Retailer replenishment policies with one-way consumer-based substitutionto increase profit and reduce food waste

Buisman, Marjolein Elize; Haijema, Rene; Hendrix, Eligius M. T. Article Retailer replenishment policies with one-way consumerbased substitutionto increase profit and reduce food waste Logistics Research Provided in Cooperation with: Bundesvereinigung Logistik (BVL) e.V., Bremen Suggested Citation: Buisman, Marjolein Elize; Haijema, Rene; Hendrix, Eligius M. T. (2020) : Retailer replenishment policies with one-way consumer-based substitutionto increase profit and reduce food waste, Logistics Research, ISSN 1865-0368, Bundesvereinigung Logistik (BVL), Bremen, Vol. 13, Iss. 1, pp. 1-15, https://doi.org/10.23773/2020_7 This Version is available at: https://hdl.handle.net/10419/297183 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Received:18 October2018 /Accepted:12 May2020 /Publishedonline:27 May2020 ©TheAuthor(s)2020 This articleis publishedwith Open Access at www.bvl.de/lore Retailer replenishmentpolicies with one-wayconsumer-based substitution to increase profit andreduce food waste MarjoleinE. Buisman, Rene Haijema, EligiusM.T. Hendrix ABSTRACT Retailerscanexploittheconsumer willingnessto substitute to improve their profit,servicelevel and waste. This paper investigates to what extentsuch improvementcanbe realised by thereplenishment decisions. Two orderpolicies arecompared: one policy neglecting productsubstitution,and a new policy that decides on orderquantities forallproducts simultaneously meanwhileanticipating stock-outbasedsubstitution. Both policies areanalysed by simulation-based optimisation.Besidesfinding theoptimalparameter values or a varietyof settings by exactenumeration (as a benchmark), we presentforthecase of one-way substitution a heuristic search procedure.The heuristic finds (nearly)optimalparametervalues quicklyand turnsoutto findoptimalparametervalues in almost allsettings. An averageprofit increase of almost 9% is obtained when anticipating on substitution, while wastelevels candecrease with more than 35%. Aclear trade-offbetweenservicelevels andprofit/wastelevels is found. Assuming theretailer aims at profit maximisation, theservicelevelof one productmaybevery low or even zero.The resultsprovide thefollowing managerial insights in:(i)theservicelevels andwastelevels that maximize theretailer’s profit, (ii) whether a product should be removedfrom theassortment,(iii)theprofit loss andwasteincrease of setting ahigher (sub optimal) servicelevel, e.g. forstrategic reasons. Reversely, one maylearnfrom theresultswhat theprofit margin of aproduct should be to justify a certainservicelevel to aprofit maximizing retailer.Theseinsights maybe useful to retailerswhoseprimaryobjectiveis beyond profitmaximisation. KEYWORDS:Retail ·Food wastereduction· Substitution · Perishable ·Multi-product 1. INTRODUCTION Fo od waste at retailersis both an economical andan environmentalissueandshould thus be prevented[1]. In this paper,we analysean innovative wayof reducing food waste at theretailer,by using a replenishment policy that incorporates substitution behaviourof the consumer. Retailerssell many differentproducts in their shop andforeach individual item,replenishmentdecisions have to be taken. Thesedecisionscan either be done manually or aresupported by computer aided ordering(CAO)orautomatedstore ordering (ASO) systems. However, bothapproaches usuallyfocus on individualproductsand therefore do notconsider product substitution.At best,product substitution is anticipated informally in practice by setting different servicelevelsfordifferent products belongingto the same productcategory.Commonly used servicelevels arethein-stockprobability andthefillrate.Theimpact of (differentiated)servicelevels on retailer profitand wasteis not(a priori)known. As the main objectiveof LogisticsResearch (2020) 13:7 DOI_10.23773/2020_7 MarjoleinE. Buisman Correspondingauthor [email protected] Production Management, WHU – Otto Beisheim School of Management, Burgplatz2, 56179Vallendar, Germany Rene Haijema Operations Research &Logistics Group, Wageningen University, Wageningen,TheNetherlands EligiusM.T. Hendrix Computer Architecture, Universidad de Málaga, Málaga, Spain 2 systemsdealingwith substitution anddescribe our contribution to theliterature. Using a simulation-based optimisation approach,whichis presented in Section 3 andthe heuristic explained in Section4. 