cost-parametric analysis of lateral transshipment policies in two-echelon supply chains

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Int. J. Production Economics 93–94 (2005) 169–178www.elsevier.com/locate/dsw

Cost-parametric analysis of lateral transshipment policies intwo-echelon supply chains

Jonathan Burton, Avijit Banerjee�

Department of Decision Sciences, Drexel University, 227 Academic Building, Philadelphia, PA 19104, USA

Abstract

In this paper, we examine the cost effects of two lateral (intra-echelon) transshipment approaches in a two-echelon

supply chain network, with a single supply source at the higher echelon and multiple retail locations at the lower,

through a series of simulation experiments under different operating conditions. An important finding is that either of

the proposed lateral shipment approaches is considerably superior to a policy of no such shipments, albeit at the

expense of increased transportation activity. Further, an ad hoc emergency transshipment approach appears to be

significantly more effective in terms of several important criteria, as compared to a more systematic transshipment

technique based on stock level equalization.

r 2004 Elsevier B.V. All rights reserved.

Keywords: Supply chains; Intra-echelon lateral transshipments

1. Introduction

The vast majority of existing studies on multi-echelon inventory systems deal largely with theinter-echelon flows of goods or commodities,occurring vertically between echelons, with thecommon assumption that intra-echelon flows (i.e.between stocking points, within the same echelon)are not permitted (Silver et al., 1998). In reality,however, it is common to resort to emergencyintra-echelon lateral shipments between inventory

e front matter r 2004 Elsevier B.V. All rights reserve

e.2004.06.015

ng author. Tel.: +1-215-895-1449; fax: +1-

ss: [email protected] (A. Banerjee).

locations, particularly at the retail level (Hoadleyand Heyman, 1977). It has been shown that suchlateral stock transfers or transshipments canresult, simultaneously, in substantial cost reduc-tions, as well as improvements in customer service(Hoadley and Heyman, 1977; Karmarkar andPatel, 1977; Tagaras, 1989). Such gains resultingfrom lateral shipments tend to be more pro-nounced if the stock locations vertically acrossthe echelons are widely separated by long dis-tances, whereas groups of stocking points within,usually, lower echelons, are located much closer toeach other (Lee, 1987; Showers, 1979). In certaincases, however, attempts to balance stock levelsamong locations within an echelon, can lead to

d.

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J. Burton, A. Banerjee / Int. J. Production Economics 93–94 (2005) 169–178170

excessive transshipments and undesirable costconsequences (Silver et al., 1998; Diks and DeKok, 1996; Jonsson and Silver, 1987). Unfortu-nately, studies investigating the efficacy of hor-izontal or lateral shipments under different supplychain structures are relatively rare and farbetween.

Some of the relatively few existing studiesexamining various aspects of intra-echelon trans-shipments assume that such stock transfers areresorted to under conditions of imminent or actualshortages (e.g. Das, 1975; Axsater, 1990; Sher-brooke, 1992), while others use such shipmentsperiodically for the equalization or balancing ofinventories amongst the various locations (see, e.g.Diks and De Kok, 1996; Jonsson and Silver, 1987;Bertrand and Bookbinder, 1998). In a recentpaper, Archibald et al. (1997) have studied thecase of both emergency vertical shipments andlateral transshipments, employed in conjunctionwith each other. Other researchers have examinedthe effectiveness of lateral shipments for repairableor recoverable items (e.g. Lee, 1987; Axsater,1990), while still others have focused on consum-able products (see, e.g., Jonsson and Silver, 1987;Archibald et al., 1997; Cohen et al., 1986;Robinson, 1990). In addition, lateral transship-ments have been analyzed from the perspective ofboth continuous time (e.g. Lee, 1987; Axsater,1990; Sherbrooke, 1992), as well as discreteperiods (see, e.g. Showers, 1979; Archibald et al.,1997; Kochel, 1998).

