Returnable packaging management in automotive parts logistics: Dedicated mode and shared mode

Int. J. Production Economics 168 (2015) 234–244

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Returnable packaging management in automotive parts logistics: Dedicated mode and shared mode Qinhong Zhang a,n, Anders Segerstedt b, Yu-Chung Tsao c, Biyu Liu d a

Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030, PR China Industrial Logistics, Luleå University of Technology, 97187 Sweden c Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan R.O.C d School of Economics and Management, Fuzhou University, Fuzhou 350116, PR China b

art ic l e i nf o

a b s t r a c t

Article history: Received 10 September 2014 Accepted 28 June 2015 Available online 9 July 2015

We compare two different modes, i.e., dedicated mode and shared mode, used in packaging management in automotive parts logistics. In dedicated mode, every parts supplier uses his own packaging; while in shared mode, packages can be shared among the suppliers. For each mode, we calculate the total costs consisting of transportation cost and inventory holding cost, and prove that the total costs, the transportation cost and the inventory holding cost are all smaller under shared mode. We further illustrate the factors that influence the cost savings of shared mode, i.e., the total cost of dedicated mode minus that of shared mode. In particular, the cost savings are proved to be negatively related to the number of package categories, and are positively related to: (1) the demand gap of packages between areas, i.e., sum of the volume difference of every kind of packages that transported in and out of one area; (2) the failed ratio factor of the returned packages, i.e., the ratio of the packages that cannot be returned to the supplier because of broken, pilferage, misplace, etc.; and (3) the time savings of short distance transportation, i.e., the transportation time consumed between areas minus the transportation time within one area. Finally, numerical examples show that the cost savings can be considerable, and the number of package categories is the most important influence factor. & 2015 Published by Elsevier B.V.

Keywords: Automotive parts logistics Returnable logistics packaging Transportation cost Inventory holding cost

1. Introduction In automotive parts logistics, returnable plastic or metal packages (including pallets, containers, racks) are used by most of the companies. Compared to disposable packages, returnable packages, because of their longer lifetime, can reduce the total amount of packages that needed, which is more environmentally friendly and better from the point view of sustainability. However, returnable packages may have higher costs of procurement, transportation, and other costs caused by cleaning, repairing, storage and management, etc. Moreover, the supply uncertainty caused by damage, theft, or misplacement, also incurs some costs and affects the supply of parts. Therefore, returnable packages management is an important issue in automotive parts logistics, especially for the automotive industry facing cost reduction pressure due to higher competition and lower profit margin. Two different modes are used in managing the returnable packages: (1) shared mode (or buyer-managed mode), which means the assembler owns the packaging and the packaging can

n

Corresponding author. Tel.: þ 86 21 62932393; fax: þ86 21 62932117. E-mail address: [email protected] (Q. Zhang).

http://dx.doi.org/10.1016/j.ijpe.2015.07.002 0925-5273/& 2015 Published by Elsevier B.V.

be shared between the suppliers; and (2) dedicated mode (or vendor-managed mode) which means suppliers own packages themselves and no package can be shared between suppliers. In China, Shanghai General Motor (SGM) uses shared mode, and has a branch called Container Management Center (CMC) to design, procure and manage the containers. While Dongfeng–Nissan (a joint venture automaker) and the other assemblers use dedicated mode, and pay packaging cost to the suppliers who are in charge of procuring and managing the packages. In Sweden, automotive assemblers Scania and Volvo also use shared mode in managing packages. In particular, Volvo Logistics Corporations is in charge of managing the packages for Volvo, and an information system called VEMS is used to support the management of the packages. Dedicated mode has its merits of easy managing, while shared mode is better in reducing safety stock and damages of packages. In specific, when dedicated mode is used, every supplier needs to hold its own safety stock of packages and the empty packages are easily got lost or misplaced; while for shared mode, since the packages are centrally managed, the risk pooling effect can reduce the total safety inventory, and misplacement or lost is reduced. However, in shared mode, information system and collaborations between suppliers and assemblers are necessary, and additional management costs are usually incurred.

Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

Practical cases give more insights about the comparison of the two modes. SGM is reported to be better in managing packages after replacing dedicated mode by shared mode from 2003. In contrast, for one assembler using dedicated system, many of its parts suppliers begin to complain the bad performance of the packaging management, like rude unloading/loading, collapsing, lost, damage, misplacement, not timely return, etc. Even though shared mode seems to be better, it is still need to be proved theoretically and more questions should be answered, including what is the cost gap between the two modes? What are the main factors that influence the cost gap? The quantitative analysis is essential since shared mode is more difficult in administration and has higher information system requirements. In this paper, based on a real project, we try to propose a simple model to calculate the logistics costs of shared and dedicated modes and, by comparing the costs, address the cost differences between the two modes. The rest of this paper is organized as follows. In Section 2, we summarize some related literature. In Section 3, we list the notation and describe the two modes. Section 4 and Section 5 propose the costs of the shared mode and the dedicated mode, respectively. We compare the two modes in Section 6. Section 7 presents the numerical examples. The conclusions are discussed in the last Section.

2. Literature The benefits and disadvantages of returnable packages are the first issues when a company wants to replace disposable packages by returnable packages. The main benefits, as argued by Leite (2009), are better product protection, decreased cost, legislation and environmental benefits, etc. These benefits have also been addressed by Silva et al. (2013), with a case, and Accorsi et al. (2014) who further discussed both the economic and environmental assessment of the reusable plastic containers based on a food catering supply chain. The disadvantages, on the other hand, include the transportation costs, flow management, reception, cleaning, repair, storage, and capital invested, etc. Ilic et al. (2009), and Mason et al. (2012) discussed the loss of returnable containers because of damage, lost, misplacement, and other costs. When comparing the two sides of the same coin, as argued by Leite (2009), the benefits usually exceed the disadvantages. Therefore there is a global trend of using returnable packaging instead of disposable packaging (Twede and Clarke, 2005). When returnable packages are used the management is a challenge, and some papers addressed such issues, mainly from the operational level. For example, Duhaime et al. (2001) carried out a case study to evaluate the system of collection and distribution of returnable packaging for Canada Post and its large mailing customers. Hellström and Johansson (2010) discussed the control strategies of the returnable packaging by simulations based on the case of a Swedish food company. Buchanan and Abad (1989) studied the

