Supply Chain Inventory Models with Refurbishment

Transcription

1 Supply Chain Inventoy Models with Refubishment DECISION SCIENCES INSTITUTE Inventoy models in a closed-loop supply chain with poduct etuns and efubishment Seung Ho Yoo Sunmoon Univesity shy1228@sunmoon.ac.k Seongpil Joo Koea Univesity Business School jsp011@koea.ac.k Myung-Sub Pak Koea Univesity Business School mspak@koea.ac.k ABSTRACT This study investigates a closed-loop supply chain, consisting of a manufactue esponsible fo the fist-maket sales of a new item and a thid-paty efubishe esponsible fo the secondmaket sales of a efubished item. We then intoduce two diffeent supply chain models with diffeent stuctues and evealed thei distinct chaacteistics. Specifically, we eveal the effect of the supply chain stuctue on poduction lot size, efubishing lot size, and sales pice of a efubished poduct, which then jointly affect the oveall sales and pofit pefomances. We also suggeste a guideline fo the selection of a thid-paty efubishe. KEYWORDS: Inventoy, Closed-loop supply chain, Sales etun, Refubishment RODUCTION In pactice, poduction and inspection systems ae often not pefect, so incu not only intenal failue costs to intenally identify and fix defect poblems but also extenal failues, causing sales etuns and evese logistics flows by passing defects to consumes. In fact, poduct etun is enomous, ecoded up to 16% of sales in the catalog etail industy (Peteson and Kuma, 2009) and 11-20% in consume electonics industy (Douthit et al., 2011), while its main eason is quality dissatisfaction due to defect poduction. Guide et al. (2006) epoted that 20% of etuns of HP pintes wee due to defect poblems, and thee wee 60% of defective etuns fo Bosch powe tools. Thus, to educe these negative consequences, fims not only invest in pevention and appaisal activities to impove pocess capability and stability, but also caefully conside disposition of defective items, including poduct etuns. Among vaious disposition options, such as salvage, ecycle, and scap, any option can be selected. Howeve, it always needs to be pofitable since a defective item can peseve technologies and featues of a new item, if ecoveed though a pope value ecovey pocess. Theefoe, in this study, we focus on a common value ecovey option nowadays, the efubishment (o emanufactuing) fo secondmaket sales. We investigate the joint decision on inventoy (lot sizing) and efubishing stategies in a closed-loop supply chain with an impefect manufactuing pocess and a sepaate efubishing pocess. A efubished (o emanufactued) poduct efes to the poduct which fomely had a quality poblem but has been estoed to the condition as functional as new. Refubishment becomes a

2 Supply Chain Inventoy Models with Refubishment common option especially in electonics industy. It helps envionment by educing waste and extending the lifecycle of a poduct. It can also enhance the pofitability since it povides a chance to open up anothe maket segment that would not puchase a new item at full pice (Voasayan and Ryan 2006, Ovchinnikov 2011). Howeve, fims need to caefully conside the possible pitfalls due to channel conflicts. The sales of a efubished item can negatively affect the fist-maket sales of a highe-magin new item. Theefoe, in this study, we will investigate the optimal decision on the sales pice of a efubished item, which subsequently affect not only the inteaction between new and efubished items but also inventoy decisions on both manufactuing and efubishing pocesses in a closed-loop supply chain. In pactice, many contempoay fims concentate on thei coe pocesses and outsouce othes in ode to enhance thei competitiveness. It leads fims to un thei businesses based on a decentalized supply chain system. Theefoe, it is pactical that we investigate the joint decision on inventoy and efubishing stategies in the context of supply chain management, consideing inteactions between independent decision makes. Specifically, in this study, we include two key playes, a manufactue esponsible fo the manufactuing pocess fo the fist-maket sales of a new item, and a efubishe handling the efubishing pocess fo the second-maket sales of a efubished item. Then, we will intoduce two diffeent supply chain stuctues one integated and the othe decentalized by consideing the integation and sepaation of manufactuing and efubishing pocesses by the manufactue, the focal company in a supply chain. Afte building two closed-loop supply chain models with diffeent stuctues based on the pincipal-agent paadigm famewok, we compae the pefomances of diffeent supply chain stuctues and eveal thei distinct chaacteistics. Specifically, we eveal the effect of the supply chain stuctue on (1) poduction lot size, (2) efubishing lot size, and (3) sales pice of a efubished poduct, which then jointly affect (4) the oveall sales and pofit pefomances in a closed-loop supply chain. In addition, we will also suggest a guideline fo the selection of a thidpaty efubishe by evealing the condition that the decentalized supply chain can outpefom the integated one. The est of the pape is oganized as follows. In Section 2, the eview analysis on the pevious liteatue is pesented. Section 3 fomulates the basic mathematical models. Section 4 intoduces two supply chain models with diffeent stuctues, and investigates thei optimal solutions. Section 5 povides numeous impotant implications by compaing the pefomances of models. Then, Section 6 concludes this study along with limitations and futue eseach diections. LITERATURE REVIEW Two eseach steams ae diectly elevant to the pesent study: (1) inventoy models with impefect poduction pocess, and (2) pice decision of a efubished item. Thee have been a vast numbe of inventoy studies consideing an impefect poduction system since Poteus (1986) and Rosenblatt and Lee (1986). Among them, the pesent study is in line with the inventoy studies of a stable poduction pocess, which assumed that the poduction pocess yields defective items, following a Benoulli pocess and thus geneating binomial yields (see Yano and Lee (1995), Gosfeld-Ni and Gechak (2004), and Khan et al. (2011b) fo detailed eviews of elevant studies). While dealing with vaious elevant issues, the main focus of many studies did not lie in the defect delivey to consumes and subsequent evese logistics issues, since they implicitly (o sometimes explicitly) assumed that thee ae no eos in the inspection pocess, such as Zhang and Gechak (1990), Cheng (1991), Anily

