HEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMS .doc

110'CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 20, No. 5, 2007SJAHANA ABDOLSHAH MDepartment of Industrial Engineering,Islamic Azad University-Semnan branch,Semnan, IranHEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMSAbstract: At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive evaluation the advanced operation research techniques can be used in continuous production systems in developing countries very widely, because of initial inadequate plant layout, stage by stage development of production lines, the purchase of second hand machineries from various countries, plurality of customers. A case of production system planning is proposed for a chemical company in which the above mentioned conditions are almost presented. The goals and constraints in this issue are as follows: ® Minimizing deviation of customer's requirements. © Maximizing the profit. © Minimizing the frequencies of changes in formula production. Minimizing the inventory of final products. © Balancing the production sections with regard to rate in production. © Limitation in inventory of re-> i?bifiial. The present situation is in such a way that various techniques such as goal proij-ji.n int, linear programming and dynamic programming can be used. But dynanir production p'og-amtiing 'is&ks are divided into two categories, at first one with lira 'cation in production capacity ».j another with unlimited production capacity. For tK« first category, a systematic vA acceptable solution has not been presented yet. Therefore Mi innovative method ;s used to convert the dynamic situation to a zero- one model. At last fhi;i isscit i.'i ch.-nged to a goal programming model with non-linear limitations with the use of GRG i>)£,)rithm rind iiat's how it is solved. Key words: Heuristic model Dynamic programming Goal programming production planning0 INTRODUCTIONProduction planning is a complicated process which needs to gather too much information from different sections of an organization to perform it properly. It is also necessary to recognize the operational conditions over the problem perfectly. Meanwhile, some items such as the kind of production system (continuous, mass production, batch, or job-shop productions), various production methods, capacities of production lines, time and costs spent to run different production processes, the available sources, profits and the amount of demand for different products, and finally the method of selling the products regarding retail, wholesale or production on the basis of order, are all considered as operational items which affect the kind and scale of complicacy over production planning systems.Nowadays, various operation research techniques are widely used in designing production planning systems and this subject is related directly to the kind of production system. At the first sight, it may seem that advanced techniques of operation research are not used enough in production planning of continuous lines in comparison with mass, batch, or job-shop production systems. But really the advanced techniques can be widely used in continuous production systems in developing countries, because such countries are encountered with initial inadequate lay out, stage by stage development of production lines, the purchase of second hand machineries from different countries, numerous customers, sharp oscillations on market demand.A case is presented to study how to design a production planning system for a chemical company in which the above mentioned conditions are presented, and its modeling requires dynamic and goal programming.Received September 7, 2006; accepted November 10, 20061 PREFACE TO GOAL PROGRAMMINGIn making decisions, sometimes we confront goal that their preferences are not equal to fulfill, so to create a model in form of linear programming is not possible and it is necessary to apply a method called goal programming.In goal programming, a suitable level is defined for all of the purposes, and a specific priority is considered for each goal to reach, goal programming doesn't regard these suitable levels absolutely, but just hopes to attain them all. Therefore, according to the devoted priorities, it attempts to solve how to reach to an improvement, so as to get closer to the suitable levels as much as possible. A general model of a goal programming is as follows(1) (2)(3) (4)JVImin Z = Z,PKiZKdl+KAs.t. Zai/X, + di - d* = bl ' = ' 2> 3>""">*y=i£c.jr,. =/,. i = l,2,3,-",mj-iEq. (1) is the function of purpose in goal programming problems that minimize the total weight of deviations from the goal function. So W and W are the weight coefficients to indicate the positive or negative deviation of the suitable levels and PK determines the priorities of the goal.In Eq. (l),/ is bigger than/+l, and the goal AT +1 will not be propounded in the problem until the K goal reaches the suitable level.Eq. (2) is the goal limitation which in goal function we wish© 1994-2007 China Academic Journal Electronic Publishing House. All rights reserved, CHINESE JOURNAL OF MECHANICAL ENGINEERING 111 to minimize its deviation from the suitable level by devoting desirable weight b for its deviation. In Eq. (3) we observe a real limitation in which there is no