Production Planning in the Inventory Limited Capacity Setting Assuming Permissible Storage Shortage Using Dynamic Programming Model

Transcription

1 Proceedings of he World Congress on Engineering 2009 Vol WCE 2009, July - 3, 2009, London, U.K. Producion Planning in he nvenory Limied Capaciy Seing Assuming Permissible Sorage Shorage Using Dynamic Programming Model Firoozeh Aarian, Habibollah Javanmard,Ali Mardani, Ehsan Kish Hazrae Solan Absrac- n he producion planning process, wo main objecives are saisfying cusomer demand and achievemen of he lowes cos which are someimes incompaible aims. he increase of invenory level, for example, may resul in increase of cusomer demand; alhough he holding coss are ofen a very high level, so he oal cos is no esimaed a minimum level. Focusing on he minimal cos may cause failing o supply he cusomer demand and is consequence is loss for he company. n he presen research, he siuaion is named as ''invenory shorage''. he main objecive is o develop producion planning model of Foulad Azarbayjan Company a ran assuming invenory limied capaciy and permissible sorage shorage (backorder). n he line wih he main objecive, following resuls are obained: () opimal producion rae a he beginning and ending of each period, (2) minimal oal cos,(3) invenory opimal level a he beginning of period, and (4) opimal back order rae. n he presen research, daa gahering and analysis were underaken using seel indusry's connoisseurs and exper's opinions in he field of producion planning and model formulaion was according o he dynamic programming mehod. Key words: nvenory, Opimum soluion, Back order, Producion planning.. NRODUCON he presen inense compeiion among manufacuring companies causes some challenges in resource allocaion and operaion iming, so he Producion planning is one of he imporan applicaion branches which have been creaed hrough he combinaion of various indusrial engineering echniques wih hisorical mehods and mahemaical opimizaion []. is somehow rare ha oher branches of indusrial engineering o have such a high level of capaciy o include and accep variey of concepual and mahemaical models. Producion planning is defined as a decision making process wih respec o some resources Firoozeh Aarian,is wih he Road and ransporaion Minisry of ran. Habibollah Javanmard,is Assisan professor of he slamic azad Universiy,Arak Branch,ran (corresponding auhor o provide phone: ; Javanmardha@ yahoo.com). Ali Mrdani and Ehsan Kish Hazrae Solan are Maser Sudens in ndusrial Managemen of slamic Azad Universiy, Arak Branch, ran which are needed for he fuure producion operaions of he organizaion and also companies are forced o be cauious in heir decision makings. he developmen of marke place has highlighed he imporance of producion efficiency in he manufacuring company's achievemen. he aim of effecive producion planning is opimized usage of needed resources and saisfying cusomer demands in he given period of ime []. n general, wo limiing facors in producion planning are producion capaciy and invenory capaciy wih more emphasize and discussion abou he former. However, in mos of indusries including paper producion, perochemical, food, seel, glass, medicine and indusrial processing, here are condiions in which he producion rae limiing facor is invenory capaciy raher han producion capaciy. For insance, in he seel indusry he producion capaciy is ofen sufficienly high and cusomer demands for producs are limied by he sorage size or in oher word by he invenory capaciy. Frequenly he sorage shorages (back orders) and is consequences are no aken ino accoun in he producion planning [2]. n he presen research i is ried o obain logical relaionship beween hese wo parameers. ncludes resources allocaion for considered producs quaniy demanded and wih minimum cos [3]. One can in fac inerpre producion planning as creaing boundary for he organizaion fuure producion operaions. Wih respec o he above menioned definiion, producion planning aims are as follows: a) Defining producion plans based on coss and managemen policies in financial issues, cusomer services and work force sabiliy fields; according o hese plans i is o decide where exra capaciy is needed. b) Helping he managemen o undersand he impacs of various policies on coss, invenory and producion [2]. here are fewer researches abou sorage shorage sraegy in limied invenory seing and is oucomes in he producion planning.wo main objecives of producion planning are supplying SBN: WCE 2009