3 Supply Chain Inventoy Models with Refubishment (1995), Lee et al. (1996), Salameh and Jabe (2000), Tipathy et al. (2003), Leung (2007), Khan et al., (2011a), Ouyang and Chang (2013), and Ullah and Kang (2014). Theefoe, most studies concentated on total cost minimization, while assuming that all defect poblems can be intenally detected and esolved. Thee ae only a few inventoy models with a moe pactical setting that the defect delivey causes extenal failues and etun-handling issues in a closedloop supply chain. Yeh and Chen (2006) investigated an impefect-quality inventoy system with the inspection eo and defect delivey to consumes. They incopoated a waanty to esolve the defect delivey poblems. Yoo et al. (2009) consideed not only the impefect poduction pocess but also Type I and II inspection eos along with subsequent sales etuns and multiple disposition options fo defects. They investigated the effect of inspection eos and sales etuns on the poduction lot size decision. Then, Yoo et al. (2012b) extended the pevious study with Type I and II inspection eos by incopoating joint investment decision on poduction and inspection eliabilities. They conducted quality cost analyses by identifying fou quality cost components, including pevention, appaisal, intenal failue and extenal failue. Yoo et al. (2012a) also extended the pevious liteatue of the impefect poduction and inspection system with quality investment by consideing continuous impovement unde the budget constaint. They evealed that the inspection option change between entie lot sceening and no inspection can yield a supeio pofit pefomance in a continuous impovement envionment. The above studies have dealt with vaious pactical issues elevant to impefect poduction and inspection systems by incopoating defect delivey and subsequent sales etun issues, but the scope of those studies was limited to a single fim s opeational envionment. Howeve, nowadays, many fims ae stuggling to enhance thei competitiveness by focusing on thei coe capabilities while outsoucing many functions to thei patnes in a supply chain. Theefoe, it is moe pactical that we conside the effect of an impefect system on a decentalized closed-loop system. In this study, we extend the basic inventoy model of Yoo et al. (2012a) with an impefect poduction and inspection system into the supply chain pespective by incopoating the inteaction between the key playes. Specifically, we conside the manufactue dealing with the manufactuing pocess fo the fist-maket sales and the thid-paty efubishe esponsible fo the efubishing pocess fo the second-maket sales. The pesent study also discoves the picing issue of a efubished item. Among vaious studies elevant to this poblem, the pesent study is diectly elated to the pevious ones consideing the maket segmentation between new and efubished items. Voasayan and Ryan (2006) consideed demand substitution between new and efubished items as in pactice, in which the efubished item competes with the new one based on its lowe pice. They investigated the picing decision of a efubished item simila to the pesent study. Aas et al. (2011) investigated a joint leasing and efubishing stategy, with which a manufactue leases a new item while efubishing an end-of-lease item. They also consideed maket segmentation and demand substitution between new and efubished items. Ovchinnikov (2011) also investigated joint decision on the sales pice of a efubished item and the amount of etuns eceived and efubished. This study evealed that a fim s picing stategy is affected by vaious aspects, including poduct chaacteistics, consume behavio, and cost stuctue. Simila to the studies above, we conside the picing decision of a efubished item, but the pesent study is diffeent fom the pevious ones, of which scope is limited to the opeational envionment of a single fim. We extend the liteatue by consideing a contempoay situation whee many fims un thei businesses in a decentalized supply chain system. Moeove, note that we intoduce this picing issue of a efubished item into the eseach steam of impefect-quality inventoy models. To the best of ou knowledge, thee ae only a few studies incopoating the picing and

4 Supply Chain Inventoy Models with Refubishment lot sizing issues in the context of closed-loop supply chain management. Oveall, the contibution of this study lies in bidging the gap between two eseach steams: impefect-quality inventoy decision and efubished item picing. We extend the liteatue by developing a compehensive inventoy and picing model in the context of supply chain management. We povide impotant implications fo the joint management of fowad and evese flows in a supply chain by incopoating the channel conflict issues between new and efubished items into the inventoy decision. In addition, we also eveal the effect of the supply chain stuctue on the oveall pefomances by consideing the pocess integation and sepaation. MATHEMATICAL FORMULATION Basic Fomulation Figue 1: Inventoy flows in the fist- and second-maket sales pocesses (solid line: physical flow of inventoy, dotted line: effect on inventoy depletion) Demand [D] (+) Poduction lot sizing Q (+) Sceened items (1-ρ)θQ [F] Fist-maket sales (with exchanges) Non-defective items (1 θ)q Defective items ρθq Note Stock o Activity qty. [ate] Net depletion [N] Poduction [M] Inspection [I] Seviceable new Items (1 (1 ρ)θ)q Retuned items ρθq Collected defects θq Manufactuing pocess (+) Exchange βρθq [E] Refund (1 β)ρθq Customes choice Supply θq (-) Second-maket sales γθq [D] Refubishment γθq [W] Refubishing lot sizing & picing Q, p Disposition method Puchasing θq Refubishing pocess Scap (1 γ)θq We investigate a closed-loop supply chain consisting of two pocesses, a manufactuing pocess fo the fist-maket sales and a efubishing pocess fo the second-maket sales. In this section, we model the pofit functions of two pocesses, and then we will chaacteize two supply chain models by consideing the integation and sepaation of pocesses in Section 4. In modeling, we extend the basic inventoy model in Yoo et al. (2012a), dealing with impefect poduction and inspection pocesses and subsequent sales etun issues. By extending the pevious study in a single fim s opeational envionment, the pesent study focuses on building a compehensive supply chain inventoy model by incopoating the inteaction between supply chain playes as in the contempoay supply chain pactice. Diffeent fom the pevious study, we also incopoate the efubishing issues in ode to investigate the channel conflict between the fist- and second-maket sales of new and efubished items. Figue 1 illustates the oveall fowad and evese flows in two pocesses in a closed-loop supply chain. Table 1 summaizes

