Web Based Multi Product Inventory Optimization Using Genetic Algorithm
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011Web based Multi Product Inventory Optimizationusing Genetic AlgorithmPriya PDr.K.IyakuttiResearch Scholar,Dept of computer science, BharathiarUniversity, CoimbatoreSenior Professor, Madurai KamarajarUniversity, MaduraiABSTRACTThis paper presents an approach to optimize the reorderlevel (ROL) in the manufacturing unit taking considerationof the stock levels at the factory and the distribution centersof the supply chain, which in turn helps the production unitto optimize the production level and minimizing theinventory holding cost. Genetic algorithm is used for theoptimization in a multi product, multi level supply chain ina web enabled environment. This prediction of optimalROL enables the manufacturing unit to overcome theexcess/ shortage of stock levels in the upcoming period.1. INTRODUCTIONInventory encompasses all raw materials, work in process,and finished goods within the supply chain. ChangingInventory policies can dramatically alter the supply chain’sefficiency and responsiveness. Inventory is an importantcross functional driver of supply chain performance. Animportant role that can be satisfied by having the productready and available when the customer wants it. Inventoryis held throughout the supply chain in the form of rawmaterials, work in progress, and finished goods.2. LITERATURE REVIEWChandra et al (2010) has developed a two-warehouseinventory model for deteriorating items when demand isprice sensitive. In this article, an attempt has been made todevelop an order-level inventory model for deterioratingitems with two-storage facility under a bulk release pattern.They have assumed that the deterioration rate of the itemsstored might be different in the two ware-houses due to thedifference in the environmental conditions or preservingconditions. Also the same model is applicable when thedeterioration rate is same in both the warehouse. Acomputational procedure is also proposed to obtain theoptimal number of shipments, optimal shipment quantityand optimal selling price, which maximizes the total profitof the system.Narmadha, et al (2010), proposed a Genetic Algorithm withuniform cross over to study the stock level that needsessential inventory management control. The authorsdiscussed that the proposed approach of inventorymanagement satisfied the objectives such as minimizationof the total supply chain cost and determination of theproducts due to which the supplier endured eitheradditional holding cost or shortage cost. The authors alsoproposed that the complexity increases when moredistribution centers, agents and multi products are involvedin the supply chain. Following the predicted stock levelsexcess storage/ shortage inventory levels can be avoided inthe upcoming period and hence the increase in the supplychain cost can be avoided.Radhakrishnan, et al (2010) proposed a novel approachbased on Genetic Algorithm to predict the most emergingstock levels of the future by considering the stock levels ofthe past periods. They have discussed the supply chainwhere multiple factories, multiple products and multipleagents are the members of the supply chain. The inventoryoptimization in the supply chain is distinctively determinedto achieve minimum total supply chain cost using theproposed approach.Kannan et al (2009), presents an integrated forwardlogistics multi-echelon distribution inventory supply chainmodel and closed loop multi-echelon distribution inventorysupply chain model for built to order environment usinggenetic algorithm and particle swarm optimization. Theyhave developed a new model that integrates the forwardand reverse logistics in a built to order supply chainenvironment. This model is used to optimize thedistribution and inventory in the supply chain using GeneticAlgorithm to minimize the total supply chain cost, whichincludes purchasing, production, distribution and inventoryrelated costs to the build to order environment.Xiuli Chao and Sean X. Zhou (2009), has presented anefficient algorithm for computing the optimal controlparameters in inventory control policy. An optimal orderingpolicy for the multi echelon system with both batchordering and fixed replenishment intervals, and also adistribution function solution for the optimal reorder pointsare given solely in terms of lead lime demand distributionfunction. They had shown that the optimal average cost isminimized when all stages are synchronized, hence theoptimal reorder point for each stage is lowest as all thestages are synchronized.Maity et al (2009), has proposed optimum production for amulti-item production inventory system with deterioratingunits, space capacity constraint. They formulated a multiitem system with a resource constraint via optimal controltheory for steady state case and transitive case respectively.In future the formulation and analysis can be extended toother production inventory problem in fuzzy , fuzzystochastic environment with different types of demand,defectiveness and deterioration.23
