A Genetic Algorithm based Approach for Cost worthy Route Selection in Complex Supply Chain Architecture

Transcription

1 A Genetic Algorithm bsed Approch for Cost worthy Route Selection in Complex Supply Chin Architecture Arft Hbib ~, Nfi Rhmn*, Jhid Alm *, Asif Jorder *, Mrji Hque * ~ Deprtment of Computer Science nd Engineering, BRAC University, Dhk, Bngldesh * Ahsnullh University of Science nd Technology, Dhk, Bngldesh Abstrct It is lwys gret chllenge to select n optiml route in cse of complex supply chin rchitecture. The chllenge lies in meeting the reverse condition of qulity of service nd money. As time is n importnt fctor, choosing the optiml route in supply chin rchitecture often becomes the most vitl. To utomte the route finding, in this pper, we propose model tht resemble to modern nd complete supply chin network. We intend to solve it with the Genetic Algorithm so tht route with lest cost is derived. For experiment purpose, we hve implemented our model on hypotheticl considertion bsed scenrio, in which the genertion, cross over nd muttion process of genetic lgorithm of the whole proposed model exhibits the optimized vlues for different routes. The lgorithm ws implemented in MATLAB bsed environment. To show the invincibility of the Genetic Algorithm, we hve lso compred the computtionl time of this lgorithm with rewrd bsed mchine lerning lgorithm Q-lerning. Simultion result shows tht Genetic lgorithm tkes lesser computtionl time. Keywords supply chin; route finding; genetic lgorithm I. INTRODUCTION The reson behind trnsporttion s hving prime role in supply chin mngement is becuse products re never produced nd consumed in the sme plce [1]. Trnsporttion modes tht re commonly used in moving products from one plce to nother re minly ir, wter, ril, truck or intermodl wy of trnsporttion [2]. The entities tht form supply chin rchitecture re retilers, distributors, crriers, mnufcturers, customers. They use different modes of trnsporttion within the network to rech ech other [3]. The min gol is to chieve n optiml route with minimum cost. Genetic lgorithm is the most populr lgorithm tht hs been used to select optiml route. Mny reserchers re working on it to optimize routes in supply chin networks using Genetic lgorithm. They hve plenty of limittions. The vitl drwbck they hve is the incomplete design of supply chin rchitecture tht hrdly reflects the prcticl models of supply chin networks. Route Optimiztion in Supply Chin Networks is multi-criterion complex decision mking problem tht hs to stisfy mny constrins [4]. According to the studies of [5], Genetic Algorithms work better where the trditionl serch nd optimiztion Algorithms fil to vil the gol performnce. Lwrynowicz et l lso ssert tht GAs re efficient tools for solving complex optimiztion problems, highlighting the problem of minimizing the totl cost for distribution network, which presents some similr fetures to the problem ddressed in this pper [6]. Wen et l proposed Genetic Algorithm, using n integer encoding to represent the crgo item sequence to be delivered in order to solve the problem of logistics scheduling problem nd optimize the totl cost for loction-routing-inventory problem [7]. The proposed pproch obtined good performnce in terms of qulity mesure but the computtion speed does not meet requirements. A genetic lgorithm bsed model ws proposed by Nfi et l tht covers only 3 key components of supply chin model [8]. They re suppliers, mnufcturing plnts nd customers. Covering these three entities do not mke supply chin network universl. The reserch lso lcks in experimentl dt tht my help the reders understnd the subtle issues of implying genetic lgorithm. Altiprmk et l in their work presented mixed-integer non-liner progrmming model for multi-objective optimiztion of Supply Chin Network nd Genetic Algorithm pproch to solve the problem but did not work with the uncertinty of the cost nd demnds which should hve been delt with [9]. Another Approch introduced by Mortz et l covers the use of RPS lgorithm in route optimiztion problem [10]. The min contribution of this reserch is the use of multi gent who cn shre their knowledge while lerning the environment. The min drwbck of this pper cn be noted s their filure to work with the reverse condition of cost minimiztion nd qulity ssurnce. To overcome these limittions, we propose fulfilled supply chin rchitecture with mximum possible number of nodes to be solved with Genetic Algorithm. The rest of the pper is orgnized s follows: section II describes the proposed model; section III elbortes the experimentl results nd lstly section IV concludes the pper with possible future works. 1