5 Supply Chain Inventoy Models with Refubishment the notation used in this study. The manufactuing pocess yields lot size Q of a new item pe each cycle T. Both poduction and inspection systems ae impefect as in pactice, which follow the Benoulli pocess and geneate binomial yields with defective popotion θ and inspection failue popotion ρ, espectively, whee 0 θ, ρ 1. Theefoe, among θq of all defective items, only (1 ρ)θq of defective items ae sceened by inspection, and ρθq of unsceened defective items ae sold to consumes along with (1 θ)q of non-defective items. Then, consumes detect defects and etun them as in pactice. Consumes can select a etun option among exchange (with its popotion β, 0 β 1) and efund (with 1 β), so thei espective quantities ae βρθq and (1 β)ρθq among ρθq of sales etuns. Q Q w p p u i k g h H H S S T Table 1: Notation fo mathematical models poduction lot size (unit, a decision vaiable) T efubishing cycle (time) efubishing lot size (unit, a decision vaiable) N net depletion ate in poduction line (unit/unit time) unit wholesale pice of a defective item ($/unit, a D demand ate of a new item in the fist maket decision vaiable) (unit/unit time) unit sales pice of a efubished item ($/unit, a D demand ate of a efubished item in the second decision vaiable) maket (unit/unit time) unit sales pice of a new item ($/unit) F sceening ate of a defective item (unit/unit time) unit poduction cost of a new item ($/unit) E exchange ate (unit/unit time) unit inspection cost of a new item ($/unit) M poduction ate (unit/unit time) unit etun handling cost ($/unit) M efubishing ate (unit/unit time) unit efubishing cost ($/unit) θ defective popotion in poduction line (faction) unit scap cost ($/unit) ρ inspection failue popotion (faction) inventoy holding cost ate faction (faction/unit β exchange popotion among etuns (faction, 1 β: time) efund popotion) inventoy holding cost ate of a new item ($/unit/unit γ efubishing popotion among defects (faction, 1 time) γ: scap popotion) inventoy holding cost ate of a efubished item Πi j pofit of playe o pocess i in Case j ($/unit/unit time) i subscipt; M (manufactue), R (efubishe), m setup cost pe poduction un ($/cycle) (manufactuing pocess), (efubishing pocess) setup cost pe efubishing un ($/cycle) j supescipt; (an integated supply chain), (a poduction cycle time (time) decentalized supply chain) Then, all defective items of θq (including the sceened defects of (1 ρ)θq and the etuned defects of ρθq) ae supplied to the efubishing pocess. We conside that the efubishing popotion γ (0 γ 1) is affected by the selling pices of both new and efubished items p and p as follows. p γ( p ) 1. (1) p Not all defects can be efubished, and only γθq among θq of defects can be efubished and sold to consumes in the second maket, while (1 γ)θq of emaining defective items ae scapped. We conside that consumes buying intention fo the efubished item is affected by its pice p, and the pice of a new item p is also consideed a efeence as in a pactical situation. If p becomes lowe given p, thee will be moe consumes selecting a efubished item, i.e., γ/ p > 0, but thee will be no consumes if p = p, i.e., γ = 0. Then, the second-maket sales of a efubished item can substitute fo the fist-maket sales of a new item as:

6 Supply Chain Inventoy Models with Refubishment D = D 0 D, (2) whee D 0 is the demand potential in the taget segment, D is the fist-maket sales of a new item and D is the second-maket sales of a efubished item, which is diectly elated to the efubishing popotion γ in Equation (1). As in Equation (2), we conside a pactical situation in many businesses whee the consumes demand consists of two pats, the fist- and secondmaket sales as found in many industies including consume electonics, appael and funitue, i.e., D 0 = D + D. On the othe hand, the manufactuing pocess yields a lot Q at a poduction ate M as in the typical EPQ models, and then Q of a new item ae depleted at the net inventoy depletion ate N in each cycle T, i.e., T = Q/N. Note that we conside vaious souces of inventoy depletion as in pactice, diffeently fom the taditional EOQ and EPQ models only consideing the demand D (T = Q/D). As shown in Figue 1 (see the dotted lines), the net depletion ate N consists of the fist-maket demand ate D in Equation (1), the exchange ate E and the sceening ate of defective items by inspection F, i.e., N = D + E + F. Consideing the elationship N = Q/T fom T = Q/N and the espective inventoy amount involving each ate, fist we obtain the secondmaket demand D as: whee γ is in Equation (1). D (p ) = γθq/t = γθn, (3) Similaly, we can also define F = (1 ρ)θq/t = (1 ρ)θn and E = βθq/t = βθn, while D = D 0 γθn fom Equations (2) and (3). Then, we obtain the net depletion ate N by solving N = D + E + F with espect to N as follows. N D ( p ) 0 1 ((1 γ) (1 β) ρ ) θ, (4) whee γ is a function of p in Equation (1). In addition, we set the inspection ate I equal to N not to incu unnecessay inventoy holding fom diffeent ates. On the othe hand, thee ae two options in the efubishing pocess, efubishment fo the second-maket sales and scap as shown in Figue 1. In the efubishing line, thee ae two types of items, the item to be efubished (befoe efubishment) and the efubished item (afte efubishment). The efubishing line accumulates the efubished item of efubishing lot size Q at a efubishing ate M, and the efubished item is depleted at the second-maket sales ate D in Equation (3) in each efubishing cycle T (T = Q /D ). Note that the accumulation of the efubished item means the depletion of the item to be efubished. Theefoe, the item to be efubished (befoe efubishment) is depleted at the efubishing ate M, and it needs to be accumulated at D in ode to satisfy the second-maket demand and avoid unnecessay inventoy holding fom the ate diffeence between two types of items. Theefoe, note that the inventoy holding quantities pe unit time ae the same between two types of items, while thei inventoy behavios ae exactly the opposite. The efubishing cycle T is diffeent fom the poduction cycle T, and thee ae n efubishing setups in each T, i.e., n = T/T. Theefoe, while thee ae γθq of items to be efubished among Q in each cycle T, the efubishing lot size Q deceases as n inceases, i.e., Q = γθq/n. In addition, we suppose that those defects fo scap