The earlier studies in this area suffer from theadoption of relatively simple problem structuresinvolving, for instance, only two stock locationsand/or a single planning period (see, e.g. Hoadleyand Heyman, 1977; Das, 1975; Herrer and Rashit,1995), thus limiting their practical usefulness.Furthermore, complex cost structures and otherconsiderations, more reflective of real worldscenarios, are not usually adopted in much of theextant literature. For example, although non-zerotransshipment lead times have been incorporatedin their respective analyses by Lee (1987), Tagarasand Cohen (1992) and a few other investigators,fixed costs have only recently been considered inthe work of Arnold et al. (1998). The simplisticassumptions are necessary, nevertheless, for keep-

ing the computations tractable in the process offinding optimal solutions, albeit at the expense ofloss of realism. In contrast, in view of thecomplexities involved in the analytical modelingand solution of multi-echelon supply chainproblems, some researchers in this area haveattempted heuristic approximations and/or simu-lation approaches, in efforts to preserve at leastsome degree of realism in their analyses (see, forexample, Diks and De Kok, 1996; Robinson,1990).As mentioned above, there appears to be two

major approaches towards making lateral ship-ment decisions within an inventory echelon. Theseare: (1) emergency ad hoc transshipments with ashort term, local focus and (2) the more measuredinventory balancing or equalization-based lateralshipments, with relatively longer term, more globalconsiderations. In a recent paper, Banerjee et al.(2003) have examined the relative merits of thesetwo approaches for two-echelon supply chains,through a series of simulation experiments, undera variety of operating conditions. One of theirimportant findings is that any type of a lateraltransshipment policy tends to be superior, in termsof customer service, to a policy of no suchshipments, under most circumstances. Further-more, although the approach of emergency trans-shipments results in generally higher service levels,the more systematic inventory equalization lateralshipment policy tends to result in fewer lateralshipments, albeit at the expense of customerservice in most of the cases studied.The aforementioned study (Banerjee et al.,

2003), however, evaluates these policies in termsof several performance measures, without assign-ing any cost parameter values to them. In thispaper, we use the results of this earlier study andexamine the relative effectiveness of these twotransshipment approaches, as well as the case ofno lateral shipments (NLS), under various operat-ing conditions with different cost structures. Wefocus on the tradeoff between customer service(measured by shortage level) and the number oflateral transshipments obtained by Banerjee et al.(2003). More specifically, a number of costparameter combinations pertaining to these twoperformance criteria are adopted in an attempt to

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J. Burton, A. Banerjee / Int. J. Production Economics 93–94 (2005) 169–178 171

identify the cost structure and operating condi-tions under which either transshipment approach,or no transshipments at all, can be recommendedfrom a cost standpoint. In other words, thesensitivity of the lateral shipment policies tospecific cost structures is explored in detail, sothat under a given set of circumstances a supplychain decision maker may have some guidelinestowards selecting an appropriate policy that islikely to be cost-effective.

2. Experimental design

The supply chain simulator, which is describedin Banerjee et al. (2003), models a supplier, or awarehouse, occupying the upper echelon of a two-echelon supply chain. Although several productsare stocked at this location, we focus on only oneconsumable item. We assume that there is un-limited inventory at the warehouse, so that theperformances of our proposed lateral shipmentpolicies are not obscured by supplier stockouts.The lower echelon consists of several retailers,each representing a distinct stock location. We alsoassume that no other supply sources exist for theretailers.

Inventory replenishment decisions are madecentrally (as would be the case in a vendor-managed system; Gross, 1963; Cetinkaya andChung-Yee, 2000) and are based on a coordinatedcommon review period of 20 days for all locations,in conjunction with appropriate individual order-up-to levels for the retailers (i.e. periodic reviewpolicy at each location). Demand for the productat each retail location is stochastic and stationary,while the delivery lead time from the supplier toany retailer is the same and is assumed to bedeterministic. Emergency lateral (i.e., intra-eche-lon) shipments between the retail locations, foralleviating impending anticipated shortages, arepossible and such transshipment lead times arenegligibly small. No safety stocks are allocatedand total backordering is allowed at any of theretail stocking points. Absence of safety stocks islikely to highlight the relative effectiveness of thevarious lateral shipment policies described below.

