Manufacturing network configuration in supply chains with product recovery

Omega 37 (2009) 757 -- 769

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Manufacturing network configuration in supply chains with product recovery夡 David Francasa,∗ , Stefan Minnerb a b

Department of Logistics, University of Mannheim, Germany Faculty of Business, Economics and Statistics, University of Vienna, Austria

A R T I C L E

I N F O

Article history: Received 1 April 2007 Accepted 2 July 2008 Available online 20 August 2008 Keywords: Product recovery network configuration Manufacturing and remanufacturing capacity Manufacturing flexibility Stochastic linear programming

A B S T R A C T

Efficient implementation of product recovery requires appropriate network structures. In this paper, we study the network design problem of a firm that manufactures new products and remanufactures returned products in its facilities. We examine the capacity decisions and expected performance of two alternative manufacturing network configurations when demand and return flows are both uncertain. Concerning the market structure, we further distinguish between the case where newly manufactured and remanufactured products are sold on the same market and the case where recovered products have to be sold on a secondary market. We consider network structures where manufacturing and remanufacturing are both conducted in common plants as well as structures that pool all remanufacturing activities in a separate plant. The underlying decision problems are formulated as two-stage stochastic programs with recourse. Based on numerical studies with normally distributed demands and returns, we show that particularly network size, investment costs of (re-)manufacturing capacity, and market structure have a strong impact on the choice of a network configuration. Concerning the general role of manufacturing configuration in a system with product recovery, our results indicate that the investigated structures can lead to very different expected profits. We also examine the sensitivity of network performance to changes in return volumes, return variability and correlation between return and demand. Based on these results, we find that integrated plants are more beneficial in the common market setting. This relative advantage tends to diminish when demand is segmented, thus investing in more specialized, dedicated resources should be considered. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction Product recovery has received increasing attention over the last decade. Not only a growing environmental concern and enforced legislation in many countries but also economic incentives are driving factors behind this development. The scope of this paper is to investigate capacity planning and network configuration choices in supply chains with product recovery. 夡 ∗

This manuscript was processed by Area Editor: B. Lev. Corresponding author. Tel.: +49 621 181 1651; fax: +49 621 181 1653. E-mail address: [email protected] (D. Francas).

0305-0483/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.omega.2008.07.007

Thierry et al. [1] distinguish five recovery options: repair, refurbishing, remanufacturing, cannibalization, and recycling. In this paper, we focus on remanufacturing which returns the product to good as new condition by replacing components or reprocessing used parts. Since specific product knowledge is required, remanufacturing tends to be performed in-house by manufacturers [2]. Government legislation such as the WEEE and ELV directives of the EU [3] certainly creates important incentives for companies to engage in remanufacturing. However, beside legal obligations such as collection and recovery targets, the business aspects of remanufacturing should not be underestimated. Benefits from cost reduction and value-added

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recovery as well as the growing demand for “green” products also provide strong economic incentives. In the U.S., remanufacturing is a $50 billion per year industry [4]. Successful business models in this industry include remanufacturing of copiers [5], engines, and car parts [6,7]. Supply chains with product recovery differ from typical forward-only systems in several aspects [2]. Generally, recovery systems form a link between the market where used products are returned and the market with demand for recovered products [8]. However, despite the fact that many remanufactured products are perfect substitutes to newly produced items, markets for new and remanufactured products tend to be segmented in particular due to lower customer valuation [9]. Furthermore, remanufacturing supply is constrained by the number of available returns. Since quan tity, quality, and timing of returns are usually difficult to predict, it is the supply side that accounts for additional uncertainty beside demand risks in recovery systems [2]. In order to exploit recovery opportunities successfully, an appropriate network infrastructure has to be in place. When designing such reverse supply chains, an important factor is the interrelation between forward and reverse flows. In many cases, the recovery network has to be established when forward network structures already exist [8]. One approach is then to add facilities to the existing forward network (sequential design). Another approach is to redesign the entire network including simultaneously forward and reverse operations (simultaneous design). Due to its strategic importance, the design of reverse supply chains has received growing attention, but few studies have been undertaken to investigate strategic issues such as capacity planning and the possible benefits of alternative network configurations [2,10]. Even though the logistic infrastructure is an important element of reverse supply chains, we focus on the facilities for (re-)manufacturing and their capabilities. In this research, we develop network configuration models for a multi-product supply chain in which a firm manufactures new products and remanufactures used products. In order to assess risk pooling advantages of network configuration and the value of shared resources such as cross-trained workers or flexible machines, we consider two different generic network structures: an integrated network (IN) where both new production and remanufacturing of each product are carried out at the same facility as well as a decentralized structure, where manufacturing and remanufacturing processes are dedicated to separate facilities but all product recovery operations are pooled in one facility. Built on a stochastic programming approach that accounts for uncertainty in demand and returns, we study capacity investment from a network perspective and compare the performance of the two considered structures. In our analysis, we consider two different market types and investigate the impact of simultaneous and sequential design. Particularly, our results suggest that market structure (a common market for both remanufactured and new products or segmented markets) has a strong impact on the choice of a network configuration. The remainder of the paper is organized as follows. Section 2 presents the related literature. In Section 3 we de-

