A heuristic for the inventory management of smart vending machine systems

Transcription

1 Journl of Industril Engineering nd Mngement JIEM, (2): Online ISS: Print ISS: A heuristic for the inventory mngement of smrt vending mchine systems Yng-Byung Prk, Jun-Su Yoo Deprtment of Industril nd Mngement Systems Engineering, College of Engineering, Kyung Hee University (Republic of Kore) ybprk@khu.c.kr, yoojs1231@gmil.com Received: October 2011 Accepted: August 2012 Abstrct: Purpose: The purpose of this pper is to propose heuristic for the inventory mngement of smrt vending mchine systems with product substitution under the replenishment point, order-up-to level policy nd to evlute its performnce. Design/methodology/pproch: The heuristic is developed on the bsis of the decoupled pproch. An integer liner mthemticl model is built to determine the number of product storge comprtments nd replenishment threshold for ech smrt vending mchine in the system nd the Clrke nd Wright s svings lgorithm is pplied to route vehicles for inventory replenishments of smrt vending mchines tht shre the sme delivery dys. Computtionl experiments re conducted on severl smll-size test problems to compre the proposed heuristic with the integrted optimiztion mthemticl model with respect to system profit. Furthermore, sensitivity nlysis is crried out on medium-size test problem to evlute the effect of the customer service level on system profit using computer simultion. Findings: The results show tht the proposed heuristic yielded pretty good solutions with 5.7% error rte on verge compred to the optiml solutions. The proposed heuristic took bout 3 CPU minutes on verge in the test problems being consisted of 10 five-product smrt vending mchines. It ws confirmed tht the system profit is significntly ffected by the customer service level

2 Journl of Industril Engineering nd Mngement - Originlity/vlue: The inventory mngement of smrt vending mchine systems is newly treted. Product substitutions re explicitly considered in the model. The proposed heuristic is effective s well s efficient. It cn be esily modified for ppliction to vrious retil vending settings under vendor-mnged inventory scheme with POS system. Keywords: heuristic, inventory mngement, smrt vending mchines, decoupled pproch 1. Introduction Smrt vending mchines tht enble sles nd inventory informtion to be remotely monitored through the Internet using embedded online messging devices were recently introduced. Webster et l. (1999) developed n experimentl Jv client-server system with specil purpose hrdwre interfce to control Pepsi vending mchine vi the Internet. Jofemr unveiled wht it clims is the world s first utonomous hydrogen-powered smrt vending mchine t the 2009 tionl Vending Mchine Exposition (Fuel Cells Bulletin, 2009). Figure 1 shows n exmple of smrt beverge vending mchine operted t G20 Seoul Summit Conference in Smrt vending mchines re expected to resolve the problems inherent to conventionl vending mchines such s run-out of products nd mchine brekdowns left for long time. Wolson (2000) insisted tht smrt vending mchines re the future of the vending mchine industry. The inventory mngement of smrt vending mchine systems with product substitution under the replenishment point, order-up-to level policy cretes decision mking problem. The problem includes the determintion of replenishment points of products t vending mchines, product lloction to vending mchine storge comprtments, replenishment thresholds t vending mchines, nd vehicle routes for inventory replenishments. Little work hs ddressed the inventory mngement of smrt vending mchine systems in the literture. Poon et l. (2010) developed n index to mke replenishment decisions for smrt vending mchines to minimize trnsporttion nd stock-out costs. Prk nd Yoon (2011) proposed two-phse solution bsed on nonliner integer mthemticl model for the opertion problem of conventionl vending mchine supply chins with stock-out bsed, onestge item substitution. Among reports regrding inventory-routing problems, some re pplicble for determining shipping policies in smrt vending mchine systems (see Archetti et l., 2007; Li et l., 2010; Moin et l., 2011)