7 Supply Chain Inventoy Models with Refubishment ae disposed instantaneously, so as not to incu unnecessay inventoy holding. Pofit Functions The objective of the manufactuing pocess is to detemine poduction lot size Q and supply contact offe to the efubishing pocess which jointly maximize its pofit. Total evenue pe cycle of the manufactuing pocess includes the fist-maket sales of a new item p((1 θ) + ρθ)q, which also include the exchange equest of consumes at no chage ( pβρθq). p is the unit selling pice of a new item. We also need to conside the evenue loss fom anothe etun option, efund ( p(1 β)ρθq). In addition, the manufactuing pocess also supplies the defective items to the efubishing pocess. Thee exist vaious contact types in pactice, but we only conside the wholesale pice contact, the most common contact fom due to its simplicity. Theefoe, the total tansfe payment fom the manufactuing pocess to the efubishing pocess is wθq, whee w is the unit wholesale pice of the defective item. In sum, total evenue pe cycle of the manufactuing pocess TR m can be fomulated as follows. TR m = p((1 θ) + ρθ)q pβρθq p(1 β)ρθq + wθq = p(1 θ)q + wθq. (5) On the othe hand, thee ae vaious souces of cost in the manufactuing pocess. Thee is a fixed cost fom poduction setup S in each cycle T. Vaious vaiable costs ae incued fom elevant activities, including poduction uq, inspection iq, etun handling ρθq, whee u, i and ae thei espective unit costs. The inventoy holding cost in each cycle of the manufactuing pocess can be defined as (H/2)(1 N/M)QT simila to the taditional EPQ model. H is the inventoy holding cost ate of a new item, whee H = hu consideing the unit cost of a new item incued in the poduction line befoe sales. Theefoe, we obtain the total cost pe cycle of the manufactuing pocess TC m as: TC m H N S ( u i ρθ) Q 1 QT, whee H = hu. (6) 2 M By subtacting TC m in Equation (6) fom TR m in (5) and then dividing it by cycle time T (= Q/N), the total pofit pe unit time of the manufactuing pocess Π m can be defined as a function of Q and w. SN H N Π m ( Q, w) [( p(1 θ) wθ) ( u i ρθ)] N 1 Q. (7) Q 2 M On the othe hand, the efubishing pocess needs to detemine its efubishing lot size Q and the unit sales pice of a efubished item p. The total evenue pe each poduction cycle T of the efubishing pocess TR is fom the sales of a efubished item to the second maket p γθq (= np Q ), whee p is the unit sales pice of the efubished item. The total cost pe cycle of the efubishing pocess TC includes the vaiable costs fom puchasing of defective items wθq, efubishment kγθq and scap g(1 γ)θq, whee k and g ae the unit efubishing and scap costs, espectively. Thee ae n (= T/T ) efubishing setups pe T, so efubishing setup cost of ns is incued in evey poduction cycle T whee S is the efubishing setup cost pe setup. In addition, the inventoy holding cost of n(h /2)(1 D / M )Q T is incued, whee D is the secondmaket sales ate of the efubished item in Equation (3) and M is the efubishing ate. In estimating the inventoy holding cost ate in the efubishing line H, we need to conside two

8 Supply Chain Inventoy Models with Refubishment types of items in the efubishing line, the item to be efubished and the efubished item. We will deal with diffeent souces of H depending on the stuctue of a closed-loop supply chain in Section 6. Consideing all the above, TR and TC can be defined as: TC TR = p γθq, and (8) H D ns ( w kγ g(1 γ)) θq n 1 QT M. 2 (9) By subtacting TC in Equation (8) fom TR in (9), we obtain the total pofit pe poduction cycle of the efubishing pocess. Then, dividing it by poduction cycle time T and also consideing n = T/T and T = Q /D, we obtain the total pofit pe unit time of the efubishing pocess Π as a function of Q and p as follows. Π ( Q, p ) [ pγ ( w kγ g(1 γ))] θn Q Q 1 2 M, (10) whee γ, D and N ae in Equations (1), (3) and (4) and H is the inventoy holding cost ate in the efubishing line, which will be defined diffeently accoding to the supply chain case in the next section. SUPPLY CHAIN MODELS We conside a typical supply chain situation whee the manufactue has stonge bagaining powe ove the thid-paty efubishe. Theefoe, the manufactue with bagaining powe can integate supply chain pocesses. The manufactue also acts as a Stackelbeg leade by offeing the supply contact of defective items fo efubishment in ode to contol the efubishe s action. Then, given the contact offe of the manufactue, the efubishe maximizes its own pofit. Case : An Integated Supply Chain We fist conside Case involving an integated supply chain, in which the manufactue integates the oveall fowad and evese pocesses including manufactuing and efubishing. This can be egaded as the ideal scenaio since thee is no moal hazad and oppotunistic behavios of supply chain playes. The supply chain behaves like one entity without double maginalization issue, so we will utilize this ideal Case as a benchmak fo the decentalized supply chain model. By the integation of manufactuing and efubishing pocesses, the manufactue s pofit Π M is the same as that of the entie supply chain, and it does not have to conside the tansfe payment between pocesses. Π M S D H ( Q, Q, p ) Π ( Q, Q, p ) Π m Π [( p(1 θ) pγθ) ( u i ρθ kγθ g(1 γ) θ)] N, (11) SN S D H N H D 1 Q 1 Q Q Q 2 M 2 M D