velop two-stage stochastic optimization models for the two considered network configurations and the two discussed market types. In Section 4 we present numerical studies comparing relative performance of both network configurations. Finally, in Section 5 we conclude with a summary of our findings and an outlook on future research. 2. Literature review Fleischmann et al. [2] distinguish different context variables that describe recovery situations and describe their potential impact on network design. They structure these factors along three dimensions: (i) product characteristics, (ii) supply chain characteristics, and (iii) resource characteristics. Important product characteristics involve economic value and physical attributes of the item to recover. Regarding profitability of the remanufacturing option, it is often assumed that bringing the product to good as new condition is on the average less costly than producing a new one and disposing the return [11]. For this reason, priority is given then to remanufacturing in satisfying demand when new and remanufactured items are perfect substitutes. Although perfect substitution is a dominating assumption in the literature, it holds true only for a relatively small number of industry cases [12]. In many cases, the product variants can be differentiated, resulting in diverse market segments and potential cannibalization effects between the segments [9]. Physical attributes of the products may limit technical feasibility of different recovery options [1], and hence, may also have an impact on the choice of a certain network design. In particular, modular product design and standardization of components (component commonality) are important design requirements for remanufacturing [1,13]. The generic network topology of a reverse supply chain is characterized by the number and locations of factories for remanufacturing and/or new production, warehouses for (re-)distribution, and additional recovery facilities where activities like testing and cleaning are carried out. For a review on network design in a reverse logistics context we refer to [8,14]. Resources in (re-)manufacturing plants involve technical equipment as (re-)assembly lines and human resources [2]. Concerning these resources, capacity and flexibility are strategic issues of prime importance in order to design the system robustly against uncertainties in return and demand volumes. An important option to mitigate uncertainty is to create flexibility by using multi-purpose resources which allow to reallocate capacity across different products and help to increase service levels and capacity utilization [15]. Seminal work on investments in such product- or mixflexible resources is by Fine and Freund [16]. They develop a single-period, two-stage stochastic program for a firm's capacity acquisition decisions of multiple dedicated resources and one flexible resource that is capable of producing all products. At the first stage, the firm chooses the capacity levels under uncertain demand. At the second stage, the firm determines production quantities after demand realization. They show that capacity investments depend on the cost

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

differential between dedicated and flexible technology and that the benefits of flexible technology are substantially decreasing when correlation between demands increases. Van Mieghem [17] develops a similar model where a firm has the option to invest in one flexible and two dedicated resources to manufacture two products and finds that mix flexibility may be even beneficial under perfectly positively correlated demand if one product is more profitable than the other. Beside demand pooling, ex-post revenue maximization through changing the product–mix is hence a further driver for investing in flexible resources. Van Mieghem and Rudi [18] introduce a class of models, called newsvendor networks, for studying such problems. The models developed in this paper may be categorized as newsvendor networks. In hybrid manufacturing/remanufacturing systems, the question arises whether to conduct both manufacturing and remanufacturing processes in a common facility or to dedicate each process to (less costly) separate facilities [11]. Debo et al. [19] identify similar choices for setting up the manufacturing/remanufacturing system when demand for new and remanufactured products is segmented into different markets. They mention that personnel and technology constraints may restrict such a choice but also give an example from a server factory where capacity for remanufacturing servers was changed from dedicated to flexible capacity. Using a case study methodology, Thierry et al. [1] investigate a recovery system in the copier industry where remanufacturing operations are performed at factories that also produce the new products of the same type. In particular, remanufactured and new products use the same assembly lines. They point out that such a system can reduce start-up costs for remanufacturing. To the best of our knowledge, the only research that has investigated the value of flexible capacity explicitly in a product recovery context is [19]. They develop a nonlinear multi-period model to study the joint life-cycle dynamics of new and remanufactured versions of the same product which are segmented into different markets. Using a diffusion model with random residence time (duration of one use of a product), they investigate capacity policies and find that the value of flexible capacity increases in diffusion and purchase rate. Georgiadis et al. [10] examine dynamic capacity planning policies for closed-loop supply chains using system dynamics methodology. Jayaraman et al. [20] present a deterministic single-period model where demand is solely satisfied by remanufactured products. Their model formulation is based on a multi-product capacitated warehouse location model and determines the locations of distribution and remanufacturing facilities. Ko and Evans [21] develop a nonlinear, deterministic network design model for third party logistics providers. The model belongs to the class of multi-period, multi-product, two echelon, capacitated location models and allows for modularized capacity expansions. A deterministic single-period, single-product, uncapacitated recovery network model is developed in [8]. They demonstrate in numerical experiments that moderate changes in the system parameters result in fairly small changes of the recovery network design. Fleischmann et al. [22] extend [8] and consider a deterministic single-period, single-product

759

setting where demand can be either satisfied by remanufacturing of returns or new production. The model is based on a capacitated warehouse location model and determines the locations of warehouses, disassembly centers, and factories for remanufacturing and/or new production. Salema et al. [23] extend [8] in order to account for multi-product environments and uncertainty of demand and return. The underlying decision problem is formulated as a two-stage stochastic program. For a similar model, Listes [24] develops a two-stage stochastic recovery network model and proposes a solution algorithm based on Benders decomposition. Although there are several papers that outline possible benefits of flexible capacity, only [19] consider this issue explicitly in a model. In our paper, we investigate the benefits of flexible (shared) capacity under different network configurations and market conditions. Furthermore, we contribute to the understanding for capacity planning under uncertainty in recovery networks which is only modeled implicitly in [23,24] as constraint once a facility is opened. 3. Models for the network configuration problem 3.1. Assumptions and definitions We consider a firm that builds and recovers i = 1, . . . , n products under uncertainty of demand and return for each product. We model the firm's recovery process on a macroscopic level and assume that a single remanufacturing resource can carry out all necessary operations to bring the product to good as new condition. Contrary to the multi-product models of [23,24], manufacturing and remanufacturing of a product i is restricted by network configuration to specific facilities. We consider two alternative configurations for the firm's recovery network. In the IN, we let, similar to [22–24], recovery and new production share a facility. Each product i and its corresponding return are dedicated to a common facility with shared capacity Kj , resulting in j = 1, . . . , n facilities. In the decentralized network (DN), manufacturing and remanufacturing of each product i are carried out decentrally in separate facilities. Manufacturing of new products is conducted in n dedicated plants with capacity Kjm while all recovery operations