The various operating conditions are describedby five selected factors: (i) the number of retaillocations (NOL), (ii) the degree of variability inthe retailers’ average order sizes (OSV), resultingfrom different demand rates, (iii) the degree ofuncertainty in retail demand (DU), (iv) supply leadtime from the upper echelon to any of the lowerechelon locations (SLT) and (v) the lateralshipment policy in effect. We examine casesinvolving 2, 4 and 8 retailers, respectively. Inaddition, two levels of OSV, two levels of DU, twocases of SLT (i.e. 0 and 2 days) and three lateralshipment procedures, inclusive of a policy of nosuch shipments, are examined.

2.1. Retailer order size variability (OSV)

Two levels of retailer OSV, arbitrarily termed‘‘low’’ and ‘‘high’’, are adopted. Note that theaverage order size for the ith retailer is DiR units(where Di is its expected daily demand rate and R

is the common review period of 20 days) and itsorder-up-to level is given by Si ¼ DiðR þ LÞ, L

being the supply lead time. In the case of low OSV,each retailer’s expected order quantity is set to 600units, implying an identical average daily demandof 30 units and order-up-to level of 660 units (if thesupply lead time is 2 days) at all locations. Underhigh OSV, the largest average order quantity istwice the smallest average order size, with theremaining order sizes, if applicable, equally spacedbetween these two limits. Thus, for the N-retailercase, we assign D1R ¼ 400, DNR ¼ 800 and DiR ¼

400þ ði � 1Þ½400=ðN � 1Þ� units, for i ¼ 2; 3; . . . ;N � 1. For example, in the case of four retailers,D1R ¼ 400, D2R ¼ 533:33, D3R ¼ 666:67 andD4R ¼ 800 units. In other words, their respectivedaily demand rates are 20, 26.67, 33.33 and 40units and, if the supply lead time is 2 days, theirorder-up-to levels are 440, 587, 733 and 880 units,respectively.

2.2. Degree of demand uncertainty (DU)

The retail demand at each location is assumed tobe uniformly distributed. Two levels (again,arbitrarily termed ‘‘low’’ and ‘‘high’’) of DU areexamined. Under low DU, the upper and lower

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limits of the ith retailer’s daily demand distributionare set at, respectively, Di � 0:333Di and Di þ

0:333Di units. For the high DU case, these limitsare set at Di � 0:667Di and Di þ 0:667Di, respec-tively.

2.3. Lateral transshipment policies (LSP)

Three LSPs (including one with no such ship-ments) among the retail outlets are considered.The concept of a lateral transshipment order pointfor the ith retail location ði ¼ 1; 2; . . . ;NÞ is definedas: si ¼ Di � 1, 8i. Since demand is stationary, atransshipment order point mechanism (similar tothe well-known two-bin system) can be easilyimplemented at each retail location. In a reviewcycle, the available inventory at one or morelocations falling at or below the respective si valueat time t indicates the likelihood of an impendingshortage. The realization of such an event isallowed only at the end of a day, so that withnegligible transshipment lead times, lateral ship-ments, if permitted, may be able to temporarilyreduce the risk of shortages. In other words,defining I jðtÞ as the available inventory at locationj at time t, the necessity for lateral shipment(s) is(are) indicated by the condition(s): I jðtÞpsj forj ¼ 1; 2; . . . ; J. These J stocking points are labeled‘‘shortage’’ locations at time t and the expectedshortages at the end of the following day,estimated at time t, are SHjðtÞ ¼ Dj � I jðtÞ, 8j,which also indicate the respective needed trans-shipment quantities.