3 Journl of Industril Engineering nd Mngement - Figure 1. Exmple of smrt vending mchine In this pper, we propose heuristic for the inventory mngement of smrt vending mchine systems with product substitution under the replenishment point, order-up-to level policy nd conduct computtionl experiments on severl test problems in order to evlute its optimlity. Furthermore, sensitivity nlysis is crried out to evlute the effect of customer service level on system profit using computer simultion. The reminder of this pper is orgnized s follows: A heuristic for the inventory mngement of smrt vending mchine systems is proposed in Section 2. Computtionl experiments re described in Section 3. Finlly, conclusions re drwn in Section A Heuristic for the Inventory Mngement of Smrt Vending Mchine Systems Input prmeters M Q number of products number of storge comprtments cpcity of storge comprtment d ri verge dily demnd for product i t smrt vending mchine r v i vlue of product i 1 rte of inventory crrying cost per dy 2 rte of smrt vending mchine operting cost 3 rte of substitution cost G A e llownce rtio of lost sles during time spn vehicle cpcity fixed trnsporttion cost per vehicle per dy vrible trnsporttion cost per kilometer

4 Journl of Industril Engineering nd Mngement - l 0 r uri Eucliden distnce from depot 0 to smrt vending mchine r replenishment point of product i t smrt vending mchine r Decision vribles r replenishment threshold t smrt vending mchine r P r time spn between the successive replenishments t smrt vending mchine r K ri number of storge comprtments for product i t smrt vending mchine r Frij mount of product i substituted by j t smrt vending mchine r during time spn Iri inventory level of product i t smrt vending mchine r t the end of time spn when product substitution is llowed B ri lost sles of product i t smrt vending mchine r during time spn when product substitution is llowed b B ri stock-outs of product i t smrt vending mchine r during time spn when product substitution is not llowed Z ri 1 if the inventory level of product i t smrt vending mchine r is below the replenishment point; 0 otherwise A smrt vending mchine is fully replenished when the number of products with inventories tht re depleted to their respective replenishment points is equl to the replenishment threshold (n integer vlue between 1 nd the mximum number of products). When customer is fced with stock-out of his or her first-choice product, he or she my choose substitute or give up the purchse. When the product substitution tkes plce, the customer s unstisfctory cost is considered s substitution cost. The replenishment point of product is determined by the verge dily demnd nd customer service level, ssuming the Poisson distribution for customer rrivls nd the led time of one dy. The number of product storge comprtments nd replenishment threshold for smrt vending mchine r re determined by solving the liner integer mthemticl model s follows: Objective function Objective function (1) mximizes the profit during the time spn between successive replenishments, which is computed by subtrcting the sum of the trnsporttion cost, inventory crrying cost, smrt vending mchine operting cost, nd substitution cost from the totl revenue

5 Journl of Industril Engineering nd Mngement - Mx. v i ( Q Kri - Iri ) - [{ A ( Q Kri - Iri ) / G e l0r} i 1 i 1 b 1 v i ( Pr - Bri / dri )( Q Kri Iri ) / 2 2 v i ( Q Kri - Iri ) 3 vifrij ] i 1 i 1 i 1 j 1 j i (1) Constrints Vrious constrints re required. The constrints for computing the inventory levels nd stockouts of products, restricting the lloction of product storge comprtments, limiting the quntities of products for substitution, nd restricting the domin of vribles re formed by modifying the ones shown in Prk nd Yoon (2011). More constrints re needed to determine the replenishment threshold t smrt vending mchine r, replenishment points. r. Constrints (2) nd (3) determine if product inventories rech their respective r is computed by counting Z ri with vlue of 1 for ll products. I ri u ri Big( 1 Zri ) i (2) I ri u ri Big Z ri i (3) Since the objective function is to mximize the profit of smrt vending mchine, the time spn my be lengthened to the period in which the lst remining product in the vending mchine is sold out, generting undesirbly lrge mount of lost sles. Therefore, Constrint (4) tht restricts the mount of lost sles during the time spn should be included. vi Bri Pr vidri i 1 i 1 (4) Once the number of product storge comprtments nd replenishment threshold is determined for ll the smrt vending mchines in the system, the vehicle routes to replenish the smrt vending mchines tht shre the sme delivery dys re constructed. For vehicle routing, the Clrke nd Wright s svings lgorithm (1964) is employed while minimizing the trnsporttion cost. The sving expected by combining two routes, s qr, is computed s follows: s qr lq l r l 0 0 qr (5) where q denotes the lst smrt vending mchine to visit on one route nd r denotes the first one to visit on the other route

