In-store replenishment procedures for perishable inventory in a retail environment with handling costs and storage constraints

Transcription

1 In-sore replenishmen procedures for perishable invenory in a reail environmen wih handling coss and sorage consrains R A.C.M. Broekmeulen* and C.H.M. Bakx School of Indusrial Engineering Technische Universiei Eindhoven Eindhoven The Neherlands * Corresponding auhor: Technische Universiei Eindhoven School of Indusrial Engineering P.O. Box 53, Pav. E0 NL-5600 MB Eindhoven The Neherlands Phone: r.a.c.m.broekmeulen@ue.nl Absrac A grocery reailers, cusomers prefer o wihdraw he newes insead of he older perishable producs ha are displayed on shelves. To reduce he subsanial cos of oudaing caused by his wihdrawal behavior, we sugges a procedure ha limis he number of baches on he shelf wih he same produc lifeime o one. The remaining invenory is sored in he backroom, where we assume o have ample sorage capaciy. We show ha for producs wih large available shelf space, shor produc lifeimes, expensive oudaing, and low handling cos his procedure leads o subsanial cos reducions compared wih in-sore replenishmen procedures ha do no ake ino accoun he wihdrawal behaviour of he cusomers and he sorage capaciy of he shelf. Keywords: Invenory, perishable, in-sore logisics, simulaion

2 . Inroducion According o an aricle in The Economis newspaper, "billions of dollars' worh of food is dumped each year because of reailers' inefficiency" []. One way of reducing shrinkage for perishables producs, such as fresh produce, dairy and mea, is reducing he amoun of produc on display in he sores. For producs wih a visible expiraion dae which are displayed in a selfservice environmen such as shelves a a grocery reailer, he cusomers prefer las in firs ou (LIFO) wihdrawal. From a supply chain poin of view, firs in firs ou (FIFO) wihdrawal is opimal [2]. Reailers as well as our whole sociey have an ineres o limi LIFO wihdrawal o avoid unnecessary wase of food. The invenory managemen of perishables a grocery reailers is eiher done manually or he process is assised by an Auomaed Sore Ordering (ASO) sysem ha was developed for nonperishables. In boh cases, he invenory is assumed o be in one locaion, bu for a large par of he assormen he invenory is spli beween he shelf and he backroom due o insufficien shelf space. For perishables wih sufficien shelf space, soring he oal invenory on he shelf leads o LIFO wihdrawal when muliple baches are presen on he shelf. A reailer can conrol he number of baches on he shelf by managing he in-sore replenishmen from he backroom o he shelf. In his paper we will invesigae he possibiliies o exend a perishable invenory sysem wih muliple sorage locaions and conrolled shipmens beween hese locaions. We expec ha a echnology like RFID will enable an efficien adminisraion of boh he quaniy and he age of he invenory a muliple locaions in he sore, which is needed for conrolling differen baches in a sore. Our paper is an exension of he work of Broekmeulen & Van Donselaar [3] in which hey presened a invenory conrol policy for producs wih a shor remaining shelf life, where he cusomer can observe he expiraion dae of he iems and is allowed o selec he iems, and invenory replenishmen is done periodically in small baches wih a lead-ime of a leas one period. Their EWA policy, which uses he age vecor of he invenory in he sore, is a good candidae o exend exising ASO sysems due o is flexibiliy in handling differen lead-imes, week paerns in demand, and cusomer wihdrawal behaviour. In his paper, we invesigae he effec of in-sore replenishmens from he backroom o he shelf on he combined cos of purchasing, los sales, oudaing and handling.