At this time, however, one or more of theremaining retail locations may have excess inven-tories for making lateral shipments, in order toalleviate the anticipated shortages at the shortagelocations. In a replenishment cycle, the expectedstock level at location i at time t is E½I iðtÞ� ¼

Diðtt;R � t þ LÞ, 8i, where tt;R is the deterministi-cally known scheduled time of receipt of the nextshipment from the supplier at the higher echelon.The candidate stock points, from which transship-ments may be made to the shortage locations, arethose K remaining locations where the availableinventory levels are above their respective expectedstock levels, i.e., for the kth such location,IkðtÞ4E½IkðtÞ� and the amount available for lateral

shipment(s) at this location at time t is given byAkðtÞ ¼ IkðtÞ � E½IkðtÞ�, k ¼ 1; 2; . . . ;K . Thus,transshipments, if allowable, may be made fromany of the K excess locations to any of the J

shortage locations. The three LSPs adopted in thispaper are outlined below.

1.
NLS Policy: Under this policy, no lateraltransshipments are allowed. Total backorderingis allowed at each retail outlet.
2.
Lateral Transshipments Based on Availability
(TBA) Policy: In this case, the first occurrence,say at time t, of the available stocks falling at orbelow the transshipment order point(s) at oneor more retail locations allows us to identify theshortage, as well as the excess locations andcompute the respective SHjðtÞ, 8j, and AkðtÞ, 8k

quantities. At this time, lateral transshipments,if possible, are made on the basis of thefollowing iterative procedure:(i) The K excess locations are rank ordered in

descending order of magnitude in terms oftheir respective quantities available fortransshipment and are labeled [1], [2], y,[K], such that A½1�ðtÞXA½2�ðtÞX . . .XA½k�ðtÞ.Similarly the J shortage locations are rankordered and labeled [1], [2], y, [J], suchthat SH ½1�ðtÞXSH ½2�ðtÞX . . .XSH ½J�ðtÞ.

(ii) Next, the lateral shipment quantity at timet from the location with the largest currentexcess stock to the location having thegreatest current need, Q½1�½1�ðtÞ, is deter-mined, breaking ties, if any, arbitrarily,using

Q½1�½1� ¼ minimumfA½1�ðtÞ;SH ½1�ðtÞg:

(iii) After appropriately allocating the shipmentquantity determined in step (ii), the mod-ified available and needed quantities at theexcess and shortage locations, respectively,are recomputed and steps (i) and (ii) arerepeated until the procedure terminates,indicated by A½1�ðtÞnSH ½1�ðtÞ ¼ 0. This im-plies that either all current transshipmentneeds have been met, or the total availabletransshipment quantity among all the ex-cess locations has been exhausted.

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With this reactive policy in effect, the set oflateral shipment decisions, described above,may have to be made more than onceduring a review cycle, based on thetransshipment order point signal. Further-more, if a transshipment need is indicated 1day prior to time tt;R, the arrival time of thenext cycle’s shipment from the upperechelon, no lateral shipments are made inthe current cycle, due to the anticipateddelivery of a relatively large quantity thefollowing day.

3.
Lateral Transshipments for Inventory Equaliza-
tion (TIE) Policy: This is a proactive policywhere transshipment decisions are based on theconcept of inventory balancing or equalizationthrough stock redistribution (see, e.g., Jonssonand Silver, 1987). In this case, inventoryredistribution (i.e. a set of lateral shipments)occurs no more than once in every review cycle.Suppose that the first signal for lateral ship-ment(s), generated by the transshipment orderpoint mechanism, occurs at time t within areview period. At this time, inventories areredistributed among the retail locations throughone or more lateral shipments, such that alllocations will have an equal number of days’supply (or, alternatively, equal runout times)just after the appropriate transshipment(s).Let EIiðtÞ represent the equalized inventorylevel at location i, after redistribution, deter-mined at time t. It follows that