2 II. PROPOSED MODEL For the impliction of Genetic Algorithm, network model hs been designed considering supplier, mnufcturing plnt, distributor, retiler nd customer s nodes. The entities re connected with four modes of communiction such s trin (t), ril (r), ir (), wter (w). Fig. 1 shows the network model of the supply chin network for the implementtion of Genetic Algorithm. Supplier w t r Mnufctu ring Plnts w Fig. 1. Designed Network Model to implement Genetic Algorithm. The entire process of pplying genetic lgorithm in our smple cse scenrio is described in the following digrm (see Fig. 2) Strt Input for the opted problem t w Fig. 2. Schemtic Digrm for Genetic Algorithm. Retiler w t r Distributor Input (Genetic Algorithms) 1. Muttion 2. Crossover Etc. GA ppliction Objective function setup with constrints t Customer r i Result Following objective function hs been designed for our formulted problem: Here, Prmeters re described below 1. m = Set of vehicle routes from supplier to mnufcturing plnt. 2. i = Number of supplier, i = 1 to n. 3. j = Number of mnufcturing plnts, j = 1 to n. 4. n = Set of vehicle routes from mnufcturing plnts to distributors. 5. k = Number of distributors, k = 1 to n. 6. o = Set of vehicle routes from distributors to retilers. 7. l = Number of retilers, l = 1 to n. 8. v = Set of vehicle routes from retilers to customers. 9. c = Number of customers, c=1 to n. 10. Zmij = Binry vrible whether the vehicle route to be opted is ir (), wter (w), truck(t) or ril(r) from suppliers to mnufcturing plnts 11. Znjk = Binry vrible whether the vehicle route to be opted is ir (), wter (w), truck(t) or ril(r) from mnufcturing plnts to distributors 12. Zokl = Binry vrible whether the vehicle route to be opted is ir (), wter (w), truck(t) or ril(r) from distributors to retilers 13. Zvlc = Binry vrible whether the vehicle route to be opted is ir (), wter (w), truck(t) or ril(r) from retilers to customers 14. Dmij = Unit trnsporttion cost from suppliers to mnufcturing plnts. 15. Dnjk = Unit trnsporttion cost from mnufcturing plnts distributors. 16. Dokl = Unit trnsporttion cost from distributors to retilers. 17. Dvlc = Unit trnsporttion cost from retilers to customers. The constrints for our cse scenrio of genetic lgorithm re: 1. Zmij = At lest one route should be open from suppliers to mnufcturing plnts. 2. Znjk = At lest one route should be open from mnufcturing plnts to distributors. 3. Zokl = At lest one route should be open from distributors to retilers. 4. Zvlc = At lest one route should be open from retilers to customers. 2

3 Fig 3 shows the best fitness nd the expecttion grph of the implemented genetic lgorithm in our cse scenrio. Fig. 4. Expecttion nd Genelogy grph. Fig. 3. Best Fitness nd Expecttion. Fig. 4 shows the expecttion nd genelogy grph for the implemented Genetic lgorithm. Fig. 5 shows the distnce nd rnge grph for the implemented genetic lgorithm. 3

4 III. EXPERIMENTAL RESULTS Approximte dt rnge for our model is given below. The dt rnge hs been decided bsed on judgment nd expert opinion. Air Trnsporttion = unit Wter Trnsporttion = unit Ril trnsporttion = unit Truck Trnsport = unit Fig. 7 shows tht the optimized vlue chieved from Genetic Algorithm. Fig. 5. Distnce nd Rnge Grph. Fig. 6 shows the selection nd mximum constrint grph for the implemented genetic lgorithm. Fig. 7. Optiml vlue selection using Genetic Algorithm Here, [Ril, 332] = Ril trnsporttion cost is close to the optimized vlue 279. So, ril is the optimized route from supplier to mnufcturing plnts. [Wter, 279] = Wter trnsporttion cost is equl to the optimized vlue 279. So, this route is the optimized route from mnufcturing plnts distributors. [Truck, 362] = Trnsporttion cost for truck is close to the optimized vlue 279. So, the optimized route from distributors to retilers is trnsporttion vi truck. [Wter, 279] = Wter trnsporttion cost is equl to the optimized vlue 279. So, wter is the optimized route from retilers to customer. Fig. 6. Selection nd mximum constrint grph. 4