3 The remainder of he paper is organized as follows. In he following secion we review he exising lieraure on perishable invenory sysems and handling models and in Secion 3 we describe he problem characerisics. In Secion 4 he in-sore replenishmen policies are described. A numerical sudy in order o compare he differen replenishmen policies is presened in Secion 5. Based on he resuls, managerial insighs and possible fuure research is discussed in Secion 6. The paper ends wih a shor summary of our conclusions. 2. Lieraure review The research on perishable invenory sysems up o 200 has been horoughly reviewed Nahmias [4], Raafa [5], and Goyal & Giri [6]. Broekmeulen & van Donselaar [3] reviewed recen research on replenishmen policies for a single echelon perishable invenory sysem wih sochasic demand and a fixed lifeime equal o m periods o compare he EWA policy wih oher available policies in he lieraure. The EWA replenishmen policy akes ino accoun he full age disribuion of he invenory and can deal wih lo-sizing and FIFO and LIFO wihdrawal. Especially for perishable invenory sysems wih LIFO wihdrawal, here hardly exiss any lieraure. Cohen and Prasacos [7] deal wih he effec of FIFO versus LIFO wihdrawal policies on boh he sysem performance and ordering decisions for producs resriced o m = 2. They derive approximaions for he criical number for LIFO sysems and compare hese wih he values for FIFO sysems. The criical numbers urned ou o be raher insensiive o he ype of wihdrawal policy alhough he opimal expeced coss were significanly higher for LIFO. Nahmias [4] menions ha his resul suggess ha simple approximaions for FIFO sysems could also be used effecively in LIFO sysems. Since Cohen and Prasacos [7] did no invesigae replenishmen policies oher han criical number policies, our paper has added value in showing wheher or no an age based replenishmen policy leads o improved performance in a LIFO sysem. The limied amoun of available shelf space in reail sores resuls in shelf space allocaions ha are ofen insufficien o accommodae he demand. Kezenberg e al. [8] propose dense reail sores, which rely on demand subsiuion and only marginal handling cos. Cachon [9] opimizes he shelf space allocaion by making a rade-off beween he shelf space cos, he invenory holding coss and he ransporaion coss. Since he assumes handling cos o be linear wih demand, he is able o omi handling coss. Broekmeulen e al. [0] find ha due o he 2

4 inflexible sorage cabines, a large number of producs have excess shelf space. According o Van Zels e al. [], handling coss are a considerable par of he logisics coss for nonperishables. The addiional aciviies needed o mainain perishables in a sore, such as oudaing, increase hese coss furher. De Koser e al. [2] describe he design and conrol of order picking in warehouses, which is he mirror aciviy of replenishing he shelves in a sore. Kozab & Teller [3] carried ou an empirical sudy of grocery reail in-sore logisics for dairy producs. They describe he siuaion wih wo sorage locaions in he sore, he shelf and he backroom, and he resuling addiional handling needed o replenish he shelves. 3. Problem characerisics We sudy a single perishable produc wih a fixed lifeime of m periods. We define he lifeime as he remaining shelf life for he producs when hey arrive in he sore. Cusomer demand is probabilisic wih mean µ and variance 2 σ for each period. We modelled he demand for each period wih a discree disribuion fied on he firs wo momens [4]. When he invenory in he sore is insufficien o saisfy he demand, he excess demand is los. The invenory is conrolled wih a periodic review sysem wih review period equal o R periods and a fixed leadime equal o L periods for he replenishmen orders. Replenishmen quaniies are limied o muliples of an exogenous deermined lo size, i.e., he case pack size. We assume ha he supplier has ample sock. The invenory in he sore a he sar of period consiss of one or more baches. A bach is defined here as a se of iems available in he sore, which all have he same remaining shelf life (i.e. he same age). The conen of he bach can be locaed on he shelf and/or he backroom. We assume ha he backroom has ample sorage capaciy, bu he shelf has a limied sorage capaciy V. The amoun of iems available in sore locaion s (0 for he shelf and for he backroom) a he sar of period having r periods remaining shelf life is equivalen o m The number of differen baches on he shelf is denoed by A sign( B ) 3 = r = B rs.. Cusomers r0 wihdraw iems wih posiive remaining shelf life from he baches on he shelf, depending on heir demand and preference for he highes remaining shelf life, i.e., LIFO wihdrawal. Oudaing O is he wihdrawal by sore clerks of iems wih period remaining shelf life a he end of period, since hese iems can no be sold he nex period.