576instances aresolved,andsome managerial insights arediscussed in Section5. Thepaper finishes with conclusionsand a discussionin Section6. 2. LITERATURE REVIEW Ourstudy considersthereplenishmentof twoproducts, of which one of them serves as substitute when theother productis out-of-stock.Although,theincorporationof substitution in replenishmentdecisions forperishable products is highlyrelevant forthegroceryretail sector, thenumber of studiesin theliteratureon thistopic is limited[9]. In contrast, therearemany studies dealingwith substitutionquestionsand non-perishable products [10].Oneof thegeneralconclusions of thesepapersis that theincorporationof substitution behaviourof consumersin theinventory decisions lead to better performances of theretailer.Therefore, it is very importantto further study theincorporationof substitution behaviourfor perishable products as well. In thissection, we will first discussthestudies on perishable products andcontinue with ashort discussiononthestudiesfor non-perishableproducts. 2.1. Replenishmentdecisions for perishable products To ourknowledge,only afewstudiesexistwhich includesubstitution in thereplenishmentdecision forperishable products.Oneof them is theanalytical study of Denizet al.[11], wherethereplenishmentis optimisedfor a productwith ashelflife of 2periods. The modelis in fact asingle product modelwith two demand classesrelated to thetwoageclasses. In case of astockout of one ageclassdemand maybe substitute toanother ageclass. Undertheassumption of zero lead time, theproblem is tractable,andan analytical solution is found. In asimilarsetting of asingle product with twoageclasses, Sainathan integrates thereplenishmentandthepricingdecision in [12].Optimalsolutionsareobtained by applying the framework of Markovdecision processes(MDP). The numerical determination of an optimalpolicy requires thestate descriptionof MDPto be lowdimensional, such that thetotalnumber of states to evaluate is not toolarge. Thestate of aperishable inventory system is thenumber of products in stockin each ageclass, hence it is avector. Forallpossible values of thestate vector, a relative state valueis determined as well as an optimal action. As thenumber of states increasesrapidlywith thedimensionof thestate vector, extending a single productMDP modelto atwo or multi-product model couldmake the modelintractable. Similarly,an MDP solution cannot be foundwhen theshelflife of the productgets toolarge[13, 14]. aretailer is profit maximisation, retailersareinterested in awayto set replenishmentquantities that maximise their profits. However, profit maximisation is not the only retail target. Most of them aim at high customer satisfaction and/or high market shares. Retailerswant to serveconsumers at anytime of the dayandthus have thetendencyto hold high inventory levels for everyproductin practice.For non-perishable productsthis is acceptable,as unsold goodscanbe sold later on.However, forperishable products, thisstrategy will lead to high wastelevels due to productspoilage. When retailersre-think their strategy andaccept outof-stock situationsforsome products,whileoffering consumers asubstitute product,inventorylevels can be loweredandthus wastelevels canbe decreased. Research shows that consumersdo accept substitute products in out-of-stocksituations, although customer satisfaction mightdecrease [2]. Thefocusof this paperis on improvingthereplenishmentdecisions in atwoperishable productsituation, wherethe productsarepartly substitutesin caseof an out-ofstocksituation. Accordingto [3], thewillingnessto substituteis forhighlyperishable products larger than fornon-perishable products.Reasonsforconsumersto consider substitutionarean out-of-stocksituationof thepreferred product, or a better value-for-money of a substitute product. Pricebasedsubstitution(asin [4]) is notconsidered in this paper.Neither do we consider quality or agebasedsubstitution(e.g., see[5]).It hasbeen shown in previousresearch [e.g.6, 7, 8] that incorporating stock-out-based substitution in thereplenishment decisions, canincrease profit. However, it is notyet fullyclear to what extendthetrade-off betweenprofit, wasteandservicelevels are affected.As theseother aspectsarealso of importance in retail,we optimise