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011Uthayakumar et al (2009), has proposed an optimalreplenishment policy by considering stock dependentconsumption rate for non instantaneous deteriorating itemswith money inflation and time discounting. The authorshave framed deterministic inventory model for noninstantaneous deteriorating items with stock dependentconsumption. Shortages are allowed and partiallybacklogged. The aim is to minimize the retailer’s totalinventory cost by considering effect of inflation and timevalue of money.From the literature study on optimizing the ROL ofinventory in a multi product environment, it is clear that aweb based attempt to monitor the stock levels across thesupply chain from the manufacturing unit through thedistributors and online optimization of the ROL usinggenetic algorithm has not been reported in the literature.2.1 Steps in Genetic AlgorithmStep1Choose a coding to represent problemparameters, a selection operator, crossover operator, and amutation operator. Choose population size n, crossoverprobability (Pc) and mutation probability, (Pm). Initialize arandom population of strings of size (I). Choose amaximum allowable generation number tmax, set t 0.Jianhui Wang et al (2006), proposed an improved GeneticAlgorithm for the spare part store management. Theobjective is to optimize the number of stores and reduce thecost of store management. The improved genetic algorithmnamely Genetic algorithm of Deuce SymmetricalCrisscross Based on Real Value (GADSC) operates on realnumber bound. The optimum value of the spare part storesis the real value. The authors constructed a multi objectiveoptimal model and single period spare part storemanagement optimal model. The authors concluded that theproposed improved methodology will aim in minimizingthe management cost and interrelated expenses.Step 2 Evaluate each string in the population.Step 3 If t tmax , or other termination criteria is satisfied,Terminate.Step 4 Perform reproduction on the population.Step 5 Perform crossover on random pair of stringsStep 6 Perform mutation on every stringGunasekaran, et al (2004), proposed a framework topromote a better understanding of the importance of supplychain performance measures and metrics. Based on selectedliteratures on supply chain performance the framework wasdesigned. He designed a seven page questionnaire dividedinto four categories addressing basic four activities ofsupply chain. The performance measures were categorizedbased on importance, highly, moderately and less.Step 7 Evaluate strings in the new population , set t t 1and go to step 3The algorithm is straight forward with repeated applicationof three operators (step 4 to step 7) to a population ofpoints.3. SYSTEM DESIGNIn the proposed system shown in Figure 1, thesales of multiple products are centralized with directinterface between retailer and manufacturer. The reorderlevel (ROL) of the inventory is optimized using geneticalgorithm in the factory. A centralized sale helps to monitorthe sales of the products throughout the supply chain withvisibility.Jeffery Jones, et al (2002) discussed a Genetic algorithmapproach for sourcing decisions within the supply chain.The authors proposed a simulation technique in theoptimization process for a multi objective problem. Insteadof a analytical evaluation, each solution was simulated todetermine its performance.Production o/pFactory(Manufacturing)DispatchingProduct MasterClosing StockCurrent StockDecision MakerProduction i/pVariableROLPositionInput GeneGeneticsAlgorithmEngineG.A.E. ROL forMultiple ProductsChromosomeOrder Vs ROLOverall SODashboardBest Data SuiteOptimized ROLFitness FunctionCross OverMutationWholesale S/wFigure 1 System design24
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011The two stages of the supply chain namely theManufacturing industry and the distribution centers areconsidered in the study. Our exemplary supply chainconsists of Manufacturing unit, Distribution center 1 anddistribution center 2, thus a three level supply chain. Theretailer’s stock level is combined with the distributor. Weconsider the stock level for 52 week, i.e., for one year. If anew entry is given that will be taken as a fifty second entryand the first entry will move off (stack, last in first out).The objective of the problem is to obtain the near optimalreorder level in the manufacturing unit, which helps theproduction unit to take decision about the productionquantity. The a novel approach based on genetic algorithmis used to predict the optimal reorder level that contributesto reduce the inventory holding cost.(i)After Mutation2597672This is done by random generation of two points and thenperforming swaps between both the genes.