5 Table : Summary of he used noaion. A Number of differen baches on he shelf in period MAX A Maximum number of differen baches allowed on he shelf B Amoun of iems available in sore locaion s a he sar of rs IP L m M period having r periods remaining shelf life Invenory posiion a period Lead-ime Produc life ime a arrival Order size a period [unis] O R s SS T Oudaing of iems wih period remaining shelf life a he end of period [unis] Review period Case pack size [unis] Reorder level a period Safey sock level Number of rips from he backroom o he shelf a period V Shelf capaciy [unis] µ Mean period demand 2 σ Variance of demand sign (x) Reurns if x > 0, - if x < 0, and 0 oherwise x Rounds up x o he neares ineger The in-sore replenishmen policy deermines where he delivered replenishmen orders from he supplier are pu in he sore and how frequen and in which quaniies he iems are moved from he backroom o he shelf. We assume ha he in-sore replenishmen quaniies are limied o he available sorage capaciy on he shelf and he number of differen baches allowed on he shelf, denoed by MAX A, such ha A A MAX. Since we assume ha case packs are unpacked in he backroom, he size of he replenishmen quaniy does no depend on he case pack size. The wihdrawals from he backroom are always FIFO. The lead-ime for he in-sore replenishmens 4

6 from he backroom o he shelf is assumed o be zero. We assume ha he relevan handling coss only depend on he number of rips summarizes he used noaion. T beween he backroom and he shelf. Table For he replenishmens from he supplier, we use an exension of he EWA policy [3] ha akes he in-sore replenishmen policy ino accoun. Compared o Broekmeulen & van Donselaar, we limied our invesigaion o environmens wih no week paern in he demand, a lead-ime of one period, a review period of one period and no holding coss. This is done because heir sensiiviy analysis showed only a marginal effec for week paern and holding cos. Nex o ha, longer lead-imes and review periods only increase he probabiliy of oudaing. To compare he differen in-sore replenishmen policies, we used a discree even simulaion model of he reail process of perishable producs a a single sore. The iming of evens during a period in he model is: afer opening he sore, invenory decreases due o cusomers' demand, afer closing he sore oudaed invenory is removed from he shelf and/or he backroom, remaining invenory is couned, and performance measures such as he service level are calculaed, goods arrive a he backroom, and finally he orders are placed. The iming of he sacking of he shelf depends on he chosen in-sore replenishmen policy. 4. In-sore replenishmen policies We assume ha he reailer uses he EWA policy, which is a modified ( R, s, n) policy following he noaion of Silver e al. [5]. In such a policy, we creae a replenishmen order only when he invenory posiion a a periodic review momen is sricly below he dynamic reorder level L review period + s. Given a safey sock SS and he expeced demand during lead-ime plus + R i= + E[ D ], we have i s + L + R = SS+ E D i i= + [ ] () In case of an order, he size of he order has o be sufficien o bring he invenory posiion back o or jus above he reorder level s, bu sricly less han deermined by he number of case packs, each wih size. We define s +. The order size is IP as he invenory posiion a period jus before an order is placed. Noe ha in he EWA policy he invenory 5

7 posiion is he sum of he invenory on hand in he sore plus he invenory in ransi minus he esimaed amoun of oudaing, i.e., The order size M is now as follows + L+ R Oˆ i i= + EWA IP = IP (2) EWA EWA s IP if IP < s hen M = (3) To disinguish he esimaed amoun of oudaing from he acual amoun of oudaing, we use he variable Ô in (2) raher han done over L + R periods, since he oudaing on he ( L+ R) O. Noe ha he esimaion of he amoun of oudaing is h period has no effec on he sales during ha period (execued afer he sales period). The esimaed amoun of oudaing is he only difference beween he EWA policy and a regular ( R, s, n) policy. sore. The sysem sudied by Broekmeulen & van Donselaar [3] has only one sorage locaion in he By inroducing a backroom sorage, we need an in-sore replenishmen policy for replenishing he shelves from he backroom. We will describe hree differen in-sore replenishmen policies, which all have differen effecs on he wihdrawal behaviour and he amoun of handling. These in-sore replenishmen policies are: A. Direc o shelf B. Full shelf C. Single bach For non-perishables we observed a grocery reailers ha deliveries are pu direcly on he shelf, hereby circumvening he backroom. This is only feasible if he shelf has ample capaciy. m = B + L+, m,0 Min M, V B+ L+, r,0 (4a) r= B + L+, m, M B+ L+, m,0 = (4b) A measure for sufficien capaciy is Maximum Invenory On Hand (MIOH), which is he upper bound on he required shelf space capaciy. Broekmeulen e al. [0] give he following equaion for MIOH in he case of a ( R, s, n) policy. + MIOH = s + = SS+ + E[ Di ] + L R i= + (5) 6