235

inventory control problem for containers and considered the returns in a given period as a stochastic function of the number of containers in the field. Kim et al. (2014) also discussed the influence of the stochastic return times on the total cost of closed loop of the perishable products. Chew et al. (2002) developed performance measures to monitor and control the deployment of containers. Das and Chowdhury (2012) proposed a mixed-integer linear programming framework and model for the design and management of reverse network for collection and recovery of products, and the method and approach proposed are very applicable for recovery and collection of packages as well. In order to improve the efficiency and reduce the mistakes happened in allocating the packages, RFID is proposed by some articles. See Johansson and Hellström (2007), Hellström (2009), and Kim and Glock (2014), for example. Our work supplements the above mentioned literature by comparing the costs of the whole system under two different modes. In contrast, the previous literature usually set the system as given and focused mainly on some parts of the packaging management system. The article that is more similar to this paper is Lützebauer (1993) who distinguished three types of systems that used to manage the empty packaging, i.e., switch pool systems, systems with return logistics, and systems without return logistics. Further, Kroon and Vrijens (1995) gave a case to show how to design the returnable packaging system according to the classification. However, the above classification mainly focused on the ownership of the packaging; while in this paper, we consider mainly on whether the packaging can be shared between suppliers; and it is easy to find that, the dedicated mode belongs to the switch pool system, while the shared mode belongs to the system with return logistics. In addition, we discuss the differences of the two modes by quantity models.

3. Assumptions and notation As a benchmark, we consider a production network consisting of two assembly factories and many parts suppliers located nearby each assembly factory. Our model can be easily extended to the case of n assembly factories. However, considering the complexity of notation, we just illustrate the two assembly factories case. As shown in Fig. 1, for the dedicated mode, packages filled with parts are transported from suppliers to the assembly factories by milk-run or/and through distribution center or by direct delivery. When parts are unloaded in the assembly factories, the packages are collected, sorted, collapse, and returned to the suppliers by the trucks that are assigned to fetch the parts. When the trucks arrive to the suppliers, the empty packages are unloaded and then cleaned and repaired by the suppliers. In the dedicated mode, the suppliers own the packages, and thus one supplier can use only his own packages, which cannot be shared among suppliers.

Fig. 1. The flows of packages in automotive parts logistics.

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Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

For the shared mode, the transportation of the packages filled with parts is the same as the dedicated mode. However, after unloading the parts at the assembly factories, the empty packages are transported to the container centers, which usually locate near assembly factories. The empty packages are transported to the suppliers by the trucks assigned to fetch parts. The packages are owned and managed by the assembler and can be used by any supplier if the package is suitable. It is worth pointing out that Fig. 1 only demonstrates the framework of the packages flows, the specific processes of the parts logistics are more complex and mainly conducted by third party logistics (3PL). Take one assembler in China for example, for the suppliers nearby, the 3PL usually uses direct delivery or milk run to transport the parts from suppliers to assembly factories. While for the suppliers located far away, the 3PL usually uses milk run to fetch the parts with mid size trucks and then reloaded the parts to larger trucks in the distribution center and then transports the parts to the assembly factories. The following notation is used in this paper. I; J: assembly factories located in area I and area J, respectively. Si : suppliers located near assembly factory I, i ¼ 1; 2; …; M. Sj : suppliers located near assembly factory J, j ¼ 1; 2; …; N. lIJ : distance between the container management centers located in area I and area J. lIi ; lJj : distance from supplier i to factory I, and distance from supplier j to factory J. ct : transportation cost rate (per unit distance per unit). hi ; hj :holding cost (per unit per unit time) of the packages of supplier i and supplier j, including inventory holding cost and depreciated cost. DIi ; DJi : demand rate (demand per unit time) of supplier i from factories I and J. TSC i ; TLC i : logistics cycle time of supplier i to factories I and J, respectively. Q Ii ; Q Ji : average order quantity (in unit) of supplier i from factories I and J. DIj ; DJj : demand rate (in unit) of supplier j from factories I and J. TSC j ; TLC j : logistics cycle time of supplier j to factories I and J, respectively. Q Ij ; Q Jj : average order quantity (in unit) of supplier j from factories I and J. αsi ; αli : ratio of the packages that cannot return to the supplier because of broken, pilferage, misplace, etc. That is, supplier i gets ð1  αsi ÞQ Ii packages returned from factory I, and αsi is a stochastic variable with value range be ½0; 1. For simplicity, we assume that the ration is mainly affected by the travel distance. In particular, we let αsi follow a normal distribution Nðμs ; σ s Þ truncated at lower bound 0 and upper bound 1. We use “s” and “l” to denote the “short distance” and “long distance”. We also let all the packages in short distance have the same return ratio, that is αsi and αsj have the same distribution with mean μs and variance σ 2s ; while αli , αlj have identical distribution with mean μl and variance σ 2l . IP i ; IP j : pipeline inventory of packages for supplier i and supplier j. ISi : safety inventory of the packages for supplier i and supplier j. β: service level (same for all suppliers), i.e., the probability that the supply of the packages is no less than the demand in one replenishment cycle.

4. Costs of the dedicated mode The costs consist of holding cost and transportation cost. Here, holding cost includes depreciation cost and inventory holding cost of the packages. The depreciation cost equals to the value of

procurement cost divided by the lifetime, which means linear depreciation. Hence, the holding cost is linear in the quantity. In the following, we first derive one supplier's total cost per unit time, and then we calculate the total costs of all suppliers. 4.1. Holding costs For supplier i, the needed packages include two parts: pipeline inventory to satisfy the average demand and safety inventory to hedge the uncertainty of the returned packages. 4.1.1. Pipeline inventory of the packages For pipeline inventory, according to Little's law, we have IP i ¼ DIi TSC i þ DJi TLC i :

ð1Þ

In Eq. (1), DIi TSC i is the quantity of the packages needed to supply factory I, and DJi TLC i is for factory J. In practice, TSC i is the cycle time spent in short distance, which consists of three parts: transport time from supplier to the assembler, TSF i , waiting time spending in the assemble factory, TW i , and return time from the assembler to the supplier for empty packages, TSRi . It is similar for TLC i . Hence, we have TSC i ¼ TSF i þTW i þ TSRi ;

ð2Þ

and TLC i ¼ TLF i þ TW i þ TLRi

ð3Þ

Then we can transfer Eq. (1) to IP i ¼ DIi ðTSF i þ TW i þTSRi Þ þ DJi ðTLF i þ TW i þTLRi Þ:

ð4Þ

It is obvious that if the demand or the cycle time is larger, the supplier should prepare more packages. In practice, the demand is determined by the production plan of the assembler, and it is usually deterministic in a short time range, like one month. However, since supplier i locates near factory I, the cycle time TSC i is smaller and thus the supplier needs fewer packages. In contrast, TLC i is larger and thus more packages are needed. Since the distance is same for “forward” and “return” transportation, we can assume TSF i ¼ TSRi and TLF i ¼ TLRi . Let TSF i ¼ TSRi ¼ TSi , TLF i ¼ TLRi ¼ TLi , then we have the pipeline inventory of supplier i IP i ¼ DIi ð2TSi þ TW i Þ þ DJi ð2TLi þ TW i Þ:

ð5Þ

4.1.2. Safety inventory of the packages Since the demand for the parts is deterministic in short time range, the uncertainty is mainly caused by the unreliability of returned empty packages because of damage, theft or misplacement. The unreliability of returned packages has been addressed in many papers; see Kim et al. (2014), and Buchanan and Abad (1989), Glock and Kim (2015) for example. In practice, the unreliability of returned packages is also the suppliers' main concerns. For supplier i, safety stock of packages should be placed to hedge this risk. Since the trucks take empty packages to the suppliers when they fetch parts, the safety inventory is used to hedge the supply risk between the two consequent replenishments. Given the service level and the uncertainty of returned packages, the safety inventory of packages is determined by
 Pr ð1  αli ÞQ Ji þ ð1  αsi ÞQ Ii þ ISi Z Q Ji þ Q Ii ¼ β: ð6Þ In the above equation, ð1  αli ÞQ Ji þ ð1  αsi ÞQ Ii is the returned packages from assemble factory J and I; ISi is the safety inventory; Q Ji þ Q Ii is the demand of the packages for the next replenishment. Eq. (6) can be simplified to
 Pr αli Q Ji þ αsi Q Ii rISi ¼ β: ð7Þ

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Since we assume αsi  N ðμs ; σ 2s Þ, αli  N ðμl ; σ 2l Þ, and αsi is independent of αli , then we have   ð8Þ αli Q Ji þ αsi Q Ii  N μs Q Ii þ μl Q Ji ; Q 2Ii σ 2s þ Q 2Ji σ 2l

þ

N
X

 ct lJj DJj þ lIj DIj j¼1

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ hj Φ  1 ðβÞ Q 2Jj σ 2s þQ 2Ij σ 2l þ μs Q Jj þ μl Q Ij #

Let y ¼ αli Q Ji þ αsi Q Ii , and F t ðyÞ be the CDF of y, then Eq. (7) is equivalent to F t ðISi Þ ¼ β, which means ISi ¼ F t 1 ðβÞ

237

þ DJj ð2TSj þ TW j Þ þ DIj ð2TLj þ TW j Þ

ð15Þ

ð9Þ 5. Packaging cost of shared mode

The safety inventory can also be expressed by standard normal distribution qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10Þ ISi ¼ Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μs Q Ii þ μl Q Ji ; where Φð:Þ is the CDF of standard normal distribution. Hence, for supplier i, the total holding cost of the packages is  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CH i ¼ hi ðI si þI pi Þ ¼ hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μs Q Ii  þ μl Q Ji þ DIi ð2TSi þ TW i Þ þ DJi ð2TLi þ TW i Þ :

ð11Þ

4.2. Transportation cost The transportation cost for filled packages are the same for both modes, and these costs are in fact the cost of parts logistics. Hence, we just consider the transportation cost of the empty packages, i.e., the returned packages. For supplier i, the transportation cost per unit time for the packages is

CT i ¼ ct lIi DIi þlJi DJi : ð12Þ From Eq. (12) we can see that the transportation costs are independent on order quantities. The total cost of supplier i is  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

TC i ¼ CT i þ CH i ¼ ct lIi DIi þ lJi DJi þhi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μs Q Ii  þ μl Q Ji þDIi ð2TSi þ TW i Þ þ DJi ð2TLi þ TW i Þ

ð13Þ

We have proposition 1 to summarize the conclusions. Proposition 1. In dedicated mode, the cost of packages per unit time for a supplier is decided by Eq. (13). The cost is positively related to the demand rates DIi ; DJi , the transportation cycle time 2TSi þ TW i , the order quantities Q Ii , the mean and the variance of the failed return factor μs ; μl ; σ 2s ; σ 2l , and the distances lJj ; lIJ . Similarly, for the suppliers located nearby factory J, we have  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

TC j ¼ CT j þ CH j ¼ ct lJj DJj þ lIj DIj þhj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μs Q Jj  þ μl Q Ij þDJj ð2TSj þ TW j Þ þ DIj ð2TLj þ TW j Þ :

ð14Þ

4.3. Total cost of the system M N P P TC i þ TC j , which The total cost of all suppliers is, TCS ¼ i¼1 j¼1 can be simplified to  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M  X

TCS ¼ ct lIi DIi þ lJi DJi þ hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l i¼1

þμs Q Ii þ μl Q Ji þ DIi ð2TSi þ TW i Þ þ DJi ð2TLi þ TW i Þ



Under shared mode, the assembler owns and manages all of the packages, and some packages can be shared among suppliers. However, since parts are different in sizes, shapes or weights, different packages may still be needed. In this section, we assume that the assembler should offer K kinds of packages to satisfy all of the suppliers, and K o M þN to denote the sharing effect. Then we can divide the suppliers into K groups, i.e., G1 ; G2 ; …; GK , and the suppliers in the same group can share the packages. The suppliers in the same group may locate in both area I and area J. Without loss of generality, we can number the suppliers of group 1 in area I from 1 to gs1 , that is supplier i; i ¼ 1; 2…gs1 , belongs to group 1. Similarly, the suppliers of group 2 in area I are numbered from i ¼ gs1 þ 1 to i ¼ gs2 ; the suppliers in the last group, group k, are numbered from i ¼ gs k  1 þ 1 to i ¼ gs k . The suppliers in area J are similarly numbered. Take group 1 for example, the suppliers of group 1 in area J are numbered from j ¼ 1 to j ¼ gl1 . Here, gs k þ gl k ¼ M þ N, is the total number of the suppliers. 5.1. Holding cost 5.1.1. Pipeline inventory Since different groups have different packages, we calculate the amount of the packages group by group. For shared mode, some of the packages that shipped from area I to the assembly factory J can be used directly by the suppliers in area J, and need not to be returned. Hence, the cycle time of these packages are reduced by eliminating the return time. However, since the demands of the packages are not balanced between the areas, some of the empty packages should be returned. In this section, we use superscript “b” to denote shared mode (also called buyer-managed mode), i.e., IP bi is the pipeline inventory for supplier i in area I in shared mode. The pipeline inventory of supplier i and j is IP bi ¼ DIi ð2TSi þ TW i Þ þ DJi ðTLi þ TW i þTSi Þ:

ð16Þ

and

IP bj ¼ DJj ð2TSj þ TW j Þ þ DIj TLj þ TW j þ TSj :