6 Journl of Industril Engineering nd Mngement - A combintion of two routes with the lrgest positive s qr is repeted while checking the fesibility with respect to vehicle cpcity nd trvel time until no more fesible pir exists for which s qr 0. Once routes hve been constructed, 2-opt lgorithm is pplied to improve the route solution. 3. Computtionl Experiments The five-product smrt vending mchine loctions were generted using uniform distribution on [0, 100]. The loction of depot ws set to (50, 50). The dily demnd t ech smrt vending mchine ws generted from Poisson distribution, the verge of which ws generted from uniform distribution on [150, 210]. The vlues of five products were set to 0.525, 0.875, 1.225, 0.7, nd 1.05, respectively. The rtes of inventory crrying cost, smrt vending mchine operting cost, nd substitution cost were set to 0.01, 0.1, nd 0.05, respectively. The vehicle cpcity ws set to The fixed nd vrible trnsporttion costs were set to 100 nd 0.4, respectively. The llownce rtio of lost sles ws set to 0.3. It ws ssumed tht the wrehouse t the business office lwys stores the sufficient mount of products to replenish the smrt vending mchines in the system. Computtionl experiments were crried out on n IBM comptible Pentium IV PC (2.21GHz CPU, 1GB RAM) Comprison of the Integrted Optimiztion Model nd the Proposed Heuristic We evluted the performnce of the proposed heuristic by compring it with the integrted optimiztion mthemticl model. The optimiztion mthemticl model determines the number of product storge comprtments nd replenishment thresholds t smrt vending mchines nd the vehicles routes for dily replenishments in n integrted wy while mximizing the system profit during plnning horizon. The integrted optimiztion model ws constructed by bsiclly combining the mthemticl model presented in Section 2 nd the constrints for vehicle routing proposed by Abdelmguid nd Dessouky (2006). In order to solve the integrted optimiztion model within resonble mount of computtion time, we formed smll-size bse problem consisting of ten smrt vending mchines with M 20 nd Q 20 nd constructed three test problems with different dily demnd. Tble 1 compres the verge dily profit per smrt vending mchine for the integrted optimiztion mthemticl model nd the proposed heuristic in the three test problems. The mthemticl models were solved using LIGO The optimiztion mthemticl model nd the heuristic took bout 45 CPU minutes nd 3 CPU minutes on verge, respectively

7 Journl of Industril Engineering nd Mngement - Problem Solution Revenue Cost Profit Error rte(%) 1 Optimiztion model Prpoposed heuristic Optimiztion model Proposed heuristic Optimiztion model Proposed heuristic Tble 1. Comprison of two solutions for the verge dily profit per smrt vending mchine 3.2. Sensitivity Anlysis We crried out sensitivity nlysis to evlute the effect of the customer service level on system profit using the proposed heuristic. We formed bse problem consisting of eighty smrt vending mchines with M 25 nd Q 30. The opertion of the smrt vending mchine system ws modeled with Aren 10.0 (Kelton et l., 2007). Slmeron (2009) stted tht simultion is one of the most commonly used methodologies employed in opertions mngement reserch nd listed some emerging res to pply including system design. During the simultion, when vehicle fces deficiencies of some products when filling smrt vending mchine, it stocks the storge comprtments s much s possible nd trvels to the next vending mchine with the remining supply. When vehicle still hs supply fter serving the lst vending mchine on its tour, it returns to the depot with the reminder. The dily opertion of vehicles is limited to 8 hours. Tble 2 shows the verge dily profit per smrt vending mchine for four different service levels in three replictions, which were obtined by simulting ech level for 365 dys. The highest verge dily profit per smrt vending mchine ws obtined t 70% service level. For sttisticl confirmtion of our finding, we performed one-wy nlysis of vrince (AOVA) using n Excel spredsheet, s shown in Tble 3. The test sttistic ws obtined s F F0.05,3, , indicting tht the customer service level hs sttisticlly significnt effect on profit t the 5% level. Repliction Customer service level Avg Tble 2. Averge dily profit per smrt vending mchine for four different service levels