5 Supply chin network tht we hve considered in our work hs mny nodes nd consists of complex rchitecture. How fst we cn get the output, is very importnt issue in this cse. Tht is why, we hve counted computtionl time s very importnt metric to mesure the performnce of the implied lgorithms. TABLE IV shows us the lesser computtion time tken by the Genetic Algorithm. TABLE IV. COMPUTATIONAL TIME OF DIFFERENT ALGORITHMS Algorithm Computtionl Time (sec) Q-lerning Genetic Algorithm 6.25 From the tble we cn see tht the lest computtionl time is tken by the Genetic lgorithm. Fig. 8 shows the grph of the computtionl time comprison of the implemented lgorithms. lgorithm hs not yet been used formlly in this field nd due to the eligibility trce prmeter in the lgorithm, it is quite predictble tht the lgorithm will tke less computtionl time nd the convergence speed will be lesser. In future, we re plnning to build jv bsed softwre tht will help people find optiml route using simple inputs with the help of this lgorithm. REFERENCES [1] S. Chopr, nd P. Meindl, Supply Chin Mngement Strtegy, Plnning, nd Opertion, 5 th Edition, Februry 5, 2012, ISBN-13: [2] S. Cohen nd J. Roussel, Strtegic Supply chin Mngement: The five Core Disciplines for Top Performnce, 2 nd Edition, McGrw-Hill, June 14, 2013, ISBN-13: [3] M. Hughos. Essentils of Supply Chin Mngement, 3 rd Edition, John Wiley nd Sons, July 2011, ISBN: K. Eliss, Title of pper if known, unpublished. [4] M. Kumr, P. Vrt nd R. Shnkr. A fuzzy gol progrmming pproch forvendor selection problem in supply chin.computer & Industril Eng., 46: [5] M. Ko, A. Tiwri nd J. Mehnen. A review of soft computing pplictions in supply chin mngement. Applied Soft Computing, 10(3): [6] A. Lwrynowicz. A survey of evolutionry lgorithms for production nd logistics optimiztion. Reserch in Logistics nd Production, 1(2): [7] C. Wen nd R. Eberhrt. Genetic lgorithm for logistics scheduling problem. In Evolutionry Computtion, CEC 02. Proc. of the 2002 Cong. on, volume 1, pges [8] N. Rhmn, A. Hbib, Z. Alm, A. Zorder, nd M. Hque, Route Optimiztion in Supply Chin Network, Imperil Journl of Interdisciplinry Reserch, vol. 2, no. 7, pp , [9] F. Altiprmk, M. Gen, L. Lin nd T. Pksoy, A Genetic Algorithm Approch for Multi-objective Optimiztion of Supply Chin Networks, vol. 51, no. 1, pp , [10] Z. Mortz, A. Selmt, nd S. M. Hshim, Route Plnning Model of Multi-gent System for Supply Chin Mngement, vol. 40, no. 5, pp , Fig. 8. Computtionl Time Comprison of the Q-lerning nd GA IV. CONCLUSION AND FUTURE WORK In this pper, we hve modeled universl supply chin rchitecture with the mximum nodes tht cn be dded. We lso compred the computtionl time with very populr reinforcement lerning Algorithm, Q-lerning. The evolutionry lerning lgorithm worked fster. We still do not know if Genetic Algorithm will outsmrt reinforcement lerning lgorithms like SARSA (Stte-Action-Rewrd-Stte- Action Algorithm). This rewrd bsed mchine lerning 5