andcomparetwopolicies andreport profit, waste, and β-servicelevels in this paper.We consider the fill rate (orβ-service level) to be an appropriate servicelevel definition in this context, as it indicatesthefraction of demand that is lost or metby asubstitute, which is more informative than thestock-outprobability (α-service level).First, we optimise for each product a base stockpolicy usingindependentlyasingle product model, that thus does not includeproductsubstitution. Next,we optimise thereplenishmentparameters simultaneously usingamulti-product modelthat includesproduct substitution.We use a multi-product simulation model to compareboth approachesand report profit, waste, andβ-service levels. Theobjectiveof thispaper is three-fold: (i)to present an approach to exploitproductsubstitution in replenishmentdecisions, (ii) to generate managerial insights in theeffect of productsubstitution on profit,wasteandservicelevels, and(iii)to present a heuristic that facilitates the(heuristic)search forgood replenishmentparameters. Theremainderof this paper is organisedas follow. In Section2we discuss therelevant literatureon inventory 3 Retailer replenishmentpolicies with one-way consumer-based substitution to increase profit andreducefood waste closed form expression, severalassumptions areput in place: e.g. zero lead time, backlogging, a short shelf life, or a replenishmentanddisposal policythat supports renewalpoint. An importantdifference to our study is thetractability of theproblem. When adding multiple time periods, thewholeproblembecomes more complexandis nottractableanymore. Thus,it is not possibleanymore to findan optimal solution analytically.Moreover,in order to obtainanalytical solutions, traditionally one assumes zero lead time and backlogging to facilitate renewaltheory. We will relax on theseassumptions. Dynamicprogramming methodsarealsopresent in literature(e.g.[27]), whichmayprovideanalytical results,but onlywhen imposing strong assumptions similarto theNewsvendor models. A numerical solution of dynamicprogramming models allows relaxedassumptions(suchas apositive lead time, lost sales,etc.)andis applicable to settingswith at most afew(non-perishable) products,butwhen extending to perishable with amaximalshelflife,thestate spaceof perishable inventory systems becomes too largeto determine an optimal solution (similarto an MDPapproach). A separate category of research on inventorypooling, whereastockout at a stockpointis resolved by issuingdemand from another stockpoint. As theproducts themselves are no different, we skip a discussingoninventory pooling models. 2.3. Contribution From theabove discussion it becomes clearthat consumer-drivenproductsubstitutionis hardly included in existing studieson thereplenishment of perishable products, andvice versamultiperiod perishabilityis hardly includedin existing models on product substitution.The main contribution of this paper is at that intersection: includingperishabilityand product substitution in the replenishmentof multiple perishable products.As theinventory dynamics is complicatedby theperishability, positive lead time, andthesubstitution between twoproducts,we adopt a simulation-based optimisation approach,whichallows agreater modelling flexibility than thenews vendor or single period models availablein literatureon productsubstitution. This methodology facilitates the evaluation of profit, waste, andservicelevels,allvery importantkeyperformanceindicators for a retailer. or thecontributionin managerial insights we referto Section5. 3. METHOD To analysetheeffect of includingsubstitution in replenishmentdecisions, asimulation-based optimisation modelhasbeen developed. Thesimulation modelprovides agood representationof thevariability in thesystem,such as thedemand andsubstitution uncertainty, andan accurate view of itseffects From thestudieson perishable products,quitea fewdo not includeconsumer drivensubstitution, butsupplierdriven substitution. In this concept, the supplier decideswhichproducts will be issued and thus decideson product substitution.In [15]optimal issuingpolicies forperishable products areinvestigated for a single productwith multiple demand classesusing MDP. Aretail example of supplier-based substitution is foundin Chen et al.