ð17Þ

where TSi , TW i and TLi have the same meanings as in dedicated mode. In Eq. (16), DIi ð2TSi þ TW i Þ is the pipeline inventory caused by the demand of the local assembly factory, and DJi ðTLi þ TW i þ TSi Þ is the pipeline inventory caused by the demand of the other assembly factory. Compared with Eq. (5), we can find that the only changed part is from “TLi ” to “ TSi ”. That is, the empty packages are returned from the local center rather than the remote center of the other area. For a group, the demands between the two assembly factories may be unbalanced. Hence, some empty packages should be transported between the package management centers. For group k ðk ¼ 1; 2:::KÞ, the quantity is

X

gsk glk X

b

IP kt ¼ DJi  DIj

TL: ð18Þ

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 where TL is the transport time between the centers. Eq. (18) means that the parts transported out of area I (or J) are more than

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Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

that transported in. Hence, the surplus empty containers should be returned to area I (or J). For group k, the quantity of packages is gsk X

IP bk ¼

glk X

IP bi þ

i ¼ gsk  1 þ 1

IP bj þ IP bkt :

gsk X



glk X

DIi ð2TSi þTW i Þ þ DJi ðTLi þ TW i þ TSi Þ

gsk X





 DJj ð2TSj þ TW j Þ þ DIj TLj þ TW j þ TSj

IP ¼

DIi ð2TSi þTW i Þ þ DJi ðTLi þ TW i þ TSi Þ

N  X



ð26Þ

ð27Þ

That is pffiffiffiffiffi ISbk ¼ Φ  1 ðβÞ Ak σ s þ μs Ak : ð21Þ

5.1.2. Safety inventory When packages are shared, we assume that the transportation of empty packages between the package centers is reliable. The rationality of this assumption can be explained by the following two facts: (1) fewer empty packages should be transported between areas under shared mode; (2) the empty packages are transported only between the two packages centers, which reduces the mistakes caused by wrong transportation destination or quantity. Further, if we relax this assumption the analysis is very complex if not impossible. However, since the transportation of empty packages within one area is similar to that under dedicated mode, we assume that the uncertainty is not changed. For group k, the packages are returned to the two centers, and thus the quantity of returned packages is glk X

ð1  αsi ÞQ Ii þ

i ¼ gsk  1 þ 1



1  αsj Q Jj :

ð22Þ

j ¼ glk  1 þ 1

The first term is the returned packages from the local suppliers of area I, and the second term is the returned packages from the local suppliers of area J. For the given service level, we have 8 gsk glk < X X

Pr ð1  αsi ÞQ Ii þ 1 αsj Q Jj :i ¼ gs þ 1 j ¼ glk  1 þ 1 k1 9 gsk glk = X X b Q Ii þ Q Jj ¼ β: ð23Þ þ ISk Z ; i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

In the above equation, the demand of empty packages is gsk glk gsk P P P Q Ii þ Q Jj , where Q Ii is the demand that i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

center I must satisfy, and

glk P j ¼ glk  1 þ 1

Q Jj is the demand center J must

ð28Þ

Then, the total safety inventory for all groups is K X

satisfy.

Q Jj :

j ¼ glk  1 þ 1

gsk glk P P αsi Q Ii þ αsj Q Jj , then we have Let x ¼ i ¼ gs þ 1 j ¼ glk  1 þ 1 k1 ( ) b xμ A ISk  μs Ak ffiffiffiffiffi Pr pffiffiffiffiffis k r p ¼ β: Ak σ s Ak σ s



 DJj ð2TSj þ TW j Þ þ DIj TLj þTW j þ TSj



gsk glk K

X X X

: D  D þ TL Ji Ij

j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1

i ¼ gsk  1 þ 1

glk X

Q Ii þ

i ¼ gsk  1 þ 1

ð20Þ

j¼1

gsk X

ð25Þ

i¼1

k

þ

¼

M  X

gsk X

Ak ¼

Then we have the total pipeline inventory IP bk



αsj Q Jj  N μs Ak ; Ak σ 2s :

j ¼ glk  1 þ 1

where

j ¼ glk  1 þ 1

X

glk X

αsi Q Ii þ

i ¼ gsk  1 þ 1



X

gsk glk X

DJi  DIj

TL: þ

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

b

ð24Þ

j ¼ glk  1 þ 1

Since αsi and αsj are independent and normally distributed, we have

i ¼ gsk  1 þ 1

þ

i ¼ gsk  1 þ 1

ð19Þ

j ¼ glk  1 þ 1

That is IP bk ¼

Eq. (23) can be simplified to 8 9 gsk glk < X = X b Pr αsi Q Ii þ αsj Q Jj r ISk ¼ β: : ;

ISbk ¼

k¼1

K X

Φ  1 ðβ Þ

K X pffiffiffiffiffi Ak σ s þ μs Ak :

k¼1

ð29Þ

k¼1

The total holding cost is CH b ¼

K X

Φ  1 ðβÞhk

K X pffiffiffiffiffi Ak σ s þ μs hk Ak

k¼1

þ

k¼1

M X



hi DIi ð2TSi þ TW i Þ þ DJi ðTLi þ TW i þTSi Þ



i¼1

þ

N X



 hj DJj ð2TSj þ TW j Þ þ DIj TLj þ TW j þ TSj

j¼1



X

gsk glk X

þ TL hk DJi  DIj

:

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 k¼1 K X

ð30Þ

where since the packages in one group are the same, we have hi ¼ hj ¼ hk , for i ¼ gs k  1 þ 1; …; gs k and j ¼ glk  1 þ 1; …; gl k . 5.2. Transportation cost For group k, the transportation cost of the empty packages is 0 1 gsk glk X X b @ CT k ¼ ct lIi DIi þ lJj DJj A i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1



X

gsk glk X

þ ct lIJ DJi  DIj

:

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 Then the total transportation cost of all the suppliers is 0 gsk glk K X X X b @ lIi DIi þ lJj DJj CT ¼ ct k¼1

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

ð31Þ

Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

1

X

gsk glk X

þ lIJ

DJi  DIj

A:

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

239

6. Comparison of the costs of the two modes ð32Þ 6.1. Cost reduction of shared mode Compared with dedicated mode, the cost reduction of shared mode is Δ TC ¼ TCS  TCSb

1 0

X

gsk glk M N K X X X X

¼ ct @ lJi DJi þ lIj DIj  lIJ

DJi  DIj

A

i ¼ gsk  1 þ 1 i¼1 j¼1 j ¼ glk  1 þ 1 k¼1

5.3. Total cost of the system For shared mode, the total cost of all suppliers is 0 1 M N X X b b b @ TC ¼ CT þCH ¼ ct lIi DIi þ lJj DJj A i¼1

j¼1

i¼1



gsk glk K K X X pffiffiffiffiffi

X

X

lIJ DJi  DIj

þ Φ  1 ðβÞhk Ak σ s þct

k¼1 j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1 K X

þ

μs hk Ak þ

N X

j¼1

  hi DIi ð2TSi þ TW i Þ þ DJi ðTLi þ TW i þTSi Þ

ð33Þ

Q Ii ; Q Jj , the mean and variance of the failed return factor μs ; σ 2s , the distances lJj ; lIJ , and the total demand gap between the areas, k¼1