8 When he shelf space is less han he MIOH, he probabiliy increases ha a delivery does no fi on he shelf and has o be sored in he backroom. This Direc o Shelf policy applied o producs wih insufficien shelf space has a poenial disadvanage for perishables, since i does no respec FIFO roaion. A fresh delivery occupies space on he shelf while he backroom could sill conain remnans from a previous delivery. Wih he Direc o Shelf policy, we also have he possibiliy of muliple baches on he shelf, i.e., A >. The upper bound on he number of baches on he shelf is here available shelf capaciy in unis. A MAX = V, since he number of baches is limied by he In he Full Shelf policy, all producs are firs delivered o he backroom, i.e., B = + L+, m, M. We only replenish he shelf if he invenory on he shelf drops o zero, based on he assumpion of zero lead-ime o he shelf. Since we assume ha case packs can be unpacked in he backroom, we have he opporuniy o replenish in larger quaniies han he expeced order size E [ M ]. The size of he in-sore replenishmen is limied by he shelf capaciy or he available invenory in he backroom. In he case of a large shelf capaciy, he shelf can conain muliple baches wih each a differen remaining shelf life, i.e., A MAX = V. MAX The Single Bach policy limis he number of baches on he shelf o one, i.e., A =. As in he Full Shelf policy, all producs are firs delivered o he backroom. This will resul in more rips from he backroom o he shelf, bu has he advanage ha he cusomer has no choice during wihdrawal. expense of addiional handling. Therefore, he Single Bach policy enforces FIFO wihdrawal a he Summarizing, he difference beween he Direc o Shelf policy and he Full Shelf policy is he primary desinaion of a fresh delivery and he difference beween he Full Shelf policy and he Single Bach policy is he number of baches allowed on he shelf. Our hypohesis is ha he handling cos increases from he Direc o Shelf policy o he Single Bach policy, while oudaing due o LIFO wihdrawal decreases. Earlier research on he EWA policy [3] showed ha LIFO wihdrawal resuled for he reailer in a cos increase of on average 7% compared o FIFO wihdrawal. The rade-off will depend on he relaive cos difference beween oudaing and handling, bu also on he size of he shelf. We hypohesize ha a larger shelf capaciy, up o MIOH, increases he difference beween he hree policies. 7

9 We sae ha he processes of cusomer wihdrawal, in-sore replenishmen and oudaing on a period follow he procedure oulined below.. Le T := Sales is he minimum of demand and available invenory, i.e., m S : = Min Brs, D i= s= 0 3. If S > 0 hen go o sep 4, else proceed o sep Wihdraw iems LIFO from he shelf, i.e., for r = m, m, K, do i. W = Min{, } : 0 B r S ii. S : = S W iii. B : r 0 = Br 0 W 5. If he shelf invenory is zero and he backroom invenory is posiive, replenish m from he backroom, i.e., if B 0 and B 0 hen go o sep 6, else proceed o sep 3. i= = r 0 m i= > r 6. Wihdraw iems FIFO from he backroom up o he shelf capaciy for sorage on he shelf, i.e., se he replenishmen quaniy o zero, i.e., F := 0, he number of = = = m baches on he shelf, i.e., A sign( B ) : and for r = K,, m do r r 0 0 MAX i. W = Min{ B, V F, ( A A) V} ii. iii. : r F : = F+ W B : r = B r W iv. B : r 0 = Br 0+ W v. If W > 0 hen A : A + = 7. If we have a posiive replenishmen quaniy, i.e., F > 0, increase he number of rips wih one, i.e., T : T +. Nex, go o sep 3. = 8. Oudae he oldes bach, i.e., O = B 0+ B, B 0 : = 0, and B : = 0. : 9. Updae he baches o accoun for aging, i.e., for r = 2K,, m le B, r s = Brs +, 8