EIiðtÞ ¼DiPNi¼1Di

XN

i¼1

I iðtÞ

" #

Thus, for any location j, if EIjðtÞ � I jðtÞ40,j ¼ 1; 2; . . . ; J, the LHS of this inequality is theamount that needs to be shipped into thislocation for achieving inventory equalization.By the same token, for any other location k, ifIkðtÞ � EII ðtÞ40, k ¼ 1; 2; . . . ;K, the LHS inthis inequality is the amount available forshipping out of this location.It is assumed that the redistribution of stockfor achieving inventory equalization occursthrough a complete tour of a single transportvehicle which visits each of the K source

locations exactly once for stock pick-up andeach of the J destination locations exactly oncefor stock delivery, representing an embeddedspecial version of the traveling salesman pro-blem. In this problem, an added complexity isthat, in constructing a tour, sufficient pickupsmust occur from the appropriate source loca-tions before deliveries can be made to thedestination nodes. Furthermore, whenever aredistribution tour occurs, the associated pro-blem structure involves J þ KpN nodes, im-plying at most N legs in a complete tour.Keeping in mind the differences between aredistribution tour through a single transportvehicle (under the TIE policy), as opposed tousing multiple smaller vehicles for meetingemergency transshipment needs (under theTBA policy), we consider a complete tour tobe roughly equivalent to an emergency trans-shipment, for simplicity.In collecting system performance data, with theTIE policy in effect, each complete tour describedabove is counted as a single lateral shipmentactivity, as opposed to the case of the TBA policy,where any shipment between any pair of locationsis considered to be a transshipment activity. Also,as alluded to above, once the location stock levelsare equalized through a set of lateral shipments ina review cycle, if so triggered by the transshipmentorder point signal, no further transshipmentsoccur during the remainder of the cycle, i.e. fromtime t to time tt;R.

The simulation study (Banerjee et al., 2003)employs a full factorial experimental design withthree levels for the factor NOL, two levels forOSV, two levels of DU, two levels of the factorSLT and three LSPs, resulting in 72 experimentalconditions or scenarios. Thus, the relative perfor-mance of each lateral transshipment policy isexamined under 24 factor level combinations oroperating conditions. Of the various systemperformance data collected, the following two areselected for our cost-parametric analysis here:

1.
The average unit-days of shortage per locationover the simulation run length of 20 replenish-ment cycles.

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2.
The average number of transshipment activitiesper retailer over 20 cycles.
It is to be noted that the overall averageinventory level for all retail locations is notaffected by the choice of a transshipment policy(or lack thereof). Clearly, since all stock transfersoccur laterally among only the retail locations,without the injection of additional stock from thehigher echelon, these transshipment policies (in-cluding NLS) have no impact on the total averageinventory across all retail stocking points, as wellas the average stock per location. Indeed, thefundamental rationale for lateral transshipments isthe potential for achieving higher customer servicelevels, without additional safety stocks. Thus, thetotal retail inventory holding cost is not consideredto be relevant in this study’s context. Furthermore,among all the stockout/shortage output dataobtained in Banerjee et al. (2003), only the time-weighted shortage criterion is selected as arepresentative measure of customer service orproduct availability. In short, in our subsequentcost analysis, the total relevant system cost underany of the 24 operating conditions consists of thecosts of time-weighted shortages and lateralshipments.

The results of the full factorial analysis ofvariance (ANOVA), the pairwise a posterioricomparisons between the factor levels, usingTukey’s procedure (Montgomery, 1991), and theirimplications are discussed in detail by Banerjeeet al. (2003). For our purposes, it is sufficient topoint out that the main effects due to the LSPfactor levels and their interaction effects with theNOL, as well as DU are statistically significant interms of the two selected criteria. Furthermore, interms of the time-weighted shortage measure, thereactive (TBA) and the proactive (TIE) ap-proaches to lateral shipments seem to be equallyeffective, but the latter policy is able to achievesubstantial improvement in service level (com-pared to the no transshipment policy) withsignificantly fewer lateral intra-echelon shipments.Thus, it appears that one or the other of thetransshipment approaches (or no transshipmentsat all) may be the most cost effective, depending onthe relative values of the critical cost parameters

and the operating environment. To shed light onsuch issues, we undertake a detailed cost-para-metric analysis in the following section.