[6]. Forperishable products, most research with supplier drivensubstitution is foundin thecontextof bloodbanks. Thedistinctionof blood typesmakesthis setting atrue multi-productsetting, wherethecustomers(medicines)set thesubstitution matrix based on theblood groupof theirpatientand the compatibility of blood groups [16].Theblood banksaimat issuing a product from thesame blood groupas that of thepatient, but it maydecide to issue asubstitute,if stocklevels at blood banksrequire. Haijemaet al.[16] uses simulation-based optimisation whichthey combinewith MDP. Duan andLiao [17] alsoappliessimulation-based optimisationapproach usingtabu search andsimulatedannealing. Other examples in theblood supply chainareDillonet al. [18] andNajafi et al.[19]. Duonget al.[20] concludesthat studies on perishable inventorieswith substitution arescarce, whilethe contextis very relevant to practice.Newsvendor models areappealing forimposing astructurethat allows formathematicalanalysis usingrenewaltheory. Nevertheless, they propose asimulationapproach by arguingthat an exact method or a Newsvendor model is toolimited, as theinventory dynamics become more complexwhen dealingwith alongershelf life, a positive lead time, and a lost sales context. An exact method becomes intractablefor most settingsin practice. Besides these modelling andoptimisation papers,it is worthwhile to mentionthe(more) empiricalstudy of Sachs[8]andKökandFischer [21]. Both studies analysethesubstitutionbehaviour of consumersbased on sales data forperishable and non-perishablegoods. 2.2. Replenishmentdecisions for non-perishable products As by far most studieson replenishmentdecisionsand productsubstitutionconcern non-perishableproducts, it is of interestto summarisethe methodsemployed the obtained resultsin thesesettings anddiscuss whether the methodsandresultscanbe appliedto perishables. Accordingto thereview of Shin et al.[10],many studies on consumer driven,inventory-basedsubstitution arevariations on theclassicalNewsvendorproblem. Several studiesdo findoptimal solutionsanalytically, like thestudyof Gaur andHonhon [22],Mahajanandv. Ryzin[23],NagarajanandRajagopalan[24],Netessine andRudi [25],andTranschel[26]. Acommon approach is to modeltheproblemas asingle period problemand applyrenewaltheory.To some extendsuch approaches canbe appliedto perishable products,as discussed in theprevious subsection. To obtain analytically a 4 Parameters: SiOrder-up-tolevelof producti µiMean demand of product i γij Substitutionfraction of productito product j piSalespriceof producti ciCost of producti aFraction FIFO consumers MiMaximumshelf life of productiupon arrival at theretailer Variables: Itir Inventory of productiat thebeginningof time period twith remainingshelf life r Dti Initial demand of productiduring time period t EOti Estimatedoutdatingof productiat time period t Qti Orderquantity of productiat time period t Xti Remaining demand of productithat should be fulfilled by asubstitute at time period t Ztir Products sold of productiat time period twith remainingshelf life rwithout substitution Utir Products sold of productiat time period twith remainingshelf life rdueto substitution WtiWasteof productiat theendof time period t ΠtTotalprofitof time period t Dti,Xti,Ztir,Utir will be splitinto FIFO (DFti,XF ti, Z Ftir,UFtir)and LIFO (DLti,XL ti, Z Ltir,ULtir), see the modelbelow. [28].Theeffect of includingsubstitutionbehaviour canbe measured in terms of profit increase,waste decrease or obtaining better servicelevels.To obtain an understandingof theinfluencing factors, several parametersareanalysed such as theremainingshelf life,thesubstitution fraction, or theprocurementcosts. Theseparameters arefurther discussedin Section5. This sectioncontinueswith theproblemdescription, followedby the notation andthemathematical model. 3.1. Problem description We focuson a product category of aretailer that consistsof Ndifferentproducts with afixed maximum shelf life Mi.Withinthis productcategory,theretailer chooses a main product (fromnow on ‘product 1’) whichserves as asubstitute when other productsof this productcategory areout-of-stock. Thewillingnessof consumersto buythis substitute is givenby afraction (γj1). Theretailer faces a Poissondemand forallN products meaningthat consumersarrive at therate of thePoisson distribution andrequest 1 item of the product. Theretailer places an order at thebeginningof theperiod,before openinghours.This orderwill arrive after closing, resultingin an effectivelead-timeof one dayandan effectiveshelflife of Mi–1. 