(ii) Objective functionThe objective function that enumerates the optimality of thesolution in a genetic Algorithm is known as fitnessfunction. The fitness function is taken from Radhakrishnanet al (2010) and is given as:Chromosome RepresentationThe weekly stock level of the Manufacturing unit,Distribution centers 1 and 2 are taken as a gene of thechromosome. Here we are using only three members of thesupply chain, hence the length of the supply chain is three.Initially two chromosomes are generated and GAoperations are performed in the GA Engine (GAE).Chromosome I25958763517243Chromosome IIA single point crossover operator is used as illustratedbelow.Before Cross-overChromosome I25958763517243Chromosome IIAfter Cross-overChromosome IChromosome II25935172587643The newly obtained chromosomes from crossoveroperation are then pushed for mutation. By performingmutation, a new chromosome will be generated asillustrated below.Before Mutation2597276f(i) log 1 -, i 1,2,3, . ,nWhere: The Average of the number of occurrencesof the stock ofmanufacturing unit, distributions centers1 and 2 within the range of 10 and -10 in 52 weeks in therecord set. The total number of data present, i.e. 52, inthe record set.But in that paper (Radhakrishnan et al, 2010), they havejust calculated the optimal stock levels at different levels ofsupply chain. But, in this paper, we intend to calculate theROL of the factory in a web enabled environment.(iii) Reorder LevelThe objective is of minimization type and the value of f(i)always lies between -1 and 0. Since we have taken therange within 10, the reorder level will be increased to 10if the value of objective function lies between -0.5 to 0 andthe reorder level will be decreased by 10 if the value of f(i)lies between -1 to -0.5.4. IMPLEMENTATION OF WEBENABLEDINVENTORYOPTIMIZATIONThe web implementation comprises the articlemodule, factory module, distribution center 1 module,distribution center 2 modules and genetic algorithmmodule. The brief description of the modules is givenbelow:(i)Article Module:The Article Module contains the “new registration”and “article view”. The New registration is used to includethe new article having the fields Article Id, Category, Type,color, Size, MRP and ROL. The article view is used to25
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011display the master view of the article, i.e., existing articlelist having the field name as article Id, category, Type,Color, Size, MRP and ROL.(ii) Factory Module:The Factory Module consists of the Stock Entry andStock Position. The stock entry is used to enter the closingstock of the week of a particular article Id as shown inFigure 2.Factory stock position with respect to the Article id isdisplayed with the fields article Id, category, type, Color,Size, Weeks number and Stock position as shown in Figure3.Figure 2 Factory stock entry screenFigure 3 Factory stock position view(iii) Distribution Center 1 and Distribution Center 2ModuleThe Distribution Centers module contains the twocategories similar to that as the factory Module, Stock andStock Position. The closing stock of the particular week ofthe respective distribution centers with article Id is entered.Distribution Center stock position with respect to the articleId is displayed with the field’s article Id, category, type,Color, Size, Weeks number and Stock position.26
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011(iv) Genetic Algorithm ModuleThe Genetic Algorithm module contains three sub-modulesChromosome Representation, Crossover and Mutation.Chromosome representation consists of Chromosome I andChromosome II with the article Id as shown in Figure 4.displays the new Chromosome with the respective fitnessfunction as shown in Figure 5.The mutation Module performs the mutation and gives thenew chromosome with the fitness function value with newoptimized ROL as shown in Figure 6.The fitness function of chromosome I can be found. Thecrossover module performs the crossover operation andFigure 4 Chromosome representationFigure 5 Illustration of cross over operation27
International Journal of Computer Applications (0975 – 8887)Volume 25– No.8, July 2011Figure 6 Illustration of mutation operationThus the developed model facilitates to optimize thereorder level each week in the automobile manufacturingunit.International Journal of Information and SystemSciences, Vol. 2, No. 1, pp: 59 – 66, 2006.[6]Kannan. G, Noorul Haq and Devika . M, “Analysis ofClosed Loop Supply Chain using Genetic Algorithmand Particle Swarm Optimization”, InternationalJournal of Production Reearch, Vol. 47, pp 1175 –1200, 2009.[7]Maiti. M and Maity. K, “Optimal Inventory PoliciesFor Deteriorating Complementary And SubstituteItems”, International Journal of System Science, Vol.40, pp:. 267 – 276, 2009.[8]Narmadha. S, Selladurai. V, Sathish. G,“Multiproduct Inventory Optimization using UniformCross Over Genetic algorithm”, IJCSIS, Vol. 7, No. 1,2010.5 CONCLUSIONSInventory is a major source of cost in a supply chain andhas huge impact on responsiveness, so inventorymanagement becomes significant entity of supply chainmanagement. This paper has demonstrated the optimizationof the ROL in manufacturing industry, wholesaler andretailer, which in turn needs the information of the stocklevel and the needed ordering quantities of the multipleproducts. A novel approach based on genetic algorithm isapplied to determine the most probable ROL required forinventory optimization in the supply chain which ensuresminimization of the total supply chain cost. The proposedfuture work is to apply the method for increased number ofdistribution centers and to implement other heuristics suchas simulated annealing for the same.6. REFERENCES[1] Beamon, B.M., “Supply Chain design and Analysis:Models and Methods”, International Journal ofProduction Economics, Vol. 55, pp: 281-294, 1998.