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

DIj j.

k¼1

i ¼ gsk  1 þ 1

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

DJi is factory J's demand of parts from the suppliers located

in area I, and

glk P j ¼ glk  1 þ 1

M X

DIj is factory I's demand of parts from the

suppliers located in area J. Therefore, j

gsk P i ¼ gsk  1 þ 1

DJi 

glk P j ¼ glk  1 þ 1

DIj j

is the difference between the packages transported in and out of area I (or J) for group k, which also denotes the unbalanced demand of the parts transported in and out any area. In particular, if



gsk glk P P

DJi  DIj a 0, the demand of group k is unba

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 lanced and the parts transported out of area I (or J) are more than that transported in, and thus empty packages should be transported gsk glk K P P P j DJi  DIj j is between the areas. Similarly, k¼1

i ¼ gsk  1 þ 1

hi DJi ðTLi  TSi Þ þ

N X

hj DIj ðTLj  TLj Þ

j¼1

j ¼ glk  1 þ 1

the total demand gap for all groups, and larger gap means more empty packages should be transported between the areas, which makes the shared mode more costly.

ð34Þ

From Eq. (34), we can divide the total cost reduction into three parts: the transportation cost reduction, the safety inventory holding cost reduction and the pipeline inventory holding cost reduction. These cost reductions are explained as follows: 6.1.1. The transportation cost reduction M N K P P P ΔTCT ¼ ct ð lJi DJi þ lIj DIj  lIJ j i¼1



glk P j ¼ glk  1 þ 1

j¼1

k¼1

gsk P i ¼ gsk  1 þ 1

DJi

DIj jÞ. Since the packages can be shared between the

suppliers of different areas, the transportation cost of the empty packages is reduced. Under dedicated mode, the long distance (from one area to another area) transportation cost of empty container is M N P P ct ð lJi DJi þ lIj DIj Þ, while under shared mode the transportation i¼1

We give more explanations about the demand gap between the gsk glk K P P P j DJi  DIj j, as follows. For group k, areas, gsk P

pffiffiffiffiffi Ak σ s



X

gsk glk X

hk DJi  DIj

:  TL

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 k¼1

Proposition 2. The total cost of the system in shared mode is expressed in Eq. (33). The cost is positively related to the demand rates DIi , DJi , DJj ; DIj , the transportation cycle time 2TSi þ TW i , TLi þTW i þ TSi , 2TSj þTW j , TLj þ TW j þ TSj , the order quantities

glk P

hk Φ  1 ðβÞ

K X

Then we have proposition 2 to demonstrate the cost of shared mode.

DJi 

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij

i¼1



 hj DJj ð2TSj þ TW j Þ þ DIj TLj þ TW j þ TSj

gsk P

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μl Q Ji

k¼1

þ



X

gsk glk K X X

þTL hk

DJi  DIj

:

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1 k¼1

j

K X



j¼1

K P

N X

þ

i¼1

k¼1

þ

M X

M X

þ

cost is

j¼1

K P k¼1

lIJ j

gsk P i ¼ gsk  1 þ 1

DJi 

glk P j ¼ glk  1 þ 1

DIj j. Because of the unba-

lanced demands between areas, some empty packages still should be transported. Hence, the transportation cost reduction achieves the maximized value if the demands of any group between the two areas are balanced. That is, gsk glk P P DJi ¼ DIj for k ¼ 1; 2; …; K.

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

6.1.2. The safety inventory holding cost reduction qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i M P ΔTCS ¼ hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μl Q Ji i¼1   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N X þ hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij j¼1



K X

pffiffiffiffiffi hk Φ  1 ðβÞ Ak σ s

k¼1

The safety inventory reduction is caused by the risk pooling effect and the improved reliability of long distance transportation of empty packages. In order to derive the risk pooling effect, we should exclude the improved reliability effect, which is caused by the assumption that αl ¼ 0, (i.e., σ 2l ¼ 0; μl ¼ 0). Letσ 2l ¼ 0; μl ¼ 0,

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Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

then we can exclude the influence of improved reliability and get the risk pooling effect as ΔTCSjσ2 ¼ 0; μl ¼ 0 ¼ l



M X

hi Φ

1

ðβÞQ Ii σ s þ

i¼1

N X

hj Φ

1

ðβÞQ Jj σ s

 ð35Þ

k¼1

i ¼ gsk  1 þ 1

Q Ii þ

glk P j ¼ glk  1 þ 1

Q Jj ; hi ¼ hj ¼ hk , for

i ¼ gs k  1 þ 1; …; gs k and j ¼ glk  1 þ 1; …; gl k . We can simplify the risk pooling effect to ΔTCSjσ2 ¼ 0; μl ¼ 0 ¼ l

K X

 pffiffiffiffiffi hk Φ  1 ðβÞσ s Ak  Ak :

ð36Þ

k¼1

Further, we can derive the improved reliability effect   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M X hi Φ  1 ðβÞ Q 2Ii σ 2s þQ 2Ji σ 2l þ μl Q Ji

i¼1

þ

N X j¼1

and

the pipeline inventory holding cost reduction M N K P P P hi DJi ðTLi  TSi Þ þ hj DIj ðTLj  TSj Þ  TL hk Δ TCP ¼ i¼1



gsk glk P P

DJi  DIj .