9 Supply Chain Inventoy Models with Refubishment whee the supescipt denotes Case and Π denotes the supply chain pofit in Case. Π m and Π ae the pofits of manufactuing and efubishing pocesses in Equations (7) and (10). Note that in this fully-integated Case, the inventoy holding cost ate in the efubishing line H needs to include the oveall cost components incued in the fowad and evese supply chain flows. This is since the manufactue deals with all pocesses in a supply chain. As aleady explained in Section 3.1, thee ae two types of inventoy holding in the efubishing line. Fo the defective item to be efubished (befoe efubishment), we need to conside the costs incued in the manufactuing pocess (u + i + ρ) including etuned defective items due to the inspection failue with its popotion ρ. On the othe hand, fo the efubished item, we need to add the efubishing cost k, i.e., (u + i + ρ + k). Theefoe, by consideing these two types of inventoies, while thei inventoy holding quantities ae the same, H becomes H = h(2u + 2i + 2ρ + k). (12) Then, the optimization poblem of Case can be simply defined as: whee Π M (= Π ) is in Equation (11). Maximize Π M (Q, Q, p ), (13) Fom the fist-ode necessay conditions of Π M, we obtain the optimal Q, Q and p as functions of each othe. p p(1 ) ( Q, Q ) θ p θ Q Q ( p (1 ) g ( p ( u i) ρθ p(1 θ) 2SN ), (14) H (1 N / M ) 2SD ), and (15) H (1 D / M ) S Q HQ 2M p(1 θ ) H Q (1 θ ) θ 2M S Q k, (16) whee Φ = (1 β)ρθ, the sales etun popotion fo efund, and N and D ae functions of p in Equations (4) and (3). Due to mathematical difficulties involving thee decision vaiables, we do not show the closed-fom solutions, but we pesent the optimal solution based on a numeical example in Section 5. We will utilize the above solution as a benchmak fo the decentalized supply chain case. Case : A Decentalized Supply Chain This section consides Case, a decentalized case in a manufactue-efubishe dyadic supply chain involving moal hazad. In Case, the manufactue and efubishe ae esponsible fo thei own basic pocesses, manufactuing and efubishing, espectively.

10 Supply Chain Inventoy Models with Refubishment Theefoe, the manufactue s pofit Π M = Π m in Equation (7), and the efubishe s pofit Π R = Π in Equation (10), while the supescipt denotes Case. Fo the inventoy holding cost ate in the efubishing line H in Case, we do not have to conside the cost incued at the manufactue s end diffeently fom H in Equation (12). Fom the efubishe s pespective, the cost incued fo the item to be efubished (befoe efubishment) is only w, the wholesale pice of a defective item. Then, the unit efubishing cost k needs to be added fo the efubished item (afte efubishment), i.e., w + k. Theefoe, by consideing two types of inventoy holding cost ates similaly in Equation (12), we obtain H as a function of w. H (w) = h(2w + k). (17) In Case, both manufactue and efubishe ae only concened with thei own pofit maximization as sepaate economic entities, so Case involves the double maginalization poblem. The manufactue, the Stakelbeg leade in a supply chain, needs to devise a contact tem in ode to contol the efubishe s action. Theefoe, the poblem of Case can be chaacteized as follows. Maximize Π M (Q, w) (18) subject to Π R (Q, p Q, w) π R (19) Maximize Π R (Q, p Q, w). (20) The manufactue detemines the poduction lot size Q and the wholesale pice of defective items fo efubishment w that jointly maximize its own pofit in the objective function (18), while satisfying Constaints (19) and (20). Constaint (19) epesents the efubishe s ationality constaint. The efubishe paticipates in the contact which guaantees its minimum esevation level π R. Constaint (20) is the incentive compatibility constaint of the efubishe. The efubishe detemines the efubishing lot size Q and the sales pice of efubished item p, maximizing its own pofit, given the manufactue s decision on Q and w. By the backwad induction, we fist obtain the best esponse of the efubishe p and Q as functions of othe decision vaiables fom the fist-ode necessay conditions of Constaint (20). p p(1 ) ( Q, w) θ p θ Q ( p wθ (1 ) g 2SD, w), and (21) H (1 D / M ) p(1 θ ) H Q (1 θ ) θ 2M S Q, (22) k whee Φ = (1 β)ρθ. H is a function of w in Equation (17), while D is a function of p in Equations (3). Then, by setting Π R = π R in Constaint (19), we can chaacteize the supply contact tem w as:

11 Supply Chain Inventoy Models with Refubishment w ( Q, p ) (( p k) γ g(1 γ)) θn S D / Q ( hk / 2)(1 D / M ) Q π R. (23) θn h(1 D / M ) Q Finally, fom the fist-ode necessay condition of (18), we obtain the manufactue s decision Q. Q ( p 2SN ), (24) H (1 N / M ) whee N is a function of p in Equations (4). In the next section, we compae the pefomance of diffeent supply chain model and suggest a guideline fo the supply chain decentalization. COMPARISON OF SUPPLY CHAIN MODELS Basic Setting We show the solutions of Cases and based on the paamete values as follows. Example paametes: unit time = yea, D 0 = 10,000 units/yea, M = 30,000 units/yea, M = 20,000 units/yea, θ = 0.15, ρ = 0.2, β = 0.5, p = $800/unit, u = $500/unit, i = $50/unit, = $100/unit, k = $100/unit, g = $50/unit, h = 0.1/unit/yea, S = $100/poduction cycle, S = $100/efubishing cycle, and π R = $100,000. By putting the paamete values into the solutions of Cases and in Equations (14-16) and (21-24) and solving them simultaneously, we obtain the esults summaized in Table 2. Table 2: Optimal solutions unde the basic numeical setting ( : decision vaiable) Manufactuing pocess Refubishing pocess Case Case Poduction lot size (unit), Q * Wholesale pice of a etuned item ($/unit), w * Net inventoy depletion ate (unit/yea), N * 10, , Demand ate of a new item (unit/yea), D * 9, , Poduction cycle time (day), T * Refubishing lot size (unit), Q * Unit selling pice of a efubished item ($/unit), p * Inventoy cost ate in the efubishing pocess ($/unit/yea), H * Pofits Refubishing popotion (faction), γ * Demand ate of a efubished item (unit/yea), D * Refubishing cycle time (days), T * Supply chain s pofit ($/yea), Π * 1,559,808 1,551,165 Manufactue s pofit ($/yea), ΠM * 1,559,808 1,451,165 Refubishe s pofit ($/yea), ΠR * - 100,000

12 Supply Chain Inventoy Models with Refubishment In Table 2, the decisions in the manufactuing pocess look vey simila between Cases and, while Q > Q and D > D. Howeve, we can obseve that thee ae significant diffeences in the decisions of the efubishing pocess between Cases and. One main eason is because diffeent supply chain stuctues induce diffeent decisions on the selling pice of the efubished item p *. In the coodinated Case, the manufactue deals with both new and efubished items. Theefoe, the manufactue needs to potect the fist-maket sales of the highe-magin new item by setting p * elatively highe, i.e., p > p, and D > D. On the othe hand, it is ational fo the thid-paty efubishe to facilitate the second-maket sales of the efubished item in Case to maximize its own pofit, while not consideing the oveall pofit pefomance of the supply chain, i.e., γ > γ and D > D. It is inteesting to obseve that the oppotunistic behavio of the efubishe lowes the selling pice of the efubished item, while the coodinated supply chain maintains the highe selling pice. This is diffeent fom a typical view that the decentalized system sets the sales pice highe due to moal hazad and double maginalization. In a closed-loop supply chain, we need to caefully conside inteaction between new and efubished items and decision dynamics involving channel conflicts. The othe diffeentiating facto is the inventoy holding cost ate in the efubishing line H *. As aleady shown in Equations (12) and (17), the cost components included in the inventoy holding cost ae diffeent with espect to the supply chain stuctue. In Case, the contact tem w is included, while the manufactue sets w low in ode to contol the efubishe s action in (19) and (23). It allows the thid-paty efubishe to maintain the lowe inventoy holding cost, i.e., H < H in Table 2. Consequently, it esults in the oveall diffeences in the efubishing line opeations, i.e., Q > Q, and T > T. Oveall, the stuctual diffeence between Cases and make these diffeences explained above, and these allow the thid-paty efubishe in Case to maintain the bette pefomance in the efubishing pocess, including the highe sales pefomance in the second maket but also less efubishing setups. Howeve, we need to note that the oveall pofit pefomance in the coodinated Case is supeio to the uncoodinated Case, i.e., Π > Π. Compaative Static Analysis We investigate the equilibium behavios in Cases and with espect to envionmental changes. We focus on impotant paametes, while inceasing them seven times, ceteis paibus as in the basic numeical setting, as: π R in [40000, ], D 0 in [8500, 11500], p in [770, 830], u in [470, 530], k in [70, 130], g in [20, 80], θ in [0.12, 0.18], ρ in [0.11, 0.29], and β in [0.2, 0.8]. Table 3 summaizes the equilibium behavios, including the ange of each esult with the change diection. It eads as follows. Fo example, in the ow Case Q * and the column u [470, 530], we can find ( ). It indicates that the poduction lot size of Case (Q ) deceases ( ) fom the maximum of 270 units to the minimum of 253 units ( ) as the unit poduction cost of a new item u inceases fom $470/unit to $530/unit ([470, 530]). The esults in Table 3 can be summaized as follows. The elationships shown in Table 2 always hold at all paamete settings. Specifically, Case maintains the lage demand equests and lot size in the manufactuing pocess, i.e., D > D and Q > Q, while Case yields those lage in the efubishing pocess, i.e., D > D, and Q > Q. The sales pice of the efubished item sets highe in