are performed in a separate facility with capacity K r , resulting in j = 1, . . . , n manufacturing facilities and one recovery facility. Therefore, remanufacturing operations form an independent supply chain as studied in [20]. For simplicity, we assume that product i (and its return i in IN) is assigned to plant j = i and let index i refer to both products and plants Ki and Kim , respectively. The decision variables in IN and DN are defined as follows: Ki capacity acquisition at plant i in IN (first-stage) Kim capacity acquisition at plant i in DN (first-stage) K r capacity acquisition at remanufacturing plant in DN (first-stage) xi units of manufactured products i (second-stage) yi units of remanufactured products i (second-stage) si units of unused returns i (second-stage)

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Furthermore, we have the following parameters:

We further consider two different market structures. The corresponding demand parameters Di , Dm , Dri and returns Ri i for each product i are modeled by multi-variate random variables with known probability distributions. In the common market setting, new and remanufactured products are perfect substitutes. Therefore, product demand Di can be satisfied with any mix of manufactured and remanufactured products. In the separate market setting, we consider a segmented market with demand for new products Dm and dei mand for remanufactured products Dri . Between the two markets, we do not consider any substitution effects as discussed in [19]. In IN, the firm purchases capacity at constant marginal costs ci in face of uncertain demand Di and returns Ri in Stage 1; in DN the firm purchases capacity at constant marginal costs cim and cr in face of uncertain demand Dm and i Dri on both markets and returns Ri in Stage 1. We model the four network design problems as single-period, two-stage stochastic programs. The stages are chronologically ordered within the single period. In Stage 2, demand and returns are observed and the firm has to solve a product–mix problem with respect to the contribution margins pm of newly produced units xi , the i margin pri of remanufactured units yi , and the salvage value (or cost) psi of the unused returns si . Although we exclude recovery quotas (as in [23]), negative values of psi may reflect legislation enforcement. The two network structures are shown in Fig. 1 with respect to the different market settings for n = 2 products. The left part of the figure shows the common market setting where market demands Di for product i can be satisfied by both new and remanufactured products while the right part displays the case where remanufactured products are sold on secondary markets with demand Dri and new products are sold on primary markets with demand Dm . Returns i Ri are inputs for the remanufacturing process and hence serve as supply for remanufacturing operations yi . The corresponding reverse flows are denoted by dotted arrows. New production of items xi is associated with the forward flows denoted by solid arrows. In the common market setting, both reverse and forward flows are assigned to the market demand Di while they are exclusively assigned to segmented markets when demand for remanufactured and

ci per unit acquisition costs for capacity i in IN cim per unit acquisition costs for manufacturing capacity i in DN cr per unit acquisition costs for remanufacturing capacity in DN pm contribution margin of a manufactured unit of product i i pri contribution margin of a remanufactured unit of product i psi salvage value of a return of product i ai capacity consumption of a manufactured unit of product i in IN am capacity consumption of a manufactured unit of product i i in DN bi capacity consumption of a remanufactured unit of product i in IN bri capacity consumption of a remanufactured unit of product i in DN Di demand on the common market for product i (realization denoted by di ) demand on the primary market for product i (realization Dm i denoted by dm ) i Dri demand on the secondary market for product i (realization denoted by dri ) Ri returns of product i (realization denoted by ri ) The firm is modeled as a price taker and all costs are linear functions. We assume that once demand and return are realized there is only a single production and recovery decision, which is a standard simplification in the capacity investment literature (e.g., see [16,17]). Since no further dynamics take place once uncertainty has revealed, the multiperiod operational decisions can be aggregated into a single period. By doing so, we exclude dynamic aspects of product recovery as studied by [10,19]. Hence, all parameters in the model can be regarded as average or appropriately discounted values. Unsatisfied demand is assumed to be lost and unused returns have to be salvaged. The corresponding contribution margins pm and pri and salvage values psi are i assumed to be identical for both IN and DN.

R1

R2

Common market setting Plant 1 m x1 Plant 1 K1 x1 D1 K1 Plant 2 y1 m x K2 2 Plant 2 x2 K2 D2 Plant 3 y2 y1 R1 Kr y2 R2

D1 R 1

D2

R2

Separate markets setting Plant 1 m x1 Plant 1 K1 m x1 D 1 K1 Plant 2 r y1 D1 m x2 K2 Plant 2 m x2 D 2 K2 Plant 3 r y2 D2 y1 R1 Kr R2 y2

Fig. 1. (i) The integrated network and (ii) the decentralized network for n = 2.

m

D1

m

D2

r

D1 r D2

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manufactured products does not coincide. Finally, available plant capacities Ki , Kim , K r constrain these flows.

(•)

To denote the expected profits V(•) of the four network models, we use the superscripts IN and DN to refer to the integrated and the decentralized network and the subscripts  and  to refer to the common market and the separate markets case, respectively. Let boldface letters denote vectors of decision variables and parameters. 3.2.1. Network models with a common market Integrated network: The formulation of the two-stage problem can be written as: Stage 1: n  VIN (K ∗ ) = max ED,R () − ci Ki n K∈R+ i=1

(1)

Stage 2:

 = max

n 

x,y,s∈Rn + i=1

(pm x + pri yi + psi si ) i i

s.t. ai xi + bi yi  Ki

Stage 2:

 = max

n 

x,y,s∈Rn + i=1

3.2. Model formulations

∀i = 1, . . . , n

(2)

(3)

xi + yi  di

∀i = 1, . . . , n

(4)

yi + si = ri

∀i = 1, . . . , n

(5)