8 Journl of Industril Engineering nd Mngement - Chnges in Sum of Degree of Mensqured F0 P-vlue F0.05,3,8 types squres freedom Tretment Residuls Totl Tble 3. Test sttistics of AOVA for the service level Tble 4 shows the prtil solutions of the five smrt vending mchines rndomly selected, which were obtined in the first repliction with the customer service level of 0.7. Tble 5 shows the monetry outputs obtined in the first repliction with the customer service level of 0.7 by simulting the system for 365 dys. Vending mchine o. of storge comprtments Replenishment threshold Product Tble 4. Prtil solutions obtined in the first repliction with the service level of 0.7 (unit: 1000) Revenue Cost Profit Purchse Inventory crrying mchine operting Trnsporttion fixed vrible Substitution Tble 5. System outputs obtined in the first repliction with the service level of Conclusions We proposed heuristic for the inventory mngement of smrt vending mchine systems with product substitution under the replenishment point, order-up-to level policy. The heuristic solves the problem in decoupled wy. First, it determines the replenishment points of products t smrt vending mchines. Second, it determines the number of product storge comprtments nd the replenishment thresholds t smrt vending mchines. Third, it determines the vehicle routes for dily replenishments

9 Journl of Industril Engineering nd Mngement - The proposed heuristic yielded pretty good solutions with 5.7% error rte on verge compred to the optiml solutions obtined by solving the integrted mthemticl model. The heuristic took bout 3 CPU minutes. It ws confirmed through the sensitivity nlysis using computer simultion tht the system profit is significntly ffected by the customer service level. Future reserch is necessry to develop more efficient nd effective solutions for the inventory mngement of smrt vending mchine systems. Furthermore, it is required to develop n lgorithm to find the optiml llownce rtio of lost sles during the time spn which mximizes the system profit. Acknowledgment This reserch ws supported by the Bsic Science Reserch Progrm through the tionl Reserch Foundtion of Kore (RF) funded by the Ministry of Eduction, Science, nd Technology ( ). References Abdelmguid, T.F. nd Dessouky, M.M.A. (2006). Genetic lgorithm pproch to the integrted inventory-distribution problem. Interntionl Journl of Production Reserch, 44(21), Archetti, C., Bertzzi, L., Lporte, G., & Spernz, M.G. (2007). A brnch-nd-cut lgorithm for vendor-mnged inventory-routing problem. Trnsporttion Science, 41(3), Clrke, G., & Wright, J. (1964). Scheduling of vehicles from centrl depot to number of delivery points. Opertions Reserch, 12(4), Fuel Cells Bulletin (2009). Jofemr lunches hydrogen-powered vending mchine. Fuel Cells Bulletin, Jnury, Kelton, W., Sdowski, R.P., & Sturrock, D.T. (2007). Simultion with ren. 4th ed., ew York: McGrw-Hill. Li, J., Chen, H., & Chu, F. (2010). Performnce evlution of distribution strtegies for the inventory routing problem. Europen Journl of Opertionl Reserch, 202(2),

10 Journl of Industril Engineering nd Mngement - Moin,.H., Slhi, S., & Aziz,.A.B. (2011). An efficient hybrid genetic lgorithm for the multiproduct multi-period inventory routing problem. Interntionl Journl of Production Economics, 133(1), Prk, Y.B., & Yoon, S.J. (2011). A two-phse solution for the opertion problem of vending mchine systems with stock-out bsed, one-stge item substitution. Proceedings of the 16 th Annul Interntionl Conference on Industril Engineering, Stuttgrt, Germny, Poon, T.C., Choy, K.L., Cheng, C.K., & Lo, S.I. (2010). A rel-time replenishment system for vending mchine industry. IEEE Interntionl Conference on Industril Informtics, Slmeron, J.L. (2009). Specil issue: ew trends in process simultion nd modeling. Journl of Industril Engineering nd Mngement, 2(2), Wolson, S. (2000). Remote technology gining cceptnce: smrt mchines. Food Service Director, 13(8), 13. Webster, R.W., Ross, P.W., Biley, T.M., Conrd, S.M., Fiorill, M.J., Flinchbugh, J.M., & Velkly, E.A. (1999). Controlling Jv enbled Pepsi vending mchine over the world wide web. IECO Proceedings of the 25 th Annul Conference of the IEEE, 1(29), Journl of Industril Engineering nd Mngement, 2012 ( El rtículo está con Reconocimiento-oComercil 3.0 de Cretive Commons. Puede copirlo, distribuirlo y comunicrlo públicmente siempre que cite su utor y Intngible Cpitl. o lo utilice pr fines comerciles. L licenci complet se puede consultr en