3. Analysis and results

For each of the 24 environmental factor levelcombinations examined, the total relevant cost,C(U, N), as a function of the average unit days ofshortage per retailer, U, and the average numberof lateral shipments per retailer, N, over thesimulation run length of 20 replenishment cycles(400 days), is structured as

CðU ;NÞ ¼ c1U þ c2N ; c1; c240;

where c1 and c2 represent, respectively, the cost perunit-day of product shortage and the cost of anintra-echelon lateral shipment. Noting that both ofthese cost parameters are non-negative, the costfunction above can be expressed as

CðU ;NÞ ¼ ðc1 þ c2Þc1

c1 þ c2

� �U þ

c2

c1 þ c2

� �N

� �:

ð1Þ

Define c2=ðc1 þ c2Þ ¼ a, so that ð1� aÞ ¼ c1=ðc1 þc2Þ and Eq. (1) can be rewritten as

CðU ;NÞ ¼ ðc1 þ c2Þ½ð1� aÞU þ aN�; 0oao1:

ð2Þ

In (2), a parametric version of the linear costfunction, the parameter ‘a’ represents the relativevalues of the cost parameters c1 and c2 in a ratioform, as defined above. Thus, in the limiting cases,a=0 implies that the transshipment cost, c2, is zeroand a=1 implies that the cost of a unit-day ofshortage, c1, is zero. In other words, a relativelyhigh value of the parameter a indicates that thecost coefficient for the number of transshipments,N, is substantially greater than that associatedwith the time-weighted shortage measure, U. Thenormalized total relevant cost is then obtained bydividing the right-hand side of (2) by c1 þ c2, i.e.

NCðU ;NÞ ¼ ½ð1� aÞU þ aN�: ð3Þ

This normalized cost expression is used incomputing the total relevant cost yielded by thethree adopted transshipment policies under the 24

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environmental conditions defined by the NOL,OSV, degree of DU and the inter-echelon SLT.Since (3) is linear, it is sufficient to determine thenormalized costs at the two limiting values ofparameter a, i.e. 0 and 1, for comparing thevarious policies over the entire domain of ‘a’.Thus, using the average unit-days of shortage andthe average number of transshipments output dataper retailer obtained by Banerjee et al. (2003), wecompute the two limiting normalized total relevantcost values yielded by each of the LSPs, NLS, TBA(reactive) and TIE (proactive), under each of the24 operating conditions or cases. These normalizedcosts are shown in Table 1.

An examination of Table 1 leads to severalinteresting observations. In 16 of the 24 cases,involving fewer stock locations, the reactive TBALSP is dominated by the no transshipments NLSpolicy and the proactive TIE policy. This phenom-enon holds for two, as well as four retail locationsunder either low or high DU. For example, the

Table 1

Normalized costs for limiting values of parameter ‘a’