VIN represents the expected value of the maximization problem and  the second-stage objective function. K ∗ represents the optimal capacity acquisition vector. At the first stage, the optimal capacity acquisitions are determined. This decision is made under uncertainty with respect to the known probability distribution of the random parameters Di and Ri . The objective in (1) is to maximize expected future profits ED,R () minus current investment costs. The second-stage problem (2)–(5) determines the amount of manufactured xi and remanufactured units yi for all products i after uncertainty has revealed. With respect to the realizations di and ri , both manufacturing and remanufacturing operations are conducted in one plant for each product and constrained by the available capacity Ki . In order to account for the fact that both activities may require different amounts of capacity, we also consider capacity consumption coefficients ai and bi in (3). Demand di can be satisfied by both xi and yi in (4). The number of remanufactured units is further constrained by the amount of available returns ri where si denotes the number of unused returns in (5). Decentralized network: In case of the DN, we have the following two-stage problem: Stage 1: n 

cim Kim − cr K r VDN (K ∗ ) = max ED,R () − n+1 K∈R+ i=1

(6)

761

s.t. am x  Kim i i n  i=1

(pm x + pri yi + psi si ) i i

(7)

∀i = 1, . . . , n

(8)

bri yi  K r

(9)

xi + yi  di

∀i = 1, . . . , n

(10)

yi + si = ri

∀i = 1, . . . , n

(11)

The expected value of the maximization problem is denoted by V DN and all other parameters and variables are  similar to those defined for the IN model with a common market, but pertaining to the DN model in this case. In contrast to the integrated structure, all manufacturing activities xi have separate capacity limits Kim in (8) while all remanufacturing operations yi are constrained by the common (shared) capacity K r in (9). Again, we allow for different capacity consumption coefficients am and bri in (8) and (9). i 3.2.2. Network models with separate markets Integrated network: For the case with separate markets the IN can be formulated as n  V IN (K ∗ ) = max ED,R () − ci Ki  K∈Rn + i=1

(12)

Stage 2:

 = max

n    pm x + pri yi + psi si i i

x,y,s∈Rn + i=1

s.t. ai xi + bi yi  Ki xi  dm i yi  dri

∀i = 1, . . . , n

∀i = 1, . . . , n ∀i = 1, . . . , n

yi + si = ri

∀i = 1, . . . , n

(13)

(14) (15) (16) (17)

Compared to the integrated model with a common market, both quantities xi and yi are constrained by the different and dri in (15) and (16). All the other market demands dm i parameters and constraints are similar to the case with a common market. Decentralized network: We have the following two-stage problem: Stage 1: n  V DN (K ∗ ) = max ED,R () − cim Kim − cr K r  n+1 K∈R+ i=1

(18)

Stage 2:

 = max

n    pm x + pri yi + psi si i i

x,y,s∈Rn + i=1

(19)

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s.t. am x  Kim i i n  i=1

∀i = 1, . . . , n

(20)

bri yi  K r

xi  dm i yi  dri

(21)

objective functions in (6) and (18).

∀i = 1, . . . , n

(22)

∀i = 1, . . . , n

yi + si = ri

In case of the DN, remanufacturing operations are conducted in a new plant and hence converting existing capacity is not ∗  required. Consequently, we subtract n cm Kˆm from the

(23)

∀i = 1, . . . , n

(24)

As in the IN model, both quantities xi and yi are constrained by the different market demands in (22) and (23). All the other parameters and constraints are identical to the case with a common market. 3.2.3. Sequential planning For both market types, the above models assume that forward and reverse infrastructure are determined simultaneously. In many cases, however, firms that start to engage in remanufacturing already have existing facilities for their manufacturing operations. As a consequence, these companies have to decide how to set up the remanufacturing operations (and hence the corresponding capacities) and how to integrate them into the existing forward structures. In order to account for such sequential planning, we assume that the firm has already established facilities to manufacture new products. As before, each product i is assigned to a single plant i. Let us denote this initial capacity decisions in the sequential design by Kˆi for IN and by Kˆim for DN. Since initial capacity Kˆ and Kˆm of both network structures is solely used i

i

for manufacturing operations, we assume that acquisition costs are identical and come at cim . We can obtain closed-form expressions for these (initial) capacity decisions (an elaborate discussion of adequate analytical methods can be found in [18]. For IN, the optimal ∗ −1 capacity is given by Kˆi = F(•) ((pm − cim )/pm ) and for DN by i i ∗ −1 −1 Kˆim = F(•) ((pm − cim )/pm ) where F(•) denotes the inverse of i i

, the underlying cumulative density functions of Di and Dm i respectively. Note that both IN and DN coincide since no remanufacturing operations take place when the first capacity decisions are made. For both network structures, we further assume that the firm is not willing to downsize its existing forward facilities. In order to investigate the impact of a sequential planning approach, we have to modify the above models. First, we have to add new constraints to the IN and DN models which ensure that downsizing of existing facilities does not ∗ ∗ take place: K  Kˆ in (1)–(5) and (12)–(17) and K m  Kˆm i

i

i

i

in (6)–(11) and (18)–(24) for i = 1, . . . , n. In order to account for the existing investments in forward capacities, we have to subtract the corresponding investment costs from the objective of the sequential planning models since these costs have to be regarded as sunk and thus are not relevant. In  ∗ case of the IN, we subtract the term ni=1 (ci − cim )Kˆi in (1) and (12). By doing so, we assume that the firm has to convert existing into flexible capacity that is capable of processing both new and remanufactured products. The investment costs per unit of converted capacity are therefore (ci − cim ).