10 The wihdrawal procedure described above is also he basis for calculaing he esimaed oudaing quaniies, which are needed in he EWA policy, as shown in formula (2). We esimae hese oudaing quaniies by calculaing for consecuive periods i, ranging from i = + o i = + L+ R, he wihdrawal, he remaining baches and he oudaing in period i under he assumpion ha in period i demand is equal o he expeced demand. This implies he following esimaion procedure, saring wih i = + :. Deermine he esimaed oudaing and he esimaed remaining baches available for he nex period in period i using he wihdrawal procedure wih he parameers applicable for he chosen in-sore replenishmen policy by assuming ha demand in period i was equal o he expeced demand and he wihdrawal in period i is equal o he esimaed wihdrawal. 2. While i < + L+ R do i : = i+ and coninue wih Sep, oherwise sop. 5. Numerical sudy In order o compare he performance of he in-sore replenishmen policies, we measured he long-erm average coss. The coss incurred during period are given by: wih unis and C = C + C Z + C K + C H (6) he amoun of unis ordered, Z K 9 T Z he amoun of unis oudaed, H he average number of rips o he backroom in period. K he los sales in We did a facorial experimen in which we esed several levels for each of he eigh inpu parameers. The experimenal seup is given in Table 2. The range of he produc lifeime is limied o siuaions for which oudaing was shown o be significan by previous invesigaions [6]. The parameers for average demand, coefficien of variaion and case pack cover (i.e. he case pack size expressed in number of periods expeced demand) are based on parameers repored in Van Donselaar e al. [6]. We also included lo-for-lo (LFL) or = o invesigae he effec of he lowes possible case pack size. We varied he shelf space for a produc beween Max { µ R, }, which is he minimum expeced order size a a service level of 00%, and he maximum invenory on hand MIOH, as defined in equaion (5). For perishables, he expeced

11 order size will be greaer han Max { µ R, } o compensae for oudaing. Wih a shelf space close o he expeced order size, he backroom is frequenly needed o sore he producs. An available shelf space equal o he MIOH makes direc deliveries o he shelf possible wihou he risk of overflows ha have o be sored in he backroom. All cos parameers in he model are normalized on he purchasing coss C, which is se equal o one cos uni. The relaive oudaing coss are varied beween -0.5 and 0.5. Here he negaive parameer reflecs he siuaion in which he oudaed producs sill generae some posiive revenue. The relaive los sales coss are varied beween 5 and 5, which resuls in relaively high service levels depending on he level of oudaing. Wih low oudaing, hese los sales coss lead o service levels up o 95%. For producs wih a shor shelf life and high oudaing cos, lower service levels down o 80% are more accepable in pracice, since he level of oudaing would oherwise far exceed he level of sales. The relaive handling coss are varied beween 0 and 0.. The value of zero corresponds o siuaions where handling coss are considered sunk. This is he case for sales deparmens for fresh producs which have already sufficien saffing levels o provide value-added services. The average logisic cos a reailers is ofen close o 0% of he oal operaing coss, including purchasing coss. This gives an upper bound of 0. for he relaive handling cos for each in-sore replenishmen. Since he average purchase price of a cusomer uni of a perishable produc such as mea is around 2.5, 0% should be enough o cover for he labour cos o execue a single replenishmen from he backroom [3]. Deliveries direc o he shelf bypass he backroom and herefore do no incur hese handling coss. We considered one day as he base period, resuling in a review period and a lead-ime of one day. These shor periods are ofen encounered for perishables a grocery reailers. 0

12 Table 2: Inpu parameers for he simulaion experimen. Inpu parameer Levels Produc lifeime m { 2,3, 4,5,6} Mean period demand µ { 2,5,0} Variance o mean raio σ 2 µ { 0.5,.0, 2.0} Case pack cover µ R {LFL,,2} Shelf capaciy { Max { µ R, }, MIOH} Oudaing cos raio Los sales cos raio Handling cos raio C C { 0.5, 0, 0.5} Z K C C { 5,0,5} T C C { 0, 0.05, 0.} Following Law and Kelon [7], he repored values for he simulaion are he averages from a leas 0 replicaions. In each replicaion, he firs 500 periods were he warming-up periods and saisics are recorded for he las 7000 periods. We replicaed unil we reached an absolue precision for he cusomer service level P ± wih 95% confidence. P 2 is he fracion of demand delivered from sock, also known as he fill rae. For each experimen e in he se of 7290 simulaion experimens E, we ran he following hree scenarios: A. Direc o shelf policy (DS); B. Full shelf policy (FS); C. Single bach policy (SB). In all scenario s we deermined for each parameer seing he opimal safey sock level SS, which minimized he average simulaed coss. For he comparison of differen policies we denoe he average coss for experimen e under he Direc o Shelf policy by C DS, e, he average coss under he Full Shelf policy by FS e C,, and he average coss under he Single Bach policy by C SB, e. The relaive deviaions of he coss for experimen e for policy p compared o policy q is defined as Cqe C pe δ pqe : = 00% e =,2, K, E (7) C qe

