Closed-loop supply chain system with energy, transportation and waste disposal costs

Abstract

Energy usage and consumption play important and strategic roles in modern manufacturing, inventory and logistics systems. The literature on inventory models for closed-loop supply chains reveals that, for no clear reasons, energy costs were ignored along with transportation and disposal costs. This paper introduces a closed-loop supply chain model that considers the economic value and energy content of products. It also offers a novel framework for studying lot-sizing policies of production processes in that context. Thus, a mathematical model for a closed-loop supply chain system with energy, transportation and disposal costs is developed. Numerical examples are provided with their results discussed. The developed model was also compared to that of Richter (1996) to stress the importance of accounting for the three noted costs. The numerical results emphasise that accounting for energy, transportation and disposal costs in supply chain modelling increases the sustainability of a production-inventory system due to the strong interdependence of the three costs on one hand, and their relationship to the environment on the other hand.

Keywords::

• closed-loop supply chain
• energy and inventory
• sustainability
• EOQ model with repair

Introduction

Managing inventory in reverse chains (backward flow) has been stressed in several studies (e.g. Fleischmann et al. 1997). Although the production/repair economic order quantity (EOQ) model first appeared in the 1960s, it was not until the 1990s with the work of Richter (1996) that it has been solved analytically. Richter developed an EOQ model where demand is fulfilled from a serviceable stock (that contains produced and recovered items). Used items, or items that reached their end or economic lives, are collected for recovery from the market at a constant rate. Recovered (e.g. repaired, remanufactured) items are considered as-good-as-new. The model of Richter has been investigated for different assumptions, some of these works are those of Dobos and Richter (2003, 2004, 2006), Teunter (2004), Konstantaras and Papachristos (2006), El Saadany and Jaber (2008, 2011), Jaber and Rosen (2008), Jaber and El Saadany (2009), Hasanov, Jaber, and Zolfaghari (2012) and El Saadany, Jaber, and Bonney (In press).

It should be noted that in the last decade there has been a significant growth in research and applications of product recovery and recycling, in particular with the view of the extended manufacturers' responsibility, which includes the recovery and safe disposal of their products. A comprehensive study on barriers, drivers and challenges for sustainable product recovery and recycling has been presented by Rahimifard et al. (2009). Winkler (2011) proposed the sustainable supply chain networks (SSCN) concept for the design of closed-loop systems and their implementation. The SSCN concept promises improvements in economic and environmental performance of a system's processes. Mitra (2012) investigated an inventory management situation for a closed-loop supply chain with correlated demands and returns of used items, where deterministic and stochastic models were developed under generalised cost structures. Paksoy, Bektaşb, and Özceylana (2011) developed a linear programming problem to investigate cases where the costs of transportation operations outweigh the emissions costs they generate in supply chains. Lambert, Riopel, and Abdul-Kader (2011) divided reverse logistics into seven important elements, which are ‘coordinating system, gatekeeping, collection, sorting, treatment, information system and disposal system’. They investigated each of these elements in terms of process mapping, decisions, economics aspects and performance measures.

Zanoni, Ferretti, and Tang (2006) developed a simulation model to study the effects of different control policies of a logistics system with manufacturing and remanufacturing processes on the bullwhip of demand. They recommended adopting some inventory policies that may help reduce the bullwhip effect, which was found to be dependent on the lead time and the return (collection) rate of used items. Recently, Alinovi, Bottani, and Montanari (2012) focused on mixed production/remanufacturing systems and proposed an EOQ model to analyse the effectiveness of a return policy of used items for a reverse logistics chain. The production/recovery models in the literature, including those surveyed above, did not consider energy, transportation and waste disposal costs (in particular, collectively), although it is well recognised that these costs hold and are important components of the total cost (TC) structure of a supply chain.

Energy is fundamental for developing economies and improving the living standards of societies. Energy sources are either renewable (RW) or non-renewable (NRW). Using a NRW energy source depletes natural resources (e.g. fossil fuel), making them scarce and expensive. Thus, the use of RW (e.g. wind) energy sources is increasing as they are environmentally friendly and their technologies are becoming more economical. When evaluating different technologies, the cost of generating electricity must also consider the external (social) costs to human health and the environment (Sahin 2004). The results from Sahin (2004) showed that generating electricity from wind energy was the least costly and the friendliest to the environment than the other energy options considered. El-Kordy et al. (2002) proposed a life cycle cost (LCC) approach to evaluate the economics of using RW and NRW energy sources to generate electricity. They suggested considering the external cost of a system's emissions in their analysis. Their results were in line with those of Sahin (2004). Further, in a study on the use of wind energy in Vietnam, Khan (2006) showed that it has ecological, social and economic benefits.

Transportation costs are incurred when delivering products to the market (customers) and when collecting used items from the market for recovery. Transportation includes modes used and distances travelled in the delivery of produced/recovered items, and the collection of used items. Ignoring these costs may result in biased inventory decisions.

Moreover, it should be considered that using transportation modes based on conventional energy is a concern, as this energy is costly and damaging to the environment. Hybrid vehicles are starting to emerge; however, the technology is not yet available to support long-haul trips.

In addition, not all the items collected from the market are repairable. Some will eventually be disposed. Disposal options remain to be limited; e.g. incineration or landfill (Dijkgraaf and Vollebergh 2004). Both options are financially and environmentally costly (e.g. Carlee 1986; Baetz and Neebe 1994; Staikos and Rahimifard 2007).

The importance of accounting for energy, transportation and waste disposal costs has been strongly emphasised in the study of Bonney and Jaber (2011) as fundamental in designing environmentally responsible inventory and logistics systems. On the first two, they wrote

Unless an economically feasible substitute energy source to fossil fuel becomes widely available, it is likely that increasing demand could lead to increasing fuel prices that could raise transportation costs so much that globalisation will face an apparent economic and social brick wall

while on the third, they wrote:

…packaging is important, not only because of its costs and the protection that it provides to the inventory items, but also because of its eventual effects on the environment in terms of the use of resources and potential landfill.

This is perhaps why these factors have compelled practitioners to look for solutions that reduce the energy, transportation and waste disposal costs of their supply chains, thus helping their firms to improve their competitiveness and sustainability. Such solutions impact firms' inventory and management policies.

The closed-loop supply chain system investigated in this paper assumes a single product that consists of two chains: forward and reverse (backward). In the forward supply chain, raw materials are produced into items, while in the reverse supply chain, used items are collected and remanufactured into ‘as-good-as new’ items.

It should be emphasised that no one has previously investigated an inventory model for a closed-loop supply chain system jointly considering energy, transportation and waste disposal costs. Thus, the contribution to the literature of the model proposed is significant, given the importance of these costs in contemporary production environments and their increasing influence on production decisions, due to stricter environmental regulations and the companies' awareness on the matter.

This paper describes a system similar to that of Richter (1996), which was further developed by Teunter (2004), except that it accounts for the three costs stressed above. The mathematical model developed in the paper minimises the sum of the classical inventory, energy, transportation and waste disposal costs of a simple closed-loop supply chain system. The remainder of this paper is organised as follows. Section 2 presents the assumptions and notations. Section 3 is for mathematical modelling where the cost of using a mixed strategy of RW and NRW energy sources is considered with transportation and waste disposal costs. Section 4 provides some numerical examples and discussion of results. Section 5 summaries the paper and highlights its main findings along with few future research directions.

Assumptions and notations

The assumptions and notations adopted in this paper are mainly the same as those of Richter (1996), except for the parameters associated with energy, transportation and waste disposal.

The assumptions of this paper are as follows:

• A single product case where items produced and recovered conform to quality characteristics.

• Instantaneous production and recovery (remanufacturing) rates.

• Demand is known and constant over time.

• Constant collection rate of used items.

• Lead time is zero.

• Unlimited storage capacity is available for serviceable and repairable items.

• Transportation truck capacity is unlimited.

• Infinite planning horizon.

The notations used in this paper are classified into input parameters and decision variables and they are:

Input parameters

d	=	demand rate
Sr	=	set-up cost for a remanufacturing cycle
Sp	=	set-up cost for a production cycle
h	=	holding cost for serviceable stock ($/unit/unit of time)
hu	=	holding cost for repairable stock ($/unit/unit of time)
pw	=	a subscript representing the present worth of a cost factor
C	=	capital cost (initial capital expense for equipment, system design, system engineering and installation)
M	=	operation and maintenance costs (salaries, inspection, insurance, etc.)
F	=	fuel cost
X	=	external costs including damage prevention or damage cost
S	=	salvage value of the system
WC	=	landfill cost
l	=	cost of landfilling per ton of material
bm	=	cost to transport one unit (item) of production for one distance unit ($/unit/km)
br	=	cost to transport one unit (item) of remanufacturing for one distance unit ($/unit/km)
dtm	=	distance travelled for a produced item (km)
dtr	=	distance travelled for a remanufactured item (km)
α	=	percentage of demand that is disposed, with αD is the waste disposal rate, where 0 < α < 1
θ	=	percentage of RW energy sources used, ((1–θ) percentage of conventional energy) from the available ones

Decision variables

m	=	number of remanufacturing cycles in T
n	=	number of production cycles in T
x	=	lot size, also referred to as x (m, n)
T	=	length of the time interval (x/d), an ancillary variable

Mathematical model

Richter's EOQ repair and waste disposal system is depicted in Figure 1, where two stocks are considered: serviceable and repairable. The serviceable stock is for storing new and recovered (repaired) items, while the repairable stock is for storing collected used items. Richter assumed that there are m remanufacturing and n production cycles in interval T, which is duplicated indefinitely.

Figure 1 Material flow for the production and a remanufacture system considered.

As already noted, Richter (1996) ignored the costs of energy, transportation and waste disposal. Energy cost parameters used in developing the model of this paper are adopted from El-Kordy et al. (2002), who considered social costs (human health, pollution, etc.) when using the LCC approach to analyse different energy generation systems, which are not reflected in the price of electricity. The social costs vary by the type and amount of pollutants emitted by the energy technology used to generate electricity.

The LCC is determined from El-Kordy et al. (2002) as:

The needed amount of electricity is generated by using different energy sources (RW and NRW).

Moreover, Staikos and Rahimifard (2007) identified landfilling cost (WC) as a function of the weight of the material and actual cost of landfilling per tonne of material, which we refer to as the waste disposal cost; i.e.

Finally, the parameters relating to transportation costs were taken from Toptal, Çetinkaya, and Lee (2003) and Bonney and Jaber (2011), which are (for the demand filled from the stock of produced items) and (for the demand filled from the stock of remanufactured items).

The TC per replenishment cycle is the sum of set-up costs for the remanufacturing and production batches (mS_r+nS_p), NRW and RW energy life cycle costs (LCC^NRW and LCC^RW) for remanufacturing and production processes, waste disposal costs from landfill activities and the cost of transporting items of a product to and from the market, respectively. The total transportation cost of items between each pair of adjacent locations in the supply chain for remanufacturing and production is , the cost of waste disposal is , the holding cost for items in the serviceable stock is

and the holding cost of items in the repairable stock is

Thus, the TC function per interval T can be written as:

where K is the number of RW energy sources available, and J is the number of NRW resources available with J+K = 6, where 6 is the total number of energy sources considered, consistently with El-Kordy et al. (2002), where

Therefore, the average cost per unit of time can be written from Equation (1) as:

where T = x/d = x(m, n)/d.

Let us now introduce the following functions:

and

Then, Equation (2) can be represented as follows:

The cost function of Equation (3) is clearly convex and differentiable in x. The optimal lot size, x^*, that minimises Equation (3) is determined by setting the first derivative of Equation (3) equal to zero and solving for x to get:

Substituting Equation (4) in Equation (3) reduces the latter to:

So, to find the optimal values of production and remanufacturing batches (i.e. m^* and n^*), Equation (5) is minimised subjected to m and n ∈ {1, 2,…}, i.e. the minimal cost is found by solving a two-dimensional non-linear integer programing problem.

Equation (4) and Equation (5) are different from those of Richter whose optimal lot size and TC expressions are:

respectively, which ignore the costs of energy, transportation and waste disposal. To have a reasonable comparison between the model presented in Equations (4) and (5) and that of Richter, it is necessary to adjust for the three noted costs so it becomes

For the given values of n and m, and subsequently , Equation (6) would produce larger values than those produced by Equation (5). To explain this, it can be simply shown that:

The above condition is always satisfied, thus suggesting that adopting Richter's optimal values (x^*, n^*, m^*) results in having larger total system cost than that obtained by the model developed in this paper, which is given by Equations (4) and (5).

Numerical analysis

In this section, a numerical analysis is presented so as to show the applicability of the model developed in the previous section. The basic parameters for the model were adopted from Richter (1996), while the parameters for LCCs of RW and NRW energy, transportation costs between adjacent locations (A) and landfill (waste disposal) costs were collected from other studies (Baetz and Neebe 1994; El-Kordy et al. 2002; Toptal, Çetinkaya, and Lee 2003; Bonney and Jaber 2011).

In the following numerical example we adopt the same values for the input parameters as those of Richter (1996), which are S_p = 20, S_r = 100, d = 10, h_u = 4, h = 6, α = 0.5. New parameters, i.e. for RW energy and NRW energy costs, are taken from the study of El-Kordy et al. (2002) where LCC^RW = 1.8085 (for wind energy) and LCC^NRW = 5.4256 (for conventional steam fuel oil fired energy). Moreover, parameters related to transportation and landfilling have been arbitrarily set to b_m = b_r = 1, dt_m = dt_r = 80, l = 0.5. According to the equations reported in the previous section, the optimal values of n and m and the corresponding lot size x*, or x (m^*, n^*), with a given θ = 0.5 are shown in Table 1.

Table 1 The optimal production and remanufacturing policy for the proposed model (θ = 0.5).

N	m	α	θ	X^*	TC^*
2	1	0.5	0.5	80.27	341.148

Moreover, we have tried to analyse the effects of different values of the percentage of waste disposal on the optimal batch size and the total system cost. The results are shown in Figure 2.

Figure 2 Optimal lot size and TC for different values of the waste disposal rate.

Figure 2 shows that increasing the percentage of waste disposal decreases the optimal lot size (x^*) and increases the TC of the system. This suggests that it is advantageous to a closed-loop supply chain, like the one considered here, to recover as many used units as possible in order for it to be economically, socially and environmentally sustainable.

The results from solving Richter's (1996) model are summarised in Table 2, where TC_R = 109.087 represents the TC with no energy and transportation costs and x_r = 25.668 is the optimal lot size. Table 2 also shows that the corresponding value of TC = 587.97 (from Equation (1)) when energy, transportation and waste disposal costs are considered (using the optimal values of m and n as determined by Richter's study) is higher than its corresponding value in Table 1. That is, using the approach proposed in this paper, the optimal policy suggests a lot size of x*(2, 1) = 80.27 (from Equation (4)) with a corresponding total cost of TC = 341.148 (from Equation (5)), which is 41.97% less than what we obtained from using Richter's model; i.e. . The structures of the two TCs are shown in Figure 3. The results clearly show that energy, transportation and waste costs hold an important part of the TC structure, suggesting that they should be properly taken into account when optimising closed-loop supply chain systems.

Table 2 Richter's (1996) optimal production and remanufacturing policy with energy, transportation and disposal costs considered (θ = 0.5).

n	m	α	xR	TCR
1	2	0.5	25.668	109.087	587.97

Figure 3 The structures of the TCs for the modes of Richter (1996) and the proposed one comparing for θ = 0.5.

It should also be noted that in the above numerical example, we have assumed θ = 0.5. This value has been set arbitrarily (i.e. assuming a situation of equally distributed usage of RW and NRW sources for energy generation). It can be clearly observed from Equation (1) that when the percentage of using RW energy sources decreases (θ approaches 0), the total system cost increases (given the fact that in the literature it is usually assumed that LCC^RW < LCC^NRW; see El-Kordy et al. 2002). This suggests that it is more economical to use RW energy sources. Besides being economically sustainable, our results also show that shifting towards using RW energy sources improves the environmental and social sustainability of the system as less pollutant and waste are generated.

Summary, conclusions and extensions

The high consumption of energy resources (mainly NRW) and raw materials by manufacturing firms is depleting the earth's natural resources at alarming rates. Transportation modes that operate on NRW energy sources and less material reuse and/or recycling result in polluting the air with greenhouse gases emissions and the soil and water tables from waste disposal activities. Given these facts, along with stringent governmental regulations on protecting the environment, it is therefore necessary that production, inventory and logistics system be environmentally responsible and sustainable.

To have a sustainable logistics system, some non-classical costs must be considered. In addition to the classical inventory costs that are commonly used in analysing closed-loop supply chain systems, which are the set-up, ordering and holding costs, this paper considers three non-classical costs that have not been jointly considered before in a study, namely, energy, transportation and waste disposal. To do so, we revisited and modified the model of Richter (1996) by accounting for these costs. The modified mathematical model was analytically and numerically compared with that of Richter (1996). The results showed that accounting for these three costs significantly impacts the production, remanufacturing and inventory policies. The results also showed that using a RW or a mixed energy source has economic and social benefits than using a NRW energy source alone.

This study was conducted to provide some insights needed to steer research directions in the field, to emphasise accounting for the effects of energy, transportation and waste disposal activities in future studies, and to be equally concerned that the models developed suggest environmentally friendly solutions. Further development to the work presented herein can be enhanced by assuming the following:

• finite production and remanufacturing rates,

• production and remanufacturing rates that are dependent on transportation costs,

• learning in production and remanufacturing, and in energy generation from RW energy sources and

• production/remanufacturing rate that are dependent energy costs.

Acknowledgements

The first author thanks the Social Sciences and Humanities Research Council of Canada (SSHRC) – Environmental issues –for supporting this research. He also thanks the Università degli Studi di Brescia for extending and partially financing his research visits to Brescia. P Hasanov thanks Ryerson University for the in-kind support they provided during his visit to the department of Mechanical and Industrial Engineering. The authors sincerely thank the reviewers for their constructive and valuable comments and suggestions that helped improve the paper.