[2][3]Chandra K. Jaggi, Aggarwal. K.K and PriyankaVerma, “Two Warehouse Inventory Model ForDeteriorating Items When Demand Is Price Sensitive”,International Journal of Operational Research, Vol.7,No. 4, Pg 530 – 543, 2010.Gunasekaran. A, Patel. C, Ronald E. McGaughey, “AFramework For Supply Chain PerformanceMeasurement”, International Journal of ProductionEconomics, Vol. 87, pp: 333 – 347, 2004.[4] Jeffery Joines, Gupta, Mahmut Ali Gokee, Michael G.Kay, Russell E. King, “Supply Chain Multi ObjectiveOptimization”, Proceeding of the 2002 WinterSimulation Conference, 2002.[5]Jianhui Wang, Lin Xu, Shufang Sun and YongliangYan, “Optimization of Spare Parts Stores Based on anImproved Genetic Algorithm in a Supply Chain”,[9] Narmadha. S, Selladurai. V, Sathish. G, “EfficientInventory Optimization of multiproduct, multiplesuppliers with lead time using PSO”, IJCSIS, Vol. 7,No. 1, 2010.[10] Radhakrishnan. P, Prasad V.M. and Jeyanthi. N,“Predictive analysis using Genetic Algorithm forEfficient SupplyChain Management”, Journal ofComputer Science and Network Security”, Vol. 10,No. 3, pp:. 1820-0186., 2010.[11] Radhakrishnan. P, Prasad. V.M and Jeyanthi. N,“Design of Genetic Algorithm based Supply chainInventory Optimization with Lead Time”, Journal ofComputer Science and Network Security”, Vol. 10,No. 3, pp: 1820-1826, 2010.[12] Sean X. Zhou and Xiuli Chao, “Optimal Policy for aMulti Echelon Inventory system with Batch Orderingand Fixed Replenishment Intervals” , OperationsResearch, Vol. 57, pp: 377-390, 2009.[13] Uthayakumar. R and Geetha. K.V, “ReplenishmentPolicy For Single Item Inventory Model With MoneyInflation”, Opsearch, Vol. 46, pp: 345-357, 2008.28
inventory in a multi product environment, it is clear that a web based attempt to monitor the stock levels across the supply chain from the manufacturing unit through the distributors and online optimization of the ROL using genetic algorithm has not been reported in the literature. 2.1 Steps in Genetic Algorithm
Balance sheet Inventory Cost / Unit Inventory Value x Holding Cost Inventory Turns Inventory Value Inventory Turns Wal Mart Stores Inc. Kmart Corp. . Restaurant; High Tech; Inventory decisions 1 Christmas Tree Problem 100 8 15 22 29 2 9 16 23 30 3 10 17 24 31 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28
An inventory valuation method that assumes the most recent products added to your inventory are the ones to be sold first. Average inventory cost . An inventory valuation method that bases its figure on the average cost of items throughout an accounting period. Average inventory . The average inventory on-hand over a given time period,
property inventory system. The PCO will also prepare annual inventory control printouts and furnish them to all ODOC facilities/units. III. Inventory Control Officers and Agents Each facility/unit will designate an inventory control officer (ICO) who may designate one or more inventory control agents (ICA) to maintain inventory records
19.Preferred Teaching Approach Inventory 20.Principles of Adult Learning Scale 21.Teacher BehaviorPreferences Survey 22.Teaching Goals Inventory 23.Teaching Methods Inventory 24.Trainer Style Inventory 25.Training Style Inventory 26.Trainer Type Inventory 27.Effective Teacher Inventory 28.Clinical Teacher Characteristics Instrument 29 .
Mississippi Forest Inventory (MFI) Inventory Unit First Inventory Second Inventory Southwest 2004 2012 Southeast 2005 2013 Central 2006 2014 North 2007 2015 Delta 2008 2016. USFS Forest Inventory and Analysis (FIA) Initiated in 1930's Continuous forest inventory Forest Area and Distribution Species, size and health of trees
The cost of ending inventory can be determined by using ABC Method of inventory accounting or the FIFO or LIFO inventory accounting methods, or any less ordinary technique. Beginning inventory for the financial year under study is ending inventory . Perpetual inventory systems provide the company owner with a proof of what is sold, when it .
Inventory Approver and an Inventory Administrator has reviewed it and marked it to be posted to the core AM tables. In Process: The inventory transaction is being posted. Posted: Inventory Code and asset information updates have been posted to the core AM tables. PS 1.Use the Inventory Status field to approve or reject an inventory .
Multi-Echelon Inventory –June 15, 2006 Net Lead Time vs. Inventory Precise relationship between NLT and inventory: NLT replaces LT in earlier formula So, choosing inventory levels is equivalent to choosing NLTs, i.e., choosing S at each stage Efficient algorithms exist for finding optimal S values to minimize expected holding cost while meeting