13 Supply Chain Inventoy Models with Refubishment Case, i.e., p > p. The supply chain can be bette off when the supply chain is integated by the manufactue, i.e., Π > Π. The changes in π R, p, u, ρ and β diffeentiate the equilibium behavios of Cases and (see the supescipt in Table 3), while the behavios ae the same with espect to the changes in D 0, k, g and θ. When the efubishe s bagaing powe inceases, insisting the highe pofit (inceasing π R), the manufactue needs to decease the contact tem w in Case, while thee is no effect in Case. Then, it makes p highe and subsequently D less. It is inteesting to see that woking with the efubishe with stonge bagaining powe lets the oveall supply chain be bette off, while damaging the manufactue pofit (inceasing Π, while deceasing Π M since Π M = Π Π R with Π R = π R). An incease of Π is because a decease in D allows D of the new item to incease, which yields the highe magin. An incease in the demand base of the fist maket (inceasing D 0 ) makes oom fo also inceasing D * by deceasing p *, egadless of the supply chain stuctues. Then, these lead to inceases in the lot sizes in both poduction and efubishing lines. All supply chain stuctues benefit fom this positive change (inceasing Π and Π ). An incease in the sales pice of a new item p induces that of a efubished item p * also to incease in both Cases and. Howeve, because the elative magnitude of its change is diffeent in each case, the behavios of D * ae diffeent (deceasing D, while inceasing D ), while it also induces the diffeences in the manufactuing pocess opeations between two cases. The supply chain is bette off by an incease in p in both Cases and. An incease in the poduction cost u affects the oveall decisions in Case since it needs to be consideed in estimating the inventoy holding costs in both manufactuing and efubishing lines as shown in Equations (6) and (12). Howeve, the efubishing line is not affected by u in Case as we can see in Equation (17). Theefoe, D is fixed since D is not affected by u in Case. It is inteesting to obseve that the equilibium behavios of vaiables ae totally opposite with espect to the changes of efubishing cost k and scap cost g, while inceases in both costs k and g deteioate Π * egadless of supply chain stuctues. Note that efubishment educes the losses fom scap, while scap educes the oppotunity savings fom efubishment. Theefoe, an incease in g makes k evaluated elatively less, vice vesa. As defects incease (inceasing θ), p * deceases in both Cases and because the second-maket sales D * need to be facilitated. Then, an incease in D * deteioates the fistmaket sales D *. Oveall, an incease in defect poduction damages supply chain pofit Π *, egadless of supply chain stuctues. An incease in the inspection failue (inceasing ρ) damages the supply chain (deceasing Π * ) by aising the sales etuns and extenal failue costs. On the othe hand, an incease in the exchange equests (inceasing β) can enhance Π * by educing the evenue loss fom efund (deceasing 1 β). Given the defective poduction (fixed θ), an incease in ρ induces the smalle Q * due to a decease in the net depletion ate in poduction line N *, while the lage Q * is induced by an incease in β and a subsequent incease in N *. Oveall, it is impotant not only to embace an integate view of the decision stuctue in a closed-loop supply chain but also to undestand diffeent chaacteistics of vaious supply chain stuctues. As we can see above, any envionmental change has an influence ove the entie supply chain by changing the inteaction between supply chain playes. Moeove, we need to note again that the supply chain stuctue can have an impotant ole in diffeentiating the oveall pefomances of a closed-loop supply chain.

14 Supply Chain Inventoy Models with Refubishment Table 3: Summay of equilibium behavios (Note: min-max(change diection); : incease, : decease, -: fixed; : diffeent behavios between Cases and ) Incease in: πr D0 p u k g θ ρ β Case Va. [40000,160000] [8500,11500] [770,830] [470,530] [70,130] [20,80] [0.12,0.18] [0.11,0.29] [0.2,0.8] Q * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) N * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) D * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Q * 32-32(-) 29-34( ) 31-32( ) 32-32( ) 31-33( ) 31-32( ) 27-36( ) 31-32( ) 31-32( ) p * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) γ * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) D * (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Π * (1k) (-) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Q * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) w * ( ) 51-71( ) 55-70( ) 62-62(-) 49-76( ) 47-79( ) 46-74( ) 62-63( ) 62-63( ) N * ( ) ( ) ( ) (-) ( ) ( ) ( ) ( ) ( ) D * ( ) ( ) ( ) (-) ( ) ( ) ( ) ( ) ( ) Q * ( ) 80-86( ) 80-86( ) 83-83(-) 81-85( ) 76-91( ) 79-87( ) 83-83( ) 83-83( ) p * ( ) ( ) ( ) (-) ( ) ( ) ( ) ( ) ( ) γ * ( ) ( ) ( ) (-) ( ) ( ) ( ) ( ) ( ) D * ( ) ( ) ( ) (-) ( ) ( ) ( ) ( ) ( ) Π * (1k) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

15 Supply Chain Inventoy Models with Refubishment Effect of the Refubishe s Capability The esults in Tables 2 and 3 demonstate a typical situation that the integated supply chain (Case ) yields a supeio pofit pefomance to the decentalized system (Case ), i.e., Π > Π. Note that, howeve, this is based on the same paamete settings. In a contempoay business envionment, we can obseve many fims which possess advantages in cost, quality and/o technological expetise by focusing on thei coe pocesses while outsoucing othes. Theefoe, nowadays, many functions and pocesses ae decentalized to the specialized patnes possessing thei own advantages, and thus we ae now unning ou businesses based on a supply chain. In this section, we conside the thid-paty efubishe s possible cost advantages in defect disposition, including efubishing efficiency and envionmental capability, which can be indicated by unit efubishing cost k and unit scap cost g. Then, we eveal the conditions unde which the decentalized supply chain (Case ) can achieve the same pofit pefomance as the coodinated supply chain (Case ), i.e., Π = Π. Table 4: Compaison of decentalized cases, including Cases -K and -G achieving the coodinated pofit pefomance ( : decision vaiable) Case with fixed k and g Case -K with vaiable k Case -G with vaiable g Refubishe s capability Manufactuing pocess Unit efubishing cost ($/unit), k Unit scap cost ($/unit), g Poduction lot size (unit), Q * Wholesale pice of a etuned item ($/unit), w * Net inventoy depletion ate (unit/yea), N * 10, , , Demand ate of a new item (unit/yea), D * 9, , , Refubishing pocess Poduction cycle time (day), T * Refubishing lot size (unit), Q * Unit selling pice of a efubished item ($/unit), p * Refubishing inventoy cost ate ($/unit/yea), H * Refubishing popotion (faction), γ * Demand ate of a efubished item (unit/yea), D * Pofits Refubishing cycle time (days), T * Supply chain s pofit ($/yea), Π * 1,551,165 1,559,808 1,559,808 Manufactue s pofit ($/yea), ΠM * 1,451,165 1,459,808 1,459,808 Refubishe s pofit ($/yea), ΠR * 100, , ,000 We utilize the basic paamete settings in Section 5.1, while letting eithe k o g a vaiable (oiginally k = $100/unit and g = $50/unit). Let Cases -K and -G denote Case with vaiables k and g, espectively. We can find eithe k o g achieving the coodinated pofit pefomance of Case by simultaneously solving Equations (21-24) along with the additional