Case no. NOL OSV SLT a High DU

NLS TB

1 2 High 0 0 730.2 48

2 High 0 1 0 1

2 2 High 2 0 787.8 56

2 High 2 1 0 2

3 2 Low 0 0 263.2 18

2 Low 0 1 0 1

4 2 Low 2 0 282.4 20

2 Low 2 1 0 1

5 4 High 0 0 659.8 32

4 High 0 1 0 5

6 4 High 2 0 723 34

4 High 2 1 0 5

7 4 Low 0 0 239.2 12

4 Low 0 1 0 3

8 4 Low 2 0 260.6 12

4 Low 2 1 0 4

9 8 High 0 0 609.6 18

8 High 0 1 0 12

10 8 High 2 0 644.6 18

8 High 2 1 0 14

11 8 Low 0 0 214.2 7

8 Low 0 1 0 8

12 8 Low 2 0 235.2 7

8 Low 2 1 0 11

patterns of the normalized costs yielded by thethree transshipment policies over the domain ofthe parameter ‘a’ for the case numbered 4,involving two retailers, low OSV, 2-day supplylead time and low uncertainty, are shown graphi-cally in Fig. 1. From this figure, it is clear that theproactive TIE policy is the most cost effective for0oao0.86 and the NLS policy is the least costlyfor 0.86oao1. The reactive TBA policy isdominated entirely by these over the domain ofa, and cannot be recommended as an effective wayto reduce the total cost.When, however, there are a relatively large

number of stocking points, the TBA policy can berecommended under certain parametric condi-tions. For instance, for the case numbered 23(with eight locations, low OSV, zero lead time andhigh uncertainty), the normalized cost patternsover the entire domain of the parameter ‘a’ aregraphically depicted in Fig. 2. In this case, forrelatively low values of parameter ‘a’, i.e. for

Case no. Low DU

A TIE NLS TBA TIE

8.6 402 13 735.6 512 464.4

9.2 15.6 0 19.6 15.6

3.4 471 14 789 584.8 505.2

1.4 15.8 0 21.2 15.8

3.6 170.6 15 265.8 190 178.2

4.2 15.6 0 14.2 15.6

7.2 179.4 16 282 188.4 191.6

4.8 17 0 14.6 17.2

9 301.4 17 661 335.2 300

2.2 19 0 51 19

8.8 321 18 685.8 356.8 321

9.2 19.4 0 59.8 19.4

2.4 116.2 19 241.6 122.8 118.6

8.2 19 0 38.4 19

8.8 124.6 20 260.8 129.8 126.2

6.6 19.6 0 44.8 19.6

0 204.8 21 604.4 184.2 202

1.6 19.8 0 124.4 19.8

3.8 209.6 22 645.8 192.8 214.2

2.6 20 0 141.4 20

4.6 80.8 23 221.8 76.4 118.4

5.2 19.8 0 86.6 19

5.8 90.4 24 235.8 80 89.4

3.6 20 0 110 20

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0

50

100

150

200

250

300

0 1a

NLS

TBA

TIENC

(U

, N)

a =.86

Fig. 1. Normalized policy costs for case 4 (NOL=2, OSV=-

low, SLT=2, DU=low).

0 1a a

0.380.38

NC

(U

, N)

NC

(U

, N)

TBATBA

TIETIE

0.840.84

NLSNLS

250

200

150

100

50

0

Fig. 2. Normalized policy costs for case 23 (NOL=8,

OSV=low, SLT=0, DU=high).

Table 2

Parametric conditions for relative cost effectiveness of policies

Case no. TBA superior TIE superior NLS superior

1 Never ao0.96 a>0.96

2 Never ao0.91 a>0.91

3 Never ao0.86 a>0.86

4 Never ao0.86 a>0.86

5 Never ao0.95 a>0.95

6 Never ao0.95 a>0.95

7 Never ao0.87 a>0.87

8 Never ao0.87 a>0.87

9 ao0.20 0.20oao0.95 a>0.95

10 ao0.17 0.17oao0.96 a>0.96

11 ao0.09 0.09oao0.87 a>0.87

12 ao0.14 0.14oao0.88 a>0.88

13 Never ao0.95 a>0.95

14 Never ao0.91 a>0.91

15 Never ao0.85 a>0.85

16 Never ao0.86 a>0.86

17 Never ao0.95 a>0.95

18 Never ao0.95 a>0.95

19 Never ao0.87 a>0.87

20 Never ao0.87 a>0.87

21 ao0.15 0.15oao0.95 a>0.95

22 ao0.16 0.16oao0.96 a>0.96

23 ao0.38 0.38oao0.84 a>0.84

24 ao0.10 0.10oao0.88 a>0.88


0oao0.38, the TBA policy is clearly superior,whereas, for a>0.84 the NLS policy appears toyield best results and for 0.38oao0.84 theinventory equalization-based TIE policy is themost cost effective. The ranges of values for theparameter ‘a’ over which each transshipmentpolicy is the most desirable for all the 24 cases orenvironments are outlined in Table 2.