3.2. Notation Sets andindices: i,j∈{1,..,N}Products t∈{1,..,T}Time periods r, m ∈{1,..,Mi}Remainingshelf life 3.3. Discrete time simulation model At thebeginningof everyperiod,theretailer places an orderQti forall N products,seeequation (1), based on the order-up-tolevel (Si), thecurrentinventory forproduct iandtheestimated outdatingduring that period.Outdatingis estimated by thedifference betweentheaverageFIFO demand perdayandthe currentinventory with aremainingshelflife of 1 day, equation (2). This approachis takenforpractical reasons. However,it mightlead to an overestimation of theoutdating. (1) (2) Demand foreach product follows a Poisson distribution with mean µi,equation (3). At aretailer, thereareusuallyconsumerswhopreferthefresher products,and some that aremoreindifferent with respectto ageandthus tendto take theolderproducts. Therefore, we splitthetotaldemand fortheproducts into aFIFO and LIFO demand equation(4)andequation (5),with abeingthefraction of demand followingFIFO withdrawal. (3) (4) (5) 5 Retailer replenishmentpolicies with one-way consumer-based substitution to increase profit andreducefood waste When thedemand is not met, substitutionmight take place. Thenumber of consumersrequesting a substituteproductis an averagefraction (γij)of the Theproduct withdrawal by consumersfor both LIFO andFIFO demand is theminimum of theproducts in stockof acertainagerandtheremainingdemand that is not satisfied yet. Without loss of generality,it is assumed that customers preferring thefreshest product arrive first at thesupermarket, andthus LIFO demand is fulfilled before theFIFO demand. (6) (7) consumersfacing astock-out andgivenby equation (8),with Ztir beingthetotaldemand whichis already met (equation(9)) (8) (9) Similarto theinitial demand,thedemand arisingdueto substitution is alsodividedinto LIFO andFIFO demand: (10) (11) As it is assumed that stock-outs are more likelyto happen at theendof aday, thedemand occurringdue to substitution takesplaceafter theinitial demand of theproductis fulfilled,first by the LIFO withdrawal, followedby theFIFO withdrawal. (12) (13) At the endof aperiod,theinventory is updated for the next period,theshelf life is reducedwith one period andoutdatingis registered,consumer withdrawal is subtracted andtheproducts orderedat thebeginning of thedaywill arrive, equation (14),with Utir being the totaldemand fulfilled by substitution(equation(15)). Note:theeffectiveshelf life of aproductis M−1. A lead-timeof 1day (L=1)is appliedfortheretailer. 6 3.4. Performanceindicators To analysetheperformanceof aretailer,severalkey performance indicators areused.To determine the optimal order-up-tolevelS,totalprofitis maximised. Profitis calculated by subtractingprocurementcosts from therevenuemade (equation(16))andreported as dailyprofit(equation(17)). Fixed ordering costsand (14) (15) holdingcostsare neglected as perishable products at aretailer areusuallyreplenisheddailytogether with many others andtherefore ordering andtransportation costsareshared among allthose products[29]. Excessiveinventory levels do not occur, as theshelf life is short. (16) (17) Wasteis calculated for everyproduct perperiod of time by equation (18).Forthefinal analysis,wasteis represented as percentage of total orderedproducts, equation (19). (18) (19) Moreover,servicelevel measures areincluded. The fraction of demand that canbe fulfilled from stockfor the non-substitute product is measured by theβ-service level. Theβi-service levelrepresentsthe fraction of fulfilled demand forproducti,equation (20).Forthe productwhichremainingdemand is fulfilled by the other product,theβj-service level measures thefraction of fulfilled demand forproductj, either by productj, or producti,equation (21),with j≠i. To specifyby which products this demand is fulfilled,we includedtheβjiandβjj-service levelas well.Theβji-service levelis the fraction of demand forproductjfulfilled by producti, equation (22),andtheβjj-service levelis thefraction of remainingdemand forproductjfulfilled by product j,equation (23).Those fractionsareestimated, perday, in thesimulation as: (20) (21) (22) (23) 7 Retailer replenishmentpolicies with one-way consumer-based substitution to increase profit andreducefood waste Theoptimisation