2 Proceedings of he World Congress on Engineering 2009 Vol WCE 2009, July - 3, 2009, London, U.K. cusomer demands and achievemen of lowes coss which are someimes incompaible aims [4]. he increase of invenory level for example may resul in he increase of cusomer demand alhough he holding coss are ofen very high so he final cos is no esimaed a minimum level. Focusing on he minimal cos may cause fail o supply he cusomer demand and loss is is oucome for he company [5]. he siuaion here is known as invenory shorage.he invenory shorage sraegy means ha we le o have back orders.. RESEARCH QUESONS. How much is opimum producion rae in each period assuming permissible back orders and aking invenory limied capaciy ino accoun? 2. How much is opimum producion rae a he beginning and end of period? 3. How much is he minimum oal cos? 4. How much is he quaniy of back orders a he end of each period?. MODEL FRAMEWORK We assume a single resource nework wih nodes. he arms connec he resource o each node and i binds node o node as =,2,,-.he arms direc each nodes o a well (figure ).he needed flow which is direced from node o well node is known as D (assuming ha primary invenory and back orders have been allocaed such ha { D } values are ne demands which mus be supplied hrough he producion). o insure he sable flow, we assume ha he sysem flow in he resource node is equal o F = = D. he resuled flow in (o, ) arm is presened by and (, ) arm flow is shown as. he back orders are permissible and so is in-hand sock and represens back order. Assuming some coss incurred in he arm flow, we define C( ) and H ( ) as coss which are funcions of flow level, and variables are in-hand invenory and back orders a he end of period respecively. So ha he ne invenory level is =. n order o deermine he possibiliy of supplying a period demand using he nex period producion, we add some arms from node o node o obain =, 2..,, -. he flow in arm (,) is known as back order level. he resuled nework is shown in he figure. Figure.nvenory flow model wih back order quaniies SBN: WCE 2009

3 Proceedings of he World Congress on Engineering 2009 Vol WCE 2009, July - 3, 2009, London, U.K. he following objec funcion is used in he formulaion of minimal cos flow: () Z C( ) [ H ( ) H ( )] = = f invenory holding cos and back orders are noed by individual funcions, he consrains are: (2) = = D = D,, 0 Cap is known as invenory capaciy of period. Model noaions =producion quaniy during period = Ne invenory a he end of period =in-hand invenory a he end of period =back order quaniies a he end of period C =producion variable cos per uni of produc H =holding cos of uni from o periods H =back order cos per uni D =demand value of period V. PROCEDURE =(,2,,) n view of objecive, he research is known as assessmen-applied research. s assessmen naure is due o daa collecing and analysis used in decision making, i is also an applied research because applied researches are hose ones ha develop some assumpions, regulaion, principles and echniques for basic researches and are used o solve real adminisraive problems. Wih respec o mehodology, he research chooses descripive mehod because i examines he presen siuaion. Some of he examined subjecs in he research include special groups of people which heir relaed informaion following analysis- is no generalized o he oher groups. Secondly, hypohesis inroduced in descripive research does no explain any reasons o clarify phenomena. means ha in his kind of research, a hypohesis does no indicae he exisence of special phenomenon raher i clarifies he relaionship beween phenomena or conceps. he descripive saisic is used in he research which applying given and limied saisical echniques, i describes saisical daa (inference saisic is used in analyical research mehod). he presen research is in fac a descripive research wihou is research ool i.e. quesionnaire and on oher hand is no assumed as analyical research because he researcher mus provide a hypohesis and using inference saisic, esimaing he parameer value hrough sample feaure values and finally, esing he hypohesis saisically. V. DAA ANALYSS he inroduced producion planning model in he presen research is dynamic programming which had been formulaed and analyzed using linear programming mehod. here is no any special algorihm o solve he dynamic programming problem [6]. Dynamic programming is generally one of he effecive and efficien mehods in problem solving in which decision making is a mulisage process. means ha a complex problem is divided ino muliple sages such ha decision making is underaken individually in each sage wih narrower focus and sub-sages. his propery is defined as decomposiion in which a complex problem soluion is achieved hrough is decomposiion ino smaller problems. he dynamic programming is a mahemaical programming specifically designed o complee he calculaion efficiency of opimizaion problems. he basic idea of he echnique is decomposiion problem. he basic idea of he echnique is decomposiion of problem ino sub-problems wih simpler soluion. V. CASE SUDY AND MODEL NUMERCAL ANALYSS he examined problem in he presen research is defined as follow. We assume he producion designing of he Foulade Azarbayjan Company,he, bar, and 2m lengh angle are main producs ;in various sizes according o he marke demand. he producion planning uni pursues is decisions based on ime and producion sae beside cos reducion iniiaives. he company producion planning has he following feaures:. Producion process will no be pending and principal producs mus be ransferred o sorages, 2. Producion process is limied by he sorage capaciy, 3. Producion capaciy is oally more han holding capaciy, SBN: WCE 2009