The observations that emerge from Table 2 andthe comments made above concerning the relativecost performance of the various policies are notsurprising. When shortages are costly and thereare relatively few stock locations, the TIE policytends to be more cost effective in alleviatingshortages through fewer of transshipments, com-pared to the TBA approach. With a relatively largenumber of stocking points, especially when thelateral shipment costs are quite small, the TBApolicy tends to overcome this drawback and tendsto be more cost effective than the inventoryequalization (TIE) approach. Needless to say that

regardless of the operating conditions, transship-ments are not a desirable means, as our analysesshow, of improving product availability, if suchshipments are comparatively expensive.

4. Summary and conclusions

Based on the results obtained in an earlier study(Banerjee et al., 2003), this paper has examined,from a cost-parametric perspective, the relativeeffectiveness of two lateral (intra-echelon) ship-ment approaches in two-echelon supply chainnetworks, characterized by a single supply sourceat the higher echelon and multiple retail locationsat the lower. One of these transshipment policies isa reactive ad hoc emergency approach (the TBApolicy), while the other is the more methodical,proactive inventory-balancing or equalization ap-proach (the TIE policy). For comparative pur-poses, the policy of no lateral shipments at all (theNLS policy) has also been considered.

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Of necessity, we have limited the scope of ourinvestigation by focusing largely on the lowerechelon of the supply chain. In structuring a totalof 24 environmental or operating conditions of thesupply chain, factors involving the number ofretail locations, retailer order size variability, inter-echelon supply lead time and the level of retail DUwere varied. Since the primary purpose of lateraltransshipments is the reduction of productshortages under uncertainty, the focus of thispaper has been on the cost tradeoff between thesetwo criteria. In our cost-parametric analyses, thetotal relevant cost has been defined as the sum oftime-weighted shortage and transshipment costs.Furthermore, in order to keep our results asgeneral and comparable across different systemstructures as possible, we have utilized the notionof a normalized cost function for evaluating thepolicies mentioned above.

Our results indicate that, from a managerialstandpoint, the notion of lateral transshipmentsappears to have substantial appeal, unless suchshipments are prohibitively expensive. If thebenefits of avoiding retail level shortages outweighthe additional delivery costs resulting from trans-shipments, customer service may be enhancedsignificantly, without the burden of additionalsafety stocks. These benefits appear to increase, asthe supply chain configuration becomes morecomplex, i.e. more stock locations. Under suchcircumstances, either of the reactive or theproactive approaches may be the most desirablepolicy, depending on the cost-parametric condi-tions, as discussed above. Under simpler struc-tures, with relatively few retail locations, inventoryequalization-based lateral shipment techniques aregenerally recommendable over a fairly wide rangeof cost-parametric configurations.

This study has examined two rather simplelateral shipment methodologies. Moreover, anumber of simplifying assumptions such as zerolateral shipment lead times, infinite supplierstocks, equal transshipment costs for both policies,etc. obviously limit the scope of this work. Futurework in this respect should relax these assump-tions, and incorporate more realistic and accuratecost parameter estimates, in the process offormulating more refined and cost-effective trans-

shipment policies. Finally, we suggest that theissue of emergency shipments from one or moreother supply sources be examined in future workin this area. It is likely that policies that combineinter-echelon, as well as intra-echelon, shipmentsfor alleviating shortages may prove to be meritor-ious in designing more flexible and cost-effectivesupply chains.

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