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

j ¼ glk  1 þ 1

inventory reduction is larger. In addition, if K ¼ 1, which means all of the suppliers use the same pattern of packages, the reduction of the safety inventory attains the maximum.

i¼1

hi DJi ðT li  T si Þ þ

j¼1

hj DIj ðT lj  T sj Þ  T l

i¼1

þ þ

k¼1

M X

hk

packages is reduced, the pipeline inventory is also reduced. Then we have Proposition 3 to demonstrate the cost reduction of the shared mode. Proposition 3. The shared mode has a lower cost than the dedicated mode, i.e., Δ TC 4 0. The reduced cost is expressed in Eq. (34), and it consists of three parts: the transportation cost

gsk M N K P P P P

lJi DJi þ lIj DIj  lIJ D reduction Δ TCT ¼ ct

i ¼ gsk  1 þ 1 Ji i¼1 j¼1 k¼1 glk P j ¼ glk  1 þ 1

Δ TCS ¼

DIj jÞ, the safety inventory holding cost reduction

M X i¼1

N X j¼1





gsk glk P P

DJi  DIj . Since the transportation of the empty

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1



j ¼ glk  1 þ 1

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μl Q Ji

j ¼ glk  1 þ 1

maximized total cost reduction, Δ TC , is 0 1 M N X X @ Δ TC ¼ ct lJi DJi þ lIj DIj A

6.1.3. The pipeline inventory holding cost reduction Δ TCP ¼

k¼1

sum of the factory I's order quantity from the suppliers in area J equals to that of the factory J's from the suppliers in area I; and (3) K ¼ 1, which means all of the suppliers use the same package. The

i¼1

K P

j¼1

Proof: see the Appendix. According to the above analysis, the maximization of the cost reduction is achieved when the following conditions are satisfied: gsk glk P P (1) DJi ¼ DIj , which means, in any group, the

i ¼ gsk  1 þ 1

ð37Þ

It is easy to show that if the order quantities between areas in a gsk glk P P Q Ji ¼ Q Ij , the safety group are balanced, i.e.,

N P

pffiffiffiffiffi Ak σ s ;

packages transported from area I to J equals to that from area J to I; gsk glk P P Q Ji ¼ Q Ij , which means, in any group, the (2)

k¼1

M P

hk Φ  1 ðβÞ

i ¼ gsk  1 þ 1

  X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij  hk Φ  1 ðβÞσ s Ak :

i ¼ gsk  1 þ 1

K X

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij

k¼1

pffiffiffiffiffi hk Φ  1 ðβÞ Ak σ s : gsk P

N X j¼1

j¼1

K X

Recall that Ak ¼

þ

K X

j¼1

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hi Φ  1 ðβÞ Q 2Ii σ 2s þQ 2Ji σ 2l þ μl Q Ji   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij M X pffiffiffiffiffi hk Φ  1 ðβÞ Ak σ s þ hi DJi ðTLi  TSi Þ i¼1

k¼1

þ

N X

hj DIj ðTLj TSj Þ:

ð38Þ

j¼1

The minimization of the cost reduction is achieved when K ¼ M þ N, which means every supplier uses a unique package and no package can be shared between suppliers. Then, shared mode is the same as dedicated mode, i.e., the minimized cost reduction, Δ TC , is Δ TC ¼ 0:

ð39Þ

Summarizing the above conclusions yields the following proposition: Proposition 4. The cost reduction of shared mode lies in the interval of ½0; Δ TC , where Δ TC is determined by Eq. (38). The cost

Table 1 The main factors that influence the cost reduction of shared mode. Expression

Definition

Direction Meaning



Demand gap between the two areas Negative gsk glk K P P P

DJi  DIj

k ¼ 1 i ¼ gsk  1 þ 1 j ¼ glk  1 þ 1 K

Package categories

Negative

σ 2l μl σ 2s TLi  TSi , TLj  TSj

Failure factor of returned package

Positive

Time saving of short distance transportation

Positive

If the transport volumes between the two areas are balanced, the cost reduction achieves maximum. If all the suppliers can share the same package, i.e., K ¼ 1, we get the maximized cost reduction. If the supply of returned containers are more unreliable, the cost reduction is higher. If the time saving of short distance transportation is higher, the cost reduction is higher.

Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

Fig. 2. Total costs under different failure factors.

241

Fig. 6. Influence of order quantity on total costs.

Fig. 3. Cost reductions of shared mode.

Fig. 7. Influence of order quantity on the cost savings.

reduction is positively related to the gap of the demands between the

gsk glk K P P P

DJi  DIj , and the mean and the areas,

j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1 variance of the failure factors, σ 2l μl , σ 2s ; while the cost reduction is negatively related to the number of the categories of the packages, K.

6.2. Factors that influence the cost reduction Fig. 4. Cost components for K ¼ 1.

From Eq. (34), we have the main factors that affect the cost reduction as shown in Table 1. We explain these factors in the follows: (1) Demand gap between the two areas, i.e.,



gs gl K k k P P P

DJi  DIj . As discussed in Section 5.3,

j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1

Fig. 5. Cost components for K ¼ 2.

this metric denotes the empty packages that should be transported between the two areas because of the unbalanced demand. Hence, for the network with balanced demands, which means smaller total demand gap, shared mode is more attractive. This factor affects “the transportations cost reduction” and “the pipeline inventory holding cost reduction”. For shared mode, if the logistics network contains more areas, more benefits can be induced from the balance of flows between areas. Hence, for the packaging management system, serving different brand assemblers is more cost efficient. Some companies, like Chep, have established big platform to rent the

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Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

Table 2 Three possible cases for the numerical examples Case

K

Specific groups

I

1

(SI1 ; SI2 ; SJ1 ; SJ2 )

II

2

III

4

(SI1 ; SJ1 ), (SI2 , SJ2 ) ðSI1 Þ; ðSI2 Þ; ðSJ1 Þ; ðSJ2 Þ

Implications All of the suppliers use the same package. Shared mode. Suppliers

SI1 ; SJ1

standard pallets and containers to their customers of different industries. (2) The number of the packaging categories, i.e., K, which is also the number of the groups that the suppliers can be divided. If K is larger, we need supply more categories of packages, and the benefits of the shared mode are smaller. An extreme example is K ¼ M þN, which means every supplier needs unique packages and thus no sharing effect can be achieved in the shared mode, i.e., Δ TC ¼ 0. Similarly, if K ¼ 1, the shared mode achieves the best situation. This factor affects “the safety inventory holding cost reduction”. In practice, SGM uses only several limited packages, and at the same time put different linings to satisfy the different requirements of parts, and the linings are used for one time. With such method, the company reduces the number of the categories and the associated management costs. (3) The mean and the variance of the failure factors, i.e., σ 2l μl , σ 2s . If the problem of failure return is more serious, shared mode is more helpful in reducing cost. These factors affect “the safety inventory holding cost reduction”. (4) The time savings of short distance transportation, i.e., TLi  TSi and TLj  TSj . The shared mode replaces the long distance transportation of some empty packages by short distance transportation, which reduces “the pipeline inventory” of the empty packages. Therefore, larger time saving yields larger cost reduction.