13 As performance measure, we consider he average of E E experimens, defined as follows pq : = δ pqe (8) E e E For each level he se of experimens o be aggregaed E is deermined by all possible parameer combinaions of he oher levels. In Table 3, we repor he relaive cos performance a seleced perceniles of he 7290 experimens. The Single Bach policy compared o he Full Shelf policy leads on average o 3.6% lower coss. In 93% of he cases, he Single Bach policy performs beer or equal han he Full Shelf policy. The worse performance of he Single Bach policy is mainly wih small shelf capaciies and longer produc lifeimes. In hese cases, he addiional handling is no compensaed by he reduced oudaing. The poenial savings are much higher when compared o he 'Direc o Shelf' policy, bu i is obvious ha he Direc o Shelf policy is a bad pracice for perishables. Table 3: Performance of he differen in-sore replenishmen policies for seleced perceniles of he experimens plus he average and sandard deviaion. Percenile SB,DS FS, DS SB, FS Average Sd. Dev Table 4 shows he relaive performance of he differen in-sore replenishmen policies for a subse of all 7290 experimens, in which one inpu parameer was kep consan a a cerain level. For he 'Direc o Shelf' policy in siuaions wih large shelf capaciy, he handling cos is zero, bu he addiional oudaing coss due o LIFO wihdrawal is large and comparable o wha was 2

14 repored earlier for he EWA policy [3]. The negaive effec becomes larger for shor produc lifeimes. In he remaining par, we will focus on he difference beween he Single Bach and he Full Shelf policy. The Single Bach policy gives he larges improvemens for a large shelf capaciy, shor produc lifeime, and low mean demand. Wih a large shelf capaciy, he probabiliy of muliple baches on he shelf in he Full Shelf policy is he highes. For shor produc lifeimes and low mean demand, we have he highes risk on oudaing, especially wih LIFO wihdrawal. In he siuaions wih large case pack sizes, he probabiliy of muliple baches drops in he Full Shelf policy, making he Single Bach policy less ineresing o reduce oudaing. As expeced, he advanage of he Single Bach policy reduces wih lower oudaing coss, lower los sales coss, and higher oudaing cos. In hese siuaions, we prefer o accep he addiional oudaing and/or he reduced cusomer service insead of inensifying he handling. Apar from coss, we also considered he effecs of he Single Bach policy on oher performance measures, such as he average invenory, he average oudaing, and he freshness of producs offered o consumers. Compared wih he Full Shelf policy, he Single Bach policy increases he average invenory wih on average 6%. Also a larger fracion of he sore invenory is locaed in he backroom: 57% compared wih 47%. Therefore, he Single Bach policy has a higher oudaing in he backroom compared wih he Full Shelf policy. The effec of keeping he newes baches in he backroom on he freshness of he producs for he cusomers is relaively small. We observe on average 6.6% less remaining shelf life of he sold producs under he Single Bach policy compared o he Full Shelf policy. 3

15 Table 4: Average cos reducions of he differen in-sore replenishmen policies. Parameer Level SB,DS FS, DS SB, FS Produc lifeime m Mean demand µ Variance o mean raio σ 2 µ Case pack cover µ R LFL Shelf space Max { R, } µ MIOH Oudaing cos raio C C Los sales cos raio Z K C C Handling cos raio C C T LFL (lo-for-lo) denoes a case pack size of, and MIOH is maximum invenory on hand. 4