algorithmconsistsof multiplesteps. Firsttheoptimal order-up-tolevelSfor a single product is determined with the help of thesimulation model. This is done foreach of theNproductsindividually, andthus substitution is notincorporated yet. The optimal order-up-tolevels aredetermined based on profit maximisation andtheir values aredenotedŜi. In thesecond step,the order-up-to levels Ŝifoundin step 1areused as reference values andtherefore the simulation modelis ranwith these order-up-tolevels when substitutiondoes play arole. In thethirdstep of theoptimisation, every order-up-tolevelcombination fortheNproducts is evaluated andtheoptimal orderup-tolevels S* iaredetermined.Forthefinal analysis, thevalues obtained in step 2arecompared with the values obtained in step 3. Both in step 1andin step 3of theoptimisation a full enumerationis performed over arangeof order-up-tolevels S({Simin,...,Simax}). ThelowerandupperlevelSimin,Simax of thesearch rangearedetermined as follow.ForPoissondemand, the order-up-tolevelScanbe calculated basedonthe lead-time (L), review period (R), theaveragedemand (µ)andthesafety factor (z), usingequation (24).In this research,thelead-timeandreview period areboth fixed to 1period. (24) To calculate the order-up-tolevelSimax,thedemand forboth products is combined (thus, µ = µ1+ µ2). A lowerbound (Simin)of 0is used as it mightbe beneficial notto have aproductin stock at all, or to have anegative safety stock. FortheBase Case scenario, also a minimisation on wastehasbeen performed. Themaximumwaste reductionis determined withoutprofit losses, compared to optimisation without anticipating substitution. We alsoinvestigated apolicy that considersthe combined agedistribution applying StochasticDynamic Programming[13].It appearedthat theimprovement over an orderup to policy forourexperiments is less than 1% forvery perishable productsand nearly absent when theshelflife is larger than 4. Therefore, we conclude that theeasier to implement order-up-to 3.5. Optimisation approach Algorithm: IN:γ, µ, pi, ci,M OUT: S* 1,S* 2, Π*,ΔΠ,Waste, Δ Wandβ-service levels 1: Determineindividual order-up-tolevels Ŝ1andŜ2by full enumeration, with thesimulation modelwithoutsubstitution. 2: Evaluate Ŝ1andŜ2in setting with thesimulation modelincludingsubstitution behaviour of theconsumer to findcorrespondingprofit(Π )andwaste (Ŵ)levels. 3: Determineoptimal order-up-tolevels S* 1,S* 2with substitution based ordering by full enumeration, with thesubstitution model. 4: Compareresultsobtained at step 2with results of step 3 policy is quiterobust with respectto theoptimalprofit that canbe reached. 4. HEURISTICTO FIND (NEAR) OPTIMALORDER-UP-TOLEVELS Optimising replenishmentforperishable products is a complextask, dueto alltheinterdependenciesbetween theproducts.Thus,thecomplete enumerationis computationallyexpensive. By developing aheuristic, theruntime needed to find a solution decrease.The heuristic developedin this study stillincludes the simulation modeldescribedin section3, andis therefore able to deal with alead-timelarger thanzero andtheperishability of theproducts.For notational convenience we present the heuristic fortwoproducts, butit canbe extendedto morethan twoproducts. Product 1 is themain productto whichsubstitution maytake place. The heuristic is basedoninteresting characteristics of theresultsof Section5, foundby complete enumeration. For everyexperiment,theoptimalS* 1level is higher than or equalto theoptimal Ŝ1-level. Fortheproduct notservingas asubstitute,theexact opposite characteristic is valid. For every experiment, theoptimalS* 2-level wasequalto or lowerthan the optimalŜ2-level.Thesestructural properties canbe used to improvetheoptimisation process, as many possible combinations of S1andS2will never be optimal. Thus,thesecombinations canbe excluded. Thedeveloped approach consistsof severalsteps. In thefirst step,theindividual order-up-tolevels Ŝ1and Ŝ2arecalculated with full enumeration overall orderup-tolevels S.Thefound order-up-tolevels serveas starting pointfortherest of theapproach.Twostarting points areused,(i)S1=Ŝ1andS2=Ŝ2(resulting in Π ˉ1)and(ii) S1=Ŝ1+Ŝ2andS2= 0 (resulting in Π ˉ2). Then, based on whichof thetwooptionsresultsin the highestprofit, theheuristiccontinueswith another step. When Π ˉ1> Π ˉ2,theheuristic continueswith step 3, otherwise it continues at step 