7. Numerical examples Assume that there are two suppliers in area I, i.e., SI1 ; SI2 and two suppliers in area J, i.e., SJ1 ; SJ2 . Here, we use superscripts “I”, “J” to distinguish the suppliers located in different areas. However, in the model analysis, since the subscript “i”,“j” can distinguish the suppliers, we neglect the superscripts to avoid confusion. Then we consider three possible cases as in Table 2. Let lIJ ¼ 10; lIi ¼ lJj I J ¼ 1; hi ¼ hj ¼ 1; ct ¼ 1; TSIi ¼ TSJj ¼ TW i ¼ TW j ¼ 1; TLIi ¼ TLJj ¼ 10. Then we discuss the costs for different cases under different demand rates, order quantities, and distribution of the failure factors. Further, let DIJ1 ¼ 10; DIJ2 ¼ 5; DJJ1 ¼ 30; DJJ2 ¼ 20; DII1 ¼ 25; DII2 ¼ 20; DI 1J ¼ 5; DJI2 ¼ 15; Q IJ1 ¼ 10; Q IJ2 ¼ 20; Q II1 ¼ 25; Q II2 ¼ 20; Q JJ1 ¼ 30; Q JJ2 ¼ 20; Q JI1 ¼ 10; Q JI2 ¼ 15, and μl ¼ σ l ¼ 0:05 þσ s ¼ 0:05 þ μs . With such settings, the demand flow gaps are 5, 15 and 35 for case I, II and III. These parameters also mean that the demand of local suppliers is larger than that of remote suppliers, and the failure factor of long distance return has larger variance and mean than that of the short distance return. Then we have Figs. 2 and 3 to demonstrate the total costs of the three cases under different failure factors. In Fig. 2, the total cost is the highest when K ¼ 4, i.e., dedicated mode; while in the case of K ¼ 1, all of the suppliers share the same pattern of package, and the cost is the lowest. In addition, the total costs of all cases are increasing along with the failure factor, and the cost of dedicated mode is more sensitive to the change of the failure factors. These conclusions can be explained

use the same package; suppliers SI2 , SJ2 use another kind container. Shared mode. Every supplier uses his own package. Dedicated mode.

by the fact that larger mean and variance of the failure factors yield larger safety inventory and thus increase the costs. The risk pooling effect in shared mode makes the safety inventory less sensitive to the unreliability of the returned packages. In Fig. 3, taking dedicated mode as benchmark, we show the cost reduction of shared mode. The percentage is calculated by TC 4  TC 1 for K ¼ 1, where TC 4 and TC 1 are the total cost for K ¼ 4 TC 4 and K ¼ 1, respectively. The calculation is similar for K ¼ 2. It is obvious that the cost reduction can be considerable, from 25% to more than 40%. When there is only one pattern of package, i.e., K ¼ 1, the cost reduction is higher. In addition, when the failure factors increase, the cost reduction percentage increases too. This can be explained by the fact that the cost of dedicated mode is more sensitive to the change of the failure factors than that of shared mode is. Fig. 4 and 5 show the components of the cost reductions of shared mode for K ¼ 1 and K ¼ 4, respectively. It is easy to see that, the transportation cost reduction and the holding cost of pipeline inventory reduction are the main components of the cost savings, and they are constant when the failure factors change. The safety inventory holding cost reduction is comparatively minor; and it becomes larger when the return of the empty packages becomes less reliable. In addition, the cost reduction of the safety inventory of the packages is not sensitive to the value of K, i.e., the package categories. In contrast, the differences of the transport cost reduction and pipeline inventory reduction are both obvious between the cases of K ¼ 1 and K ¼ 2. We also study the influences of the order quantity on the total cost and cost savings of shared mode. With other parameters being the same as in the above numerical examples, we show the total costs and cost savings for different order quantities for the case of K ¼ 1. The results are similar for K ¼ 2, and K ¼ 4. Hence, we do not show them. In Figs. 6 and 7, }Q } means the values of the order quantities are set as the above examples, while }Q =2} and }2Q } are the cases with half and double of the original quantities.  TC 1 In Fig. 7, the percentages are calculated by TC 4TC . 4 In Fig. 6, the total costs of the shared mode for the two cases are shown. It is obvious that the cost is smaller when we decrease the batch sizes, however, the differences are very minor, from 0 to 9. Similar findings can be derived from Fig. 7, for the cost reduction percentage. Hence, the influence of order quantity on the cost reduction for the packages is very minor.

8. Conclusions In this paper, we have compared two modes, i.e., shared mode and dedicated mode, used in packaging system management for automotive parts logistics. We have proved that shared mode has lower transportation volume, lower pipeline inventory and lower safety inventory, which means shared mode has lower total cost. We have also shown that the cost reduction of the shared mode is positively affected by the gap of the demands between the areas, the mean and the variance of the failure factor, the time savings of short distance transportation and negatively affected by the number of the categories. Further, we have derived the maximized and minimized values of the cost reduction. In particular, the

Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244

maximized value is achieved when (1) all of the suppliers use the same pattern of packages; and (2) the transportation volume between areas is balanced within every group; and (3) the sum of the factory I's order quantity from the suppliers in area J equals to that of the factory J's from the suppliers in area I. The minimized value is zero, and it is attained when every supplier use unique packages. The numerical examples show that the cost reductions can be considerable, and the main cost reductions are the pipeline inventory holding cost reduction and the transportation cost reduction. The lot size, in contrary, has minor influence on the total cost. Besides the packages' holding and the transportation costs that discussed in this paper, other neglected costs, such as procurement cost of the packages, the management costs, also should be considered in practice. In particular, since the procurement quantity is much larger for the shared mode, it may get a much lower procurement price. Further, because of specialization, the shared mode may perform better in designing and handling the packages. For future research, some related issues might be possible. First, relaxing some assumptions of this paper, and giving more considerations of the operational processes to extend or examine the conclusions of this paper is one possible direction. In addition, consider the situation that the packaging management platform may provides service for different assemblers and their suppliers, then the network design of the packaging management system and the coordination between customers are important issues for this situation.

243

2

3 M N X X

¼ ct 4 lJi  lIJ DJi þ ðlIj lIJ ÞDIj 5  0: i¼1

ðA2Þ

j¼1

Hence, the transportation cost reduction is positive. In other words, shared mode reduces the transportation of empty packages between the areas. The second part of the cost reduction, the safety inventory holding cost reduction, satisfies   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M X hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ μl Q Ji i¼1

þ

N X j¼1

4

  X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K pffiffiffiffiffi hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l þ μl Q Ij  hk Φ  1 ðβÞ Ak σ s k¼1

M X i¼1

þ

N X

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l

h j Φ  1 ðβ Þ

j¼1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K X pffiffiffiffiffi Q 2Jj σ 2s þ Q 2Ij σ 2l  hk Φ  1 ðβÞ Ak σ s :

ðA3Þ

k¼1

We can prove that the cost reduction is positive if the right part of the inequality is positive, i.e., M X i¼1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N X hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l j¼1



K X

pffiffiffiffiffi hk Φ  1 ðβÞ Ak σ s Z0:

ðA4Þ

k¼1

The above inequality can be proved if we have M X

Acknowledgment

i¼1

This research is supported in part by National Science Foundation of China Grants (71001063). This paper is also a part of the project supported by China Scholarship Council (CSC) and the joint project between SJTU and Fengshen Logistics Company (FLS).