16 6. Managerial insighs and fuure research Our main insigh from his research is ha good in-sore replenishmen policies for perishables are imporan o reduce he oudaing caused by LIFO wihdrawal. The suggesed policy o limi he number of baches on he shelf o one can lead o ineresing cos savings. The Single Bach policy is no difficul and easy o explain o people in he sores who are responsible for managing he invenory of perishable producs. Wih he Single Bach policy, he cusomer wihdrawal is changed from LIFO wihdrawal o FIFO wihdrawal. In such an environmen, he benefi of he EWA policy over a more common ( R, s, n) invenory conrol policy is less pronounced, especially wih a review period and a lead-ime of one day. In such siuaions, he invesmens in deailed regisraion based on RFID can be avoided. Bu in order o implemen a Single Bach replenishmen policy, frequen inspecion and imely replenishmen of he shelves is needed. Real-ime feedback from he poin-of-sale daa colleced a he check ous o he sore clerk responsible for mainaining he shelves wih perishables is a possible alernaive o frequen inspecions in siuaions wih accurae sore execuion. The siuaion wih posiive lead-ime for he shelf replenishmen is an area for fuure research. From our numerical sudy we also observe ha for he Full Shelf policy large case pack sizes and/or small shelf capaciies also resul in a siuaion wih a limied number of baches on he shelf, which is he aim of he Single Bach policy. Too small shelf capaciies will resul in excessive handling wihou any benefi on he oudaing. Too large case pack sizes can cause exra oudaing if he case pack size is greaer han he average demand during he produc lifeime. We hink ha by using he Single Bach policy, he reailer achieves a beer balance beween handling and oudaing. The resuls for he Direc o Shelf policy show ha his insore replenishmen policy is no suiable for perishables. An ineresing area for fuure research is he in-sore replenishmen of perishables wih a random produc lifeime such as fresh produce. For hese producs, regular inspecion by rained sore clerks is needed o sor he producs on display and o remove producs ha are below he qualiy level accepable for sale [8]. For unobservable qualiy aspecs, advanced measuremen sysems and qualiy change models could be used by he sore clerks o improve he soring [9]. By combining he handling aciviies needed for soring wih he replenishmen of he shelves, a 5

17 reailer can reduce he oudaing for hese producs or increase he qualiy of he producs on display. 7. Conclusions By limiing he number of baches on he shelf o one, he reailer can reduce he amoun of oudaing due o LIFO wihdrawal a he expense of addiional handling. This research shows ha producs wih a shor produc lifeimes, large shelf capaciies, expensive oudaing and low handling cos profi mos from a single bach in-sore replenishmen policy. More aenion from he reailer, resuling in jus in ime replenishmen of he shelf and improved execuion of he sore operaions, has also a posiive impac on he use of our naural resources beyond a mere cos saving. References [] Shrink rapped: America's food reailers should wage a ougher war on wase, The Economis, May 5 h [2] Pierskalla WP, Roach CD. Opimal issueing policies for perishable invenory. Managemen Science 972; 8(): [3] Broekmeulen RACM, Donselaar K van. A heurisic o manage perishable invenory wih bach ordering, posiive lead-imes, and ime varying demand. Compuers & Operaions Research 2009; 36: [4] Nahmias S. Perishable invenory heory: a review. Operaions Research 982;30: [5] Raafa F. Survey of lieraure on coninuously deerioraing invenory models. Journal of he Operaional Research Sociey 99;42: [6] Goyal SK, Giri BC. Recen rends in modeling of deerioraing invenory. European Journal of Operaional Research 200;34:-6. [7] Cohen, MA, Prasacos, GP. Criical number ordering policy for LIFO perishable invenory sysems. Compuers & Operaions Research 98:8(3): [8] Kezenberg M, Meers R, Vargas V. Invenory policy for dense reail oules. Journal Operaions Managemen 2000; 8(3): [9] Cachon G. Managing a reailer s shelf space invenory, and ransporaion. Managemen and Service Operaions 200; 3(3): [0] Broekmeulen RACM, Donselaar KH van, Fransoo JC, Woensel T van. Excess Shelf space in reail sores: an analyical model and empirical assessmen. Working paper Technische Universiei Eindhoven, Neherlands, Bea 09: 26pp. [] Zels S, Donselaar KH van, Woensel T van, Broekmeulen RACM, Fransoo JC. Logisics drivers for shelf sacking in grocery reail: poenial for efficiency improvemen. Inernaional Journal of Producion Economics 2009; 2(2):

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