4. Thethirdstep consists of twoparts. First, we keep thetotalinventory level (S1 +S2)thesame, but increase S1anddecrease S2by 1 8 identical meansforboth products: µ1=µ2=5. The shelf life is set to three (Mi=3),andtheprocurement costsareset to c1=c2=€0.5. Thesellingpriceis fixed to (pi)of €1for both products,thus resulting in a profitmargin of =50%, whichis realistic formany perishable groceryproducts, like packed meat andfreshcutlettuce. Thesymmetry in thebase case between theproducts gives a good understanding abouttheeffect of substitution behaviourthat will not be influencedby other parameters. In thebase case,we set a= 0.5,i.e. 50%of theconsumersareof theFIFO type (acceptingtheoldest availableproduct),theother 50%select thefreshest availableproducts. To calculate theupper order-up-tolevelSimax,used in theheuristic, a safety factor zequalto 3is used for everyexperiment. Forthegiven a Poisson distribution forthedemand wouldresult in aservicelevel of 99.99%.Moreover, a 100% servicelevelwouldresult very high wastelevels andthus lowprofitlevels and would be an unrealistic target fortheretailer. Therearemultiple factors influencing the performance of theretailer.An obvious one is the demand perproduct. Besides an equaldemand per product, it is analysed how a differentdemand per productinfluencestheresults. Moreover,different procurement costscanlead to adifferentoptimal solution.Furthermore, we expect theshelf life of theproduct to be of greatinfluence on theretailer performance, as alonger shelflife gives more time to sell theproductinsteadof wastethem [29].Therefore, unit.This is iterativelydone until no better solution is foundfor 3 consecutiveruns. Then the neighbourhood of thebest solutionis checked, to seeif abetter solution exists, by either fixingS1or S2andin-/decreasing the other by 1unit.When the best solution is found, and 3consecutiveruns do not give abetter solution,the search stops. When step 4is applied, S2is always equal to 0, andS1is iterativelyin-/decreasedby 1unit until no better solution is found(intermsof profit) for3 consecutiveruns.Then theoptimalsolution is found, andtheprocedurestops. 5. NUMERICALRESULTS In this section, we first discuss theexperimental design.Next,we provide an overview of resultsand discuss thebenefitsof exploiting product substitution in thereplenishmentdecision. We will zoominto the base case,andderive managerial insights,e.g. on profit maximisation versus wasteminimisation (with aprofitconstraint), on theassortment decision, and on suboptimalservicelevels andprofitmargins. Finally, we discuss the(nearly optimal) performance of the heuristic. 5.1. Experimental design Thebase case studiedin this sectionis asetting where twohighlyperishable products (N=2) areconsidered. We assume thedemand to be Poissondistributed with Heuristic IN:γ, µ, pi, ci,M OUT: S* 1,S* 2, Π*(and Wasteandβ-service levels) 1: Determineindividual order-up-to levels Ŝ1andŜ2 2: Set Π with S1=Ŝ1andS2=Ŝ2anddetermine Πxwith S1=Ŝ1+Ŝ2andS2= 0 anddetermine highestprofit. If Π ≥ Πxcontinue with step 3, else continue with step 4 3.1: Iterativelyincrease S1(S1+1) anddecrease S2(S2−1) untilbest solution is foundin terms of profit. Update S1andS2 3.2: Iterativelycheck neighbourhood {(S1+1, S2)/(S1−1, S2)/(S1,S2+1)/(S1,S2−1)}of best solution found so faruntil no better solution is found. Update S1andS2.STOP 4: Iterativelyin-/decrease S1untilno better solution is found. Update S1,keep S2=0. STOP Table 1: Experimentalvalues forthe576experiments Fa ctor Notation Values Substitutionrate γ21 ∈ {0.5, 0.75,0.9, 1} Mean demands (µ1, µ2)∈ {(5,5), (3,7), (7,3)} Shelf life (M1, M2)∈ {(3,3),(5,5),(3,5),(5,3)} Procurementcosts (c1, c2)∈ {(0.5,0.5), (0.7,0.7), (0.5,0.7), (0.7,0.5)} Fraction FIFO consumers a∈ {0, 0.5, 1} 15 Retailer replenishmentpolicies with one-way consumer-based substitution to increase profit andreducefood waste 26. Transchel, S..Inventorymanagement underpricebasedandstockout-based substitution. European JournalofOperationalResearch 2017;262:996– 1008.doi:10.1016/j.ejor.2017.03.075. 27.Honhon, D.,Gaur,V., Seshadri,S..Assortment PlanningandInventory DecisionsUnder Stockout-Based Substitution. Operations Research 2010;58(5):1364–1379.doi:10.1287/ opre.1090.0805. 28. Robinson, S..Simulation: thepractice of model developmentanduse. 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