waste created = amount of waste collected  N c    d R1T This amount of waste includes the main product waste as well as the packaging waste. Both types of waste are consumed during production of the secondary product and recycling of the primary product packaging, respectively. As already discussed, all the waste created from the packaging material is consumed through recycling. However, the consumed quantity of the primary product waste per cycle is estimated based on the production quantity of the secondary manufacturer. Thus, Amount of waste consumed = production quantity of secondary manufacturer  N P 2   DR 2  N D 2 By using the above values, efficiency of waste removal of the primary product is exhibited below; Efficiency of waste removal WR  

DR 2  N D 2 x100  d R1T

For the numerical experiment, by using input parameters and the optimal value of the cycle time, the waste removal efficiency is calculated. As explained in the mathematical model, the value of DR 2 and that of

N D 2 are calculated by using the following expressions; DR 2  d R 2T  650x1.46  946.5 units ND2 

dR2

2

e

 2T



  2T  1  0.005 units

The value of N D 2 (number of deteriorated units of the secondary product per cycle) is negligible because its rate of deterioration  2  0.0000077  is negligible. The value of the waste created per cycle is calculated from the following equation;

 d R1T  0.33x2000x1.46  961 units 30

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By using the calculated values for “waste created” and “waste consumed,” efficiency of waste removal is calculated in the following equation; Efficiency of waste removal WR  

946.5 x100  98.4% 961

The obtained results show that the efficiency of waste removal of the PSCLSC is very close to 100%, which means the waste is completely eliminated from the system. Thus, the proposed system of PSCLSC is an efficient system to provide a “zero waste” strategy within supply chain management to avoid environmental pollution and attain the objectives of GSCM. The efficiency of waste elimination depends on the efficiency of waste collection. Our model assumes that all of the waste is collected at the collection center. However, in reality, the systems are not perfect and a fraction of waste often remains unattended. Nevertheless, this fraction can be minimized by employing incentive methods to encourage consumers to return their waste products. We suggest the following research articles on effective return policies: Giri and Sharma (2016), Zhao et al. (2017), Shaharudin et al. (2017), Cui et al. (2017), and Modak et al. (2018). Sensitivity analysis Variations in certain cost parameters differently affect the optimal values of the decision variable and the objective function. A sensitivity analysis is presented to demonstrate the effect on the optimal values for cycle time and total cost when specific cost parameters are varied. The results of varying the percentages (– 50%, – 25%, + 25%, + 50%) of key cost parameters are provided in Table 2. Figure (4) illustrates the obtained results of the sensitivity analysis regarding optimal value of the total cost. The results of the sensitivity analysis are discussed next. The total cost decreases with a decrease in individual cost parameters. However, the extent of this decrease is different for different cost parameters. The optimal value of total cost is most sensitive to material and production costs of the primary product. The production cost of the secondary product affects the total cost to some extent. Thus, the cost of material and the cost of production are the most important cost parameters, and the total cost can be reduced significantly by reducing these costs. However, there is a tradeoff between material cost and production cost. A decrease in the value of one cost may increase the other. Therefore, the cost of material should not be decreased by compromising its quality but it can be decreased by negotiating with suppliers and reducing the cost of transportation. Similarly, the cost of production should be improved by reducing work-in-process inventory, implementing prompt feedback loops to spot and

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correcting mistakes, and creating an agile facility that can quickly switch to creating new products on short notice (Bragg, 2010). Table 2 Sensitivity analysis Percentage variation in parameters

hR1

hR 2

CPa1

a CMT 1

CP 2

Crem

Cc

CE

– 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50% – 50% – 25% + 25% + 50%

Percentage variation in the value of cycle time and total cost T* + 7.80 + 3.55 – 3.55 – 6.38 + 2.84 + 1.42 – 1.42 – 2.84 + 1.42 + 0.00 – 0.71 – 1.42 + 3.55 + 1.42 – 2.13 – 4.26 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 + 3.55 + 1.42 – 2.13 – 3.55

TC * – 1.50 – 0.74 + 0.71 + 1.40 – 0.54 – 0.27 + 0.26 + 0.52 – 10.37 – 5.18 + 5.18 + 10.36 – 25.92 – 12.96 + 12.95 + 25.90 – 2.52 – 1.26 + 1.26 + 2.52 – 0.13 – 0.06 + 0.06 + 0.13 – 1.26 – 0.63 + 0.63 + 1.26 – 0.77 – 0.38 + 0.37 + 0.74

The optimal value for cycle time decreases with an increase in several cost parameters. Specifically, by decreasing the inventory holding cost of the primary product, the optimal value of cycle time can be increased significantly, which can reduce the fixed expenses per unit time. Among other cost parameters, 32

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cost of energy consumption, material and production costs of the primary product, and inventory holding cost at the secondary retailer affect the cycle time to some extent. An increase in cost of energy consumption reduces the optimal value of the cycle time. Hence, the production period for both manufacturers decreases. In the context of energy consumption per unit time, it is more economical to have long manufacturing cycles.

Percentage variation in total cost per unit time 𝑇𝐶

The variation in production cost and collection cost has no effect on the optimal value of the cycle time.