4 Proceedings of he World Congress on Engineering 2009 Vol WCE 2009, July - 3, 2009, London, U.K. 4. he company producs demands are more han he exised capabiliies and capaciies, 5. Producs mus be held in he company sorage a predeermined period and by he end of specified deadline, 6. Esablishmen coss are high and so i is no possible o esablish new producion line. he company idenified limiaions are: a) Producion capaciy limiaions which are resuled from producion equipmen speed for various producs, b) Minimum producion limiaion: n direcion of he company macro scale objecives he op managemen believes ha he company mus supply 58000s producs, according o he annual demands, he company should produce s unil Augus for achieving he goals.. c) Back orders and invenory limiaions: his limiaion deermines he primary pars balance in produc invenory, d) nvenory capaciy limiaion: he limiaion is due o he sorage capaciy o accep primary pars and producs, e) Limiaions due o he produc specificaions: Wih respec o he marke demand and also considering he company benefis, managemen deermines 40 percen producion rae for he firs and second producs and 60 percen producion rae for he hird and fourh producs. n he company business process, i may happen ha he company do no supply cusomer demands in which case los sale will be occurred, bu he company will resolve he problem whenever i has in-hand invenory, if no orders will be considered as los orders. V. OPMUM APPROACH We examined he company problem in 6 periods each wih one monh duraion. During hese periods, we underook he producion planning of he company four producs assuming sable producion coss and availabiliy of demand quaniies which are shown in ables and 2. he oucome is as follows: is necessary o know ha alhough here is sufficien capaciy o supply he demands of hird and fifh periods for second produc, fourh and sixh periods for fourh produc and sixh period for he firs produc, we will no succeed o supply cusomer demands a he end of specified period. means ha a his poin our goods have been depleed. During he hird and second periods cusomer demands for he firs and second producs have been supplied hrough he sorage invenory, supplying he demand of oher periods is achieved hrough producion process (able 3.4 and 5). V. RESUL AND CONCLUSON n he paper, we consider a form of producion designing and planning in which good sorage capaciy is a limiing facor. he problem is more complicaed considering he following iems: - Good sorage capaciy has sable limiaion, 2- Good sorage is no permissible, 3- Coming orders will be los by he good shorage 4- Producion coss and good shorage cos are sable. n he presen discussions, above problems were examined bu in pracice we will see ha in processing companies, here are various problems which are ou of conrol. - Wih respec o he research findings and in comparison o he pas incurred coss, i can be concluded ha he company using he policy will be able o implemen broader markeing aciviies o arac more cusomers if i loses is cusomers due o failing o saisfy heir demands, considering he allocaed coss. - Considering he presen inflaion rae and wih respec o he pas financial year, i can be said ha oal incurred cos is accepable. - he mos of he company invenory capaciy has been uilized such ha from he able 3 i is obvious ha only 0000 of invenory from he oal have no been consumed.hrough he process of planning, he company will be ready for risk of invenory shorage in he producion. REFRENCES [] Riggs, J., Producion Sysems: Planning, Analysis and Conrol. Wiley, New York, NY. 98. [2] Cohen MA, Lee HL. Sraegic analysis of inegraed producion disribuion sysems: models and mehods. Operaions Research 988; 36(2): [3] Pohlheim H. Evoluionary algorihms: principles, mehods, and algorihms. Online; 200. Available from _hp:// index.hml, [accessed on 6 May 2004]. [4] Wee HM, Yu J, Chen MC. "Opimal invenory model for iems wih imperfec qualiy and shorage backordering". Omega 2007; 35:7. [5] Park KS, Yun DK." Opimal scheduling of periodic aciviies". Operaions Research 985; 33: [6] Seinberg E, Parks MS.A preference order dynamic program for a knapsack problem wih sochasic rewards. Journal of Operaional Research, Sociey 979; 30(2):4 7. SBN: WCE 2009

5 Proceedings of he World Congress on Engineering 2009 Vol WCE 2009, July - 3, 2009, London, U.K. APPEND-ABLES able. he model cos parameers Produc Firs produc Second hird produc Fourh produc Coss produc Cos price per on consumed iron bar Holding coss Back order coss Monh Producion able2. Producs demand values Bar, size8 Bar, size6 Bar, size20 Bar, size22 Demand Sum March April May June July Augus Monh Producion able3. Producion Orders Bar, size6 Bar, size8 Bar, size20 Bar, size22 Sum March April May June July Augus oal Monh Monh able4. Produc invenories a he beginning and end of period Back order Bar, size6 Bar, size8 Bar, size20 Bar, size22 March April May June July Augus able5. Back orders a he end of period Back order Bar, size6 Bar, size8 Bar, size20 Bar, size22 March April May June July Augus SBN: WCE 2009