16 Supply Chain Inventoy Models with Refubishment condition Π = Π = $1,559,808/yea in Table 2 (o Π M = Π Π R = $1,459,808/yea with Π R = π R = $100,000/yea). The esults ae summaized in Table 4. Figues 2(a) and 2(b) also illustate the behavios of supply chain pofits in Cases -K and -G with espect to the changes in k and g, espectively, along with Π in Case at fixed k and g fo compaison. Table 4 indicates that the caeful assessment of the efubishe s capability is impotant to enhance pofitability, i.e., Π -K* = Π -G* > Π. Specifically, to achieve the coodinated esult, i.e., Π -K* = Π -G* = Π, the thid-paty efubishe needs to be efficient enough to handle the efubishing activity at unit cost k = $85.63/unit, o it needs to have envionmental capabilities to scap each defective item at g = $41.46/unit. Moe inteestingly, Figues 2(a) and 2(b) also indicate that the supply chain can be bette off even in the decentalized supply chain stuctue than in the integated system. This happens if the manufactue can sign a contact with the efubishe which is capable of maintaining eithe k o g less than each theshold of k = $85.63/unit (see Figue 2(a)) o g = $41.46/unit (see Figue 2(b)). Figue 2: Compaison of supply chain pofit Π * among Cases -K, -G and ( : Case -K (Case with vaiable k); : Case -G (Case with vaiable g); : Case (at fixed k = $100/unit and g = $50/unit)). (a) Π -K* (1k) in k and Π (1k) (b) Π -G* (1k) in g and Π (1k) The focal company needs to thooughly assess coe capabilities of supply chain patnes fom the caeful ationalization and selection pocesses, and it should evaluate possible inefficiencies in a closed-loop supply chain in ode to ceate a synegy in an enabling coopeative envionment. It is also impeative fo a closed-loop supply chain not only to undestand that the evese pocess can ceate a value steam, not a nuisance, but also to have an integated pespective in ode to closely coodinate the fowad and evese flows (Guide and Van Wassenhove 2006). CONCLUDING REMARKS This study investigated a closed-loop supply chain, consisting of a manufactue esponsible fo the fist-maket sales of a new item and a thid-paty efubishe esponsible fo the secondmaket sales of a efubished item. We then intoduced two diffeent supply chain models with

17 Supply Chain Inventoy Models with Refubishment diffeent stuctues, and evealed thei distinct chaacteistics. The implications we obtained though the investigation can be summaized as follows. Fist, the demand and poduction lot size of a new item ae yielded lage in the integated supply chain than in the decentalized one. Second, the sales pice of a efubished item is set lowe in the decentalized system. This is since the thid-paty efubishe intends to boost up the second-maket sales, while the manufactue needs to potect the fist-maket sales of the highe-magin new item. It is inteesting to obseve that the oppotunistic behavio of the efubishe lowes the selling pice of the efubished item, while the coodinated supply chain maintains the highe selling pice. This is diffeent fom a typical view that the decentalized system sets the sales pice highe due to moal hazad and double maginalization. In a closedloop supply chain, we need to caefully conside inteaction between new and efubished items and decision dynamics involving channel conflicts. Thid, the decentalized supply chain maintains the lage lot size and cycle time in the efubishing line. This is mainly because the cost components included in the inventoy holding cost ae diffeent with espect to the supply chain stuctue. The manufactue sets the wholesale pice low in ode to contol the efubishe s action. It allows the thid-paty efubishe to maintain the lowe inventoy holding cost. Fouth, when the efubishe s bagaing powe inceases, the sales pice of the efubished item inceases. It is inteesting to see that woking with the efubishe with stonge bagaining powe lets the oveall supply chain be bette off, while damaging the manufactue pofit. Fifth, an incease in the demand base of the fist maket makes oom fo also inceasing the secondmaket sales by deceasing the sales pice of the efubished item, egadless of the supply chain stuctue. Then, these lead to inceases in the lot sizes in both poduction and efubishing lines. All supply chain stuctues benefit fom this positive change. On the othe hand, an incease in the sales pice of the new item induces that of the efubished item also to incease and lets the supply chain bette off, egadless of the supply chain stuctue. As defects incease, the sales pice of the efubished item deceases in both stuctues because the second-maket sales need to be facilitated, while this change deteioates the fist-maket sales. Finally, the caeful assessment of the efubishe s capability is impotant to enhance pofitability and achieve the coodinated esult in the decentalized system. The focal company needs to thooughly assess coe capabilities of supply chain patnes fom the caeful ationalization and selection pocesses, and it should evaluate possible inefficiencies in a closed-loop supply chain in ode to ceate a synegy in an enabling coopeative envionment. We aim to contibute to the body of knowledge and supply chain pactices by evealing unique chaacteistics of diffeent supply chain stuctues and by poviding impotant implications. REFERENCES Anily, S. (1995). Single-machine lot-sizing with unifom yields and igid demands: Robustness of the optimal solution. IIE Tansactions, 27(5), Aas, N., Güllü, R., & Yüülmez, S. (2011). Optimal inventoy and picing policies fo emanufactuable leased poducts. Intenational Jounal of Poduction Economics, 133(1), Cheng, T. C. E. (1991). An economic ode quantity model with demand-dependent unit poduction cost and impefect poduction pocess. IIE Tansactions, 23(1),

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