Appendix

1

X

gsk glk X

@ 4ct lJi DJi þ lIj DIj  lIJ DJi þ DIj

A:

i¼1 j¼1 j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1 0

M X



N X

K X

" The right part of (A1) is ct

M P i¼1

ðA1Þ #

N

P lJi  lIJ DJi þ ðlIj  lIJ ÞDIj : In j¼1

practice, lJi is the distance from assembly factory J to supplier i located in area I (lIj has similar meaning), and lIJ is the distance between the package management centers located in area I and J. The difference between lJi , lIJ and lIj is minor. Therefore, it is safe to M N

P P lJi  lIJ DJi  0 and ðlIj  lIJ ÞDIj  0, which means assume that i¼1 j¼1

1 0

X

gsk glk M N K X X X X

@ ct lJi DJi þ lIj DIj  lIJ DJi þ DIj

A

j ¼ g lk  1 þ 1 i¼1 j¼1 k ¼ 1 i ¼ g sk  1 þ 1

j¼1

K X

hk Φ  1 ðβÞAk σ s Z 0:

ðA5Þ

k¼1

gsk glk P P Q Ii þ Q Jj into the above Submitting Ak ¼ i ¼ gsk  1 þ 1 j ¼ glk  1 þ 1 inequality yields 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gsk glk K X X X 4 hi Φ  1 ðβÞ Q 2Ii σ 2s þQ 2Ji σ 2l þ k¼1

Proof of Δ TC 4 0. The first part of the cost reduction, the transportation cost reduction, satisfies

1 0

X

gsk glk M N K X X X X

@ ct lJi DJi þ lIj DIj  lIJ DJi  DIj

A

i¼1 j¼1 j ¼ glk  1 þ 1 k ¼ 1 i ¼ gsk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N X hi Φ  1 ðβÞ Q 2Ii σ 2s þ Q 2Ji σ 2l þ hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hj Φ  1 ðβÞ Q 2Jj σ 2s þ Q 2Ij σ 2l 0 gsk X 1 Q Ii þ  hk σ s Φ ðβÞ@ i ¼ gsk  1 þ 1

13

glk X

Q Jj A5 Z 0:

ðA6Þ

j ¼ glk  1 þ 1

The above inequality can be proved if we can prove gsk X

hi Φ  1 ðβÞ

i ¼ gsk  1 þ 1

0  hk σ s Φ  1 ðβÞ@

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Ii σ 2s þ Q 2Ji σ 2l þ gsk X

Q Ii þ

i ¼ gsk  1 þ 1

glk X

hj Φ  1 ðβÞ

j ¼ glk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Jj σ 2s þ Q 2Ij σ 2l

1

glk X

Q Jj A Z0:

ðA7Þ

j ¼ glk  1 þ 1

That is, if each group can reduce safety inventory, then the total system can certainly reduce safety inventory. Since the same group use the same pattern of packages, we have hi ¼ hj ¼ hk . Then the above inequality is gsk X

Φ  1 ðβ Þ

i ¼ gsk  1 þ 1

 σsΦ

1

0 ðβ Þ@

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Ii σ 2s þ Q 2Ji σ 2l þ gsk X

i ¼ gsk  1 þ 1

Q Ii þ

glk X

Φ  1 ðβ Þ

j ¼ glk  1 þ 1 glk X

j ¼ glk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Jj σ 2s þQ 2Ij σ 2l

1

Q Jj A Z 0:

ðA8Þ

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Q. Zhang et al. / Int. J. Production Economics 168 (2015) 234–244



X

gsk glk X

 TL hk

DJi  DIj

4 0:

i ¼ gsk  1 þ 1 j ¼ glk  1 þ 1 k¼1

It is easy to show that gsk X

Φ  1 ðβÞ

i ¼ gsk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Ii σ 2s þ Q 2Ji σ 2l þ

qffiffiffiffiffiffiffiffiffiffiffi Φ  1 ðβÞ Q 2Ii σ 2s þ

gsk X

4

K X

i ¼ gsk  1 þ 1

¼ σsΦ

Φ  1 ðβ Þ

j ¼ glk  1 þ 1

gsk X

ðβ Þ@

glk X

Q Ii þ

i ¼ gsk  1 þ 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q 2Jj σ 2s þ Q 2Ij σ 2l

1

Q Jj A:

ðA9Þ

j ¼ glk  1 þ 1

References

Hence, (A8) is satisfied and then (A3) is proved. Therefore, the second part of cost reduction is positive. The third part of the cost reduction, i.e., the pipeline inventory reduction, satisfies M X

hi DJi ðTLi TSi Þ þ

i¼1

N X



hj DIj TLj  TSj

j¼1



X

gsk glk M X X

hk

DJi  DIj

4 hi DJi ðTLi  TLi Þ  TL

i ¼ gsk  1 þ 1

i¼1 j ¼ glk  1 þ 1 k¼1 0 1 gsk glk N K X X X X

hj DIj TL  TSj  TL hk @ DJi þ DIj A þ K X

j¼1

k¼1

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

ðA10Þ In practice, the empty packages are transported directly from one center to the other, which means TL is much smaller compared with the long distance transport time of the automotive parts, i.e., TLi or TLj . According to Dongfeng–Nissan's practice, TLi is much larger than TL, and TSi . Hence, we usually have TLi 4TL þ TSi and TLj 4 TL þ TSj . Then we have M X

hi DJi ðTLi TSi Þ þ

i¼1

T l

K X

4

M X

gsk X

hk @

1

glk X

DJi þ

DIj A

i ¼ gsk  1 þ 1

j ¼ glk  1 þ 1

N X

K X

hi DJi T l þ

i¼1



hj DIj TLj  TSj

j¼1

0

k¼1

N X

hj DIj T l  T l

j¼1

k¼1

0

gsk X

hk @

i ¼ gsk  1 þ 1

¼0

i¼1

hi DJi ðTLi TSi Þ þ

DJi þ

1

glk X

DIj A

j ¼ glk  1 þ 1

ðA11Þ

That is M X

N X j¼1



hj DIj TLj  TSj

ðA12Þ

Hence, the pipeline inventory is reduced because of the time reduction of the returned empty packages. This completes the proof.

qffiffiffiffiffiffiffiffiffiffiffi Φ  1 ðβÞ Q 2Jj σ 2s

glk X j ¼ glk  1 þ 1

0

1

glk X

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