Percentage variation in the value of cost parameters Fig. 4. Variation in total cost by varying several cost parameters

7. Managerial insights Insight 1 – Reduction of food waste and pollution Increasing concerns regarding food waste and environmental pollution have led to legislation that engages industries to deal with the waste of their products. Today, food supply chain managers are responsible for reducing and removing food waste. In addition to food waste, the packaging material for food products also creates pollution. These materials need to be collected and recycled in order to comply with legislative requirements. The proposed study provides a comprehensive model to completely remove food and packaging waste from the supply chain system. By using this model, food supply chain managers can decide the optimum length of cycle time, the production time, and the lot size that will reduce their food waste as well as help them recycle the packaging material for reuse. The proposed study is a step forward in addressing “unavoidable food waste,” as informed by Papargyropoulou et al. (2014), and protecting quality 33

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of life for future generations. As suggested by Lee (2012) for by-product synergy (BPS), our model combines BPS with recycling of packaging material, thus giving a threefold benefit: (a) converting waste product into a new product, (b) recycling of packaging material, and (c) removing waste. Different regions of the world can be categorized for application of this model, based on the amount of food waste being produced in those regions. As mentioned in the introduction section, 33% of produced food is currently being wasted in the world, which is a large quantity. The suggested model is most applicable for regions or countries where the amount of food waste is high and may not be economically viable in areas where the amount of food waste is very low. Insight 2 – Minimization of energy consumption The growing need for energy by modern industries is drastically affecting the world’s natural resources. There is a dire need to reduce energy consumption and to develop more sustainable energy systems, so that there remains enough energy resources for future generations. While all types of industry consume energy, production houses consume a lot of energy, which needs to be minimized by optimizing their production processes with respect to energy consumption. Production managers are responsible for finding optimal solution that minimize total energy consumption. The model provided in this study minimizes energy consumption at production facilities by optimizing the production cycle time. By using this model, production managers are able to find an optimal value for the production time of their machines, at which the energy consumption would be minimum. This will improve the manufacturer’s overall energy consumption and help in maintaining a sustainable energy system. The proposed energy model is a simplified version of the model presented by Jeon et al. (2015) but extends the energy consumption model by considering several types of machines such as production and recycling machines. Insight 3 – Cost reduction The purpose of any business is to earn profit by selling their products or services. Several types of costs are involved in preparing a product or providing a service. The managers responsible for maintaining the supply chains and production houses strive to reduce these costs so that the total cost to the manufacturer is minimized and profit is maximized. This study presents a comprehensive food supply chain model and provides an optimal solution for managers to minimize total cost.

Insight 4 – Inventory planning 34

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The model proposed in this study deals with food products with a short lifetime and deteriorating over time. For such products, longer inventory cycle causes more product to deteriorate, which makes the system less profitable. Therefore, in such a system, managers should decide the length of the planning horizon by considering deterioration as well as total cost, so as to minimize both. Long inventory cycle may save some operational cost but causes more deterioration. Conversely, short inventory cycle reduces deterioration but increases total cost. This study provides an optimal solution, through a mathematical model, to estimate the length of the planning horizon so that minimal deterioration occurs and total cost is minimized in a food supply chain.

8. Conclusions This paper presented a supply chain model to meet the dual objectives of “zero waste” and “minimum energy consumption” to protect the environment and conserve energy resources. The model has been constructed by joining primary, secondary, and reverse supply chains at a collection center. The central idea of “zero waste” was based on the consumption of waste within secondary and reverse supply chains. The waste of the primary product was consumed as raw material within the secondary and reverse supply chains, which not only reduced pollution but also saved on the cost of material within these supply chains. Consumption of energy has been minimized with total cost. The explained theory has been exhibited in the form of a nonlinear mathematical model of total cost, which has been solved through the classical optimization technique. The optimal length of the planning horizon has been obtained by solving the model, which minimized total cost and energy consumption. Several results of the numerical experiments verified the practical implications of the proposed model. The optimal values for total cost, energy consumption, cost of energy consumption, optimal production time for manufacturers, and optimal purchasing quantities for retailers were calculated by using the obtained optimal solution. The results of the experiments demonstrated that all of the waste from the primary supply chain was consumed by the secondary and reverse supply chains, with 98.4% percent efficiency of waste removal. The proposed model is limited to applications that meet the assumptions of the model. It is applicable for deteriorating products, more specifically, food products. Shortages are not allowed in the model, which is a limitation of the model and an avenue to extend the proposed idea. This model can also be improved by considering energy consumption during transportation. This study considered a lifetime-dependent rate of deterioration, whereas the rate of deterioration also depends on temperature and storage time. Effects of these parameters can be explored within the proposed model. This model can also be extended by considering deterioration of products while at the manufacturer. Another extension can be made by considering preservation conditions for deteriorating products. 35

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Acknowledgements This work was supported by the Hongik University new faculty research support fund.

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Highlights 

Zero waste policy is provided by introducing a secondary supply chain for food products.



Closed-loop supply chain is adopted for recycling of packaging waste.



Results obtain minimization cost and energy consumption as well as complete removal of the waste from system.



Nonlinear mathematical model is provided as the objective of the study which is solved through analytical optimization method.