i=1 i

i

3.3. Solution method The above models are two-stage linear programs with recourse and belong to the class of concave optimization problems [25]. A key difficulty when solving this type of model represents the evaluation of the objective's expected value. For continuous distributions of the random parameters, an exact computation of the recourse function ED,R () would result in evaluating multiple integrals and is not practical even for given values of the first-stage variables [26]. A common approach for dealing with these difficulties is to approximate the random variables with a sample of  realizations drawn from underlying probability distributions. For solving the above models with such a discrete approximation of the probability distributions, different solution methods can be considered (an overview is given in [27]). We use a mathematical programming approach and represent the two-stage programs by their deterministic equivalents which are linear programs [15]. For example, given a sample of demand d1 , . . . , dX and returns r1 , . . . , rX , we can rewrite (1)–(5) as linear program:

1 VIN (K ∗ ) = max −

n  i=1

s.t. ai x + bi y  Ki i i

ci Ki +

 n 1   m  r  s  (pi xi +pi yi +pi si )  =1 i=1

∀i = 1, . . . , n,  = 1, . . . , 

x + y  d i i i

∀i = 1, . . . , n,  = 1, . . . , 

y + s = ri i i

∀i = 1, . . . , n,  = 1, . . . , 

Ki , x  , y s  0 ∀i = 1, . . . , n,  = 1, . . . ,  i i i Each realization (or scenario) is equally weighted when computing the expected value of the objective and thus   ED,R () is approximated by the sample average  =1 ( ). The index  for the second-stage decisions indicates that the values are selected for specific realizations di and ri of the random variables. The first-stage variables Ki are independent of the particular demand and return realizations and therefore independent of a particular scenario realization (non-anticipatory condition). This approach applies obviously also to discrete probability distributions and has the advantage that the deterministic equivalents can be easily solved by appropriate optimization techniques for linear problems. For the other models, the approximate deterministic equivalents are straightforward and not explicitly shown here. 4. Numerical analysis The main scope of the subsequent numerical studies is to compare the two presented network structures and their sensitivity to the underlying model parameters. We address thereby the differences between the discussed settings, i.e.,

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

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Table 1 Average solution time (in seconds) for the base case . Size

Simultaneous planning

Sequential planning

IN

n=1 n=2 n=3

DN

IN

DN

















4.09 8.52 14.48

1.99 4.17 6.81

4.20 21.45 38.83

0.55 0.98 1.59

3.89 9.06 15.50

1.64 3.77 5.88

4.89 21.17 41.20

0.86 1.72 2.70

1.05 Relative performance

Relative performance

1.2 1.15 1.1 1.05 1

n=1 n=2 n=3

0.95

1 0.95 n=1 n=2 n=3

0.9 0.85

10 9 8 7 6 5 Investment costs for remanufacturing plant (c = 10)

10 9 8 7 6 5 Investmentcosts for remanufacturing plant (c = 12)

Fig. 2. Sensitivity to variations in cr .

the difference between the two market settings (common market versus separate markets) and the impact of a sequential planning approach compared to a simultaneous design of the forward and the reverse network. In order to compare the expected performance of the integrated and the DN IN /V DN as structure, we define the ratio of expected profit V(•) (•) performance measure. Values larger than one indicate a better performance of IN while values below one show a better performance of DN. 4.1. Experimental design For simplicity and clarity of presentation, we assume that all parameters have the same values among all products. We therefore drop the index i for parameters in the following. We assume the random variables (demand and return) to be truncated (± 2 · standard deviation) and normally distributed. We define the following parameter values as a base which is varied throughout the numerical analysis. In the common market setting, the CoV vD of demand Di is 0.2, while in the m on the separate market case the CoV vD of demand Dm i r

primary market is 0.2 and the CoV vD of demand Dri on the secondary market is 0.3. The corresponding expected values m r and D = 100 for Dri . are D = 100 for Di , D = 100 for Dm i CoV of return Ri is vR = 0.5. The expected values of Ri are

margin pm of newly produced products is 30, the margin pr of remanufactured products is 40, and the salvage value ps for unused returns is assumed to be negative: ps = −5. These disposal costs account for a situation where the company has to take responsibility for unused returns, e.g., due to legislative obligations. For the relationship between acquisition costs of the different capacity types in IN and DN we make the following assumption: c  cm  cr . This refers to a situation where remanufacturing operations are assumed to be less complex than new production and hence require lower investments in machines and workers. Furthermore, it is reasonable to assume that the more flexible capacity of IN is more costly than the dedicated manufacturing capacity in DN. We set c = cm = 10 and cr = 7 in the base case. In line with [19,22,23], we set a = b = am = br = 1 in order to ease interpretation of the numerical results. The distributions of the (continuous) random parameters are approximated via 5000 scenarios using a Monte Carlo approach. The resulting linear programs were implemented in Xpress IVE and solved by Xpress Optimizer. The experiments were run on a Windows machine with a 2.8 GHz processor and 500 MB of ram. For the sake of completeness, the average run times of the base case (five runs with different random seeds) are shown in Table 1 with respect to the number of products n, although an elaborate discussion of the computational results is beyond the scope of this paper.

R = 50 in the common market setting and R = 100 in the separate market setting. In order to analyze the benefits of matching supply with demand, we consider the correlation between returns Ri and corresponding demand for remanufactured products (Di and Dri ) denoted by the coefficient of correlation . In the base case,  is set to 0. The contribution

4.2. Study 1: simultaneous planning 4.2.1. Common market Fig. 2 shows the impact of variations in investment costs cr for the remanufacturing plant. The left part displays the

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D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

1.01 Relative performance

Relative performance

1.08 n=1 n=2 n=3

1.06 1.04 1.02 1

0.99 0.97 0.95 0.93 n=1 n=2 n=3

0.91 0.89 0.87

0.98 0 12.5 25 37.5 50 62.5 75 87.5 100

0 12.5 25 37.5 50 62.5 75 87.5 100

Expected return quantity (c = 10)

Expected return quantity (c = 12)

Fig. 3. Sensitivity to variations in R .

Table 2 Performance measures in the common market setting . Size

Performance measure

Integrated network n=1 Profit Sales Disposal costs Capacity costs Capacity utilization n=2

Profit Sales Disposal costs Capacity costs Capacity utilization

Decentralized network n=1 Profit Sales Disposal costs Capacity costs Man. capacity utilization Reman. capacity utilization n=2

Profit Sales Disposal costs Capacity costs Man. capacity utilization Reman. capacity utilization

R = 25

R = 62.5

R = 100

vR = 0.1

vR = 0.3

vR = 0.5

=0

 = 0.5

=1

2039 3126 0 1086 0.88

2359 3466 14 1093 0.88

2467 3702 110 1125 0.86

2288 3374 0 1086 0.88

2275 3361 1 1086 0.88

2288 3384 3 1093 0.88

2284 3373 3 1086 0.88

2534 3627 7 1086 0.88

2704 3812 15 1093 0.88

4073 6250 0 2177 0.88

4734 6951 29 2188 0.88

4923 7390 221 2246 0.86

4571 6749 0 2177 0.88

4565 6738 1 2172 0.88

4568 6757 6 2183 0.88

4557 6740 6 2177 0.88

5087 7272 14 2172 0.88

5398 7611 30 2183 0.88

1992 3085 13 1079 0.84 0.74

2216 3315 46 1054 0.70 0.76

2375 3476 131 970 0.54 0.79

2394 3362 5 963 0.78 0.93

2274 3308 17 1017 0.77 0.83

2165 3269 32 1072 0.76 0.76

2162 3258 32 1064 0.76 0.76

2619 3603 17 967 0.64 0.82

3004 3812 15 793 0.42 0.92

4041 6173 23 2493 0.84 0.83

4553 6642 84 2906 0.69 0.84

4866 6930 255 3039 0.54 0.85

4814 6728 9 1905 0.78 0.96

4631 6640 30 1979 0.77 0.89

4428 6532 55 2049 0.76 0.84

4417 6521 55 2798 0.75 0.84

5357 7227 39 3003 0.66 0.89

5998 7611 30 2983 0.42 0.92

expected relative performance VIN /VDN for c = 10 and the right part for c = 12. The figure shows the high sensitivity to variations in cost parameters. Another observation is the high impact of pooling effects when increasing the network size n. The results indicate that the DN structure highly benefits from pooling several products in the remanufacturing plant which is reflected by the downward shifts of the curves. The role of return quantities in this context is examined in the subsequent paragraph. In Fig. 3 we vary the expected return quantity R . The left part of the figure shows again the expected relative performance for c = 10 and the right part for c = 12. Increasing r first leads to a better performance of IN in both cases. However, in both cases, when exceeding a certain level of R , DN becomes more profitable than IN. The explanation for this behavior is as follows: The analysis of the corresponding capacity levels of IN and DN shows that Ki is only

slightly increasing in R while we observe a strong substitution from forward capacities Kim to K r due to the more ben-

eficial remanufacturing option. For smaller values of R one can benefit in IN from the opportunity to substitute remanufacturing with new production when return quantities are low and thus avoid the risk of low utilization of K r in DN. As expected return quantities rise, the expected quantities of remanufactured products also increase. Then a company can benefit from lower investment costs cr for K r which now process the major proportion of the overall production. Apparently, these effects are more pronounced when pooling of products (n > 1) allows for a more stable utilization of K r or when the cost differential c − cr increases. Table 2 displays these effects in detail. For IN we observe a relatively stable capacity utilization while the variability of capacity utilization is much higher in DN. The utilization of K r increases in R and n, although at the expense of lower utilization of Kim due to substitution effects. However, the benefits

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

from 0 to 1. The figure shows that increasing  leads to a relative advantage in performance of DN. Table 2 shows that both network structures benefit from this better match of supply with demand in terms of increased profits. We see again that DN is more exposed to the risk of lower capacity utilization while the utilization in IN remains stable for different values of . When demand and return move more and more in lockstep, the percentage of remanufactured items can be increased and the firm can benefit from lower investment costs in DN and avoid the risk of low capacity utilization of the remanufacturing capacity.

Relative performance

1.1 n=1

1.05

n=2 n=3

1

0.95

0.9 0

0.1

0.2

0.3

0.4

0.5

0.8

1

CoV of return Fig. 4. Sensitivity to variations in vR .

Relative performance

1.1 1.05 1 0.95

n=1 n=2

0.9

n=3

0.85 0

765

0.2

0.4

0.6

Coefficient of correlation Fig. 5. Sensitivity to variations in .

of flexibly shifting from remanufacturing to new production (higher utilization and larger sales) in IN can be outweighed by higher investments costs. The impact of return variability is displayed in Fig. 4. We vary vR in steps of size 0.1. Larger values of vR lead to an increasing relative advantage of IN since we have the opportunity to switch from new production to product recovery and maintain high capacity utilization. In contrast, when return flows are more stable (smaller values of vR ), we can benefit from investing in less expensive equipment dedicated to either manufacturing or remanufacturing. The impact of variability is shown, in detail, in Table 2. Again, we see that capacity utilization in IN does not change while in DN the system is very exposed to the risk of low utilization. In order to avoid lost sales and less profitable new production, DN requires sufficient slack capacity when vR increases. Then IN can better respond to the uncertain environment and the more expensive capacity is compensated by higher sales and lower disposal costs. However, these effects are less severe for n = 2 due to pooling of returns. In Fig. 5, we demonstrate the impact of the coefficient of correlation between Di and Ri by varying  in steps of 0.2

4.2.2. Separate markets Fig. 6 shows the impact of variations in investment costs cr for the remanufacturing plant in the separate market setting. The left part displays the expected relative performance V IN /V DN for c = 10 and the right part for c = 12.   Compared with the results of the common market setting in Fig. 2, we observe again a high sensitivity to changes of the cost parameters c and cr and a distinct risk pooling benefit of DN with increasing n. However, the relative performance of IN is significantly worse than in the common market setting. Only for cr ∈ [9, 10] and c = 10, we can observe a small advantage of pooling manufacturing and remanufacturing operations for each product in an integrated plant. These benefits diminish considerably fast when cr decreases and particularly when c increases. The better performance of DN in the separate market case can be explained by the fact that the processed quantities of remanufactured products are larger and no substitution with newly manufactured products is possible. For this reason, an integrated structure does not pay off since investment costs for (flexible) capacity are too high. Acquiring (more) specialized capacity as in DN is then the more profitable approach. In Fig. 7, we vary the amount of expected returns R . As in Fig. 3, we see first increasing and then downward sloping curves with the maximum indicating the value of R with the best relative performance of IN. However, in comparison to Fig. 3, the peak of the curves is shifted to the left and DN is the more beneficial alternative except for some (smaller) values of R and n = 1. The lower investment costs for remanufacturing in DN induce higher profitability of DN. Only for small amounts of R and n=1, the higher utilization risks of K r in DN outweigh the higher investment costs in IN. Due to the absence of substitution of more profitable product recovery with new production, we observe only small changes in capacity utilization. Table 3 shows that particularly the capacity utilization in DN remains quite stable, in contrast to the common market setting. Sales and disposal costs are similar, but lower investment costs and the opportunity to pool demands Dri of the secondary markets in one plant explain the better performance of DN. Fig. 8 displays the impact of variations in vR . For n = 2, 3, expected relative performance is not significantly affected by changes in vR while we observe small changes for n = 1 (as depicted by the slightly upward sloping curve for n = 1). As in the common market setting, IN then benefits from pooling demands Dm and Dr1 in one plant. These benefits di1 minish when pooling of recovery operations is possible for

1.08 1.06 1.04 1.02 1 0.98 0.96 0.94 0.92 0.9 0.88

Relative performance

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

Relative performance

766

n=1 n=2 n=3 10

9

7

8

6

0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8

5

n=1 n=2 n=3 10

Investment costs for remanufacturing plant (c = 10)

9

8

7

6

5

Investment costs for remanufacturing plant (c = 12)

0.91

1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93

Relative performance

Relative performance

Fig. 6. Sensitivity to variations in cr .

n=1 n=2 n=3

0.9 0.89 0.88 0.87 n=1 n=2 n=3

0.86 0.85 0.84

0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 10)

0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 12)

Fig. 7. Sensitivity to variations in R . Table 3 Performance measures in the separate markets setting . Size

Performance measure

Integrated network n=1 Profit Sales Disposal costs Capacity costs Capacity utilization n=2

Profit Sales Disposal costs Capacity costs Capacity utilization

Decentralized network n=1 Profit Sales Disposal costs Capacity costs Man. capacity utilization Reman. capacity utilization n=2

Profit Sales Disposal costs Capacity costs Man. capacity utilization Reman. capacity utilization

R = 25

R = 62.5

R = 100

2483 3833 0 1350 0.89

3359 5111 21 1730 0.87

3804 5873 116 1952 0.87

4278 6340 61 2001 0.91

4071 6125 84 1970 0.90

3804 5873 116 1952 0.87

3774 5826 111 1942 0.87

3949 6052 85 2018 0.86

4261 6446 40 2145 0.86

4979 7682 0 2702 0.89

6725 10229 43 3461 0.87

7590 11707 228 3889 0.87

8562 12687 123 4003 0.91

8159 12264 166 3938 0.90

7590 11707 228 3889 0.87

7573 11687 224 3889 0.87

7919 12130 172 4039 0.86

8545 12922 82 4296 0.86

2468 3817 5 1345 0.88 0.64

3397 5115 31 1687 0.88 0.65

3895 5883 128 1861 0.88 0.68

4453 6332 66 1813 0.88 0.83

4183 6116 94 1840 0.88 0.75

3895 5883 128 1861 0.88 0.68

3866 5844 123 1856 0.88 0.68

4049 6064 98 1917 0.88 0.67

4415 6470 51 2004 0.88 0.69

5024 7670 7 2640 0.88 0.73

6961 10284 57 3266 0.88 0.73

7962 11791 244 3585 0.88 0.75

8989 12689 130 3570 0.88 0.87

8538 12301 180 3583 0.88 0.81

7962 11791 244 3585 0.88 0.75

7950 11767 242 3575 0.88 0.75

8336 12222 191 3694 0.88 0.75

9044 13014 98 3872 0.88 0.75

n > 1. Table 3 shows that the profits of both structures decrease in vR . As a consequence of the less stable amount of supply, the capacity levels in IN decrease (as indicated

vR = 0.1

vR = 0.3

vR = 0.5

=0

 = 0.5

=1

by the lower capacity costs) while the capacity costs in DN increase. In case of the distributed network, the lower investment costs for K r make building up slack capacity in

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

1

767

0.99

Relative performance

Relative performance

0.98

0.95 n=1 n=2

n=1

0.97

n=2 0.96

n=3

0.95 0.94

n=3

0.93

0.9 0

0.1

0.2 0.3 CoV of return

0.4

0.5

0

0.2 0.4 0.6 0.8 Coefficient of correlation

1

Fig. 8. Sensitivity to variations in vR .

Fig. 9. Sensitivity to variations in .

the remanufacturing plant rewarding, despite lower capacity utilization. In Fig. 9, we display the impact of positive correlation between return and demand on the secondary market. Opposite to the common market case in Fig. 5, we cannot observe strong changes in the expected relative performance when  increases. The main reason for the less pronounced differences between IN and DN compared to the common market setting stems from the fact that a substitution from remanufacturing to new production when returns are low is not possible. This opportunity of switching flexibly from remanufacturing to new production in the integrated plant allows for a better capacity utilization in IN compared with the separate resources for new production and remanufacturing in DN. In this way, DN is in the common market setting more exposed to return uncertainty than IN. Therefore, increasing  is more beneficial for DN since it reduces the overall variability of the system. When regarding separate markets, this advantage of IN disappears and both structures are comparably exposed to return uncertainty.

relative performance of IN, but these benefits are not sufficient to outweigh the advantages of the distributed structure. Therefore, DN remains the more beneficial network configuration in the separate market case.

4.3. Study 2: sequential planning 4.3.1. Common market Fig. 10 depicts the effect on the optimal network configuration when forward capacities are already in place and expected return quantities R are varied with c ∈ {10, 12}. Less surprisingly, the existing (and convertible) forward capacities increase the profitability of an integrated approach since the equipment already in place can be further used while in the distributed structure the necessary capacity re-allocation (a shift from Kim to K r ) makes existing capacities less valuable. Therefore, existing (forward) capacities increase the effects already described in Fig. 3. 4.3.2. Separate markets When considering already existing forward structures, a similar effect can be observed for separate markets as displayed in Fig. 11. As in the common market case, the opportunity to use already existing capacities improves the

4.4. Summary and discussion Our numerical results indicate that both demand and return characteristics play a prominent role when assessing the benefits of a certain network structure. Conducting both remanufacturing and manufacturing in one facility allows for allocating capacity to the (more profitable) recovery option while pooling all recovery activities in one separate facility can counterbalance fluctuations in returns of several products. The question of which structure better mitigates uncertainty in returns hinges therefore crucially on return characteristics and the corresponding investment costs. Furthermore, when demand for both product variants is segmented, the benefits of the integrated facilities tend to diminish regardless of whether a simultaneous or sequential network design approach is used. These results require discussion since we made some simplifying assumptions within our analysis. First, we focused on the (re-)manufacturing process and the corresponding capacity decisions and resource types in a simplified way. Extending the models for logistics infrastructures and disaggregating the recovery process into different resources will certainly add additional and maybe interfering effects. However, we believe that our main findings will tend to remain valid. In particular, the results of [22] suggest the optimal reverse logistics network design is quite robust to changes in parameters. Thus, incorporating aspects such as location and transportation decisions should not completely change the advantages of the presented network configurations. Furthermore, disaggregating the recovery resource into separate resources should not alter our results fundamentally as long as each resource is necessary for remanufacturing each product. In that case, we would observe distinct complementary effects between the resource capacities (i.e., more or less capacity of one

768

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

1.2

1.15 1.1 1.05 n=1 n=2 n=3

1 0.95

Relative performance

Relative performance

1.2

1.15 1.1 1.05 1

n=1 n=2 n=3

0.95 0.9

0.9 0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 10)

0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 12)

Fig. 10. Sensitivity to variations in R .

0.95 Relative performance

Relative performance

1.05

1

0.95

n=1 n=2 n=3

0.9 n=1 n=2 n=3 0.85

0.9 0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 10)

0 12.5 25 37.5 50 62.5 75 87.5 100 Expected return quantity (c = 12)

Fig. 11. Sensitivity to variations in R .

resource implies more or less capacity, respectively, of other resources). Another important simplifying assumption is the singleperiod nature of the models. The diffusion of new and remanufactured products is considerably influenced by component durability and product life cycle. Debo et al. [19] have demonstrated that these factors can also influence the value of flexible capacity. Moreover, such dynamics may require dynamic capacity strategies. Incorporating such multiperiod aspects in our models would undoubtedly generate additional insights, but we believe that even in a more complex setting the numerically found properties of the two alternative network structure will endure to a certain degree. 5. Conclusion We have studied optimal capacity acquisition and expected network performance in a supply-chain setting with remanufacturing options under uncertain demand and returns. Using a two-stage programming approach, we have presented basic network design models for two different generic network structures and two different market structures. Our numerical studies show significant differences in the performance of the two structures, indicating the important role of the network configuration. Generally, a DN structure is more beneficial in a multi-product environment. Furthermore, the optimal choice of a network type hinges particu-

larly on the underlying market structure and the acquisition costs of the resources. While an IN with the opportunity of flexibly switching between manufacturing and remanufacturing on the same resource pays off in a common market setting, the more specialized distributed structure tends to be more beneficial in the separate market setting. The expected amount of return is another important factor. In the separate market case, higher return volumes enhance the advantage of the more specialized resources in the distributed network. In contrast, the integrated structure is more beneficial in the common market setting even for comparatively high return volumes. The underlying market type also affects the impact of return variability and (positive) correlation between demand and return on the expected relative performance. In the common market setting, the distributed structure benefits more from reduced return variability and increased correlation between demand and return. On the other hand, this relative advantage diminishes in the separate market case and both network structures are influenced by return variability and correlation to a similar extent. In many cases, firms already have existing (forward) manufacturing networks. For this reason, we considered a sequential planning approach. The IN tends to benefit more from converting existing resources since start up costs can be reduced. However, in order to choose an appropriate network configuration, these benefits have to weigh up against the general advantages of a certain structure.

D. Francas, S. Minner / Omega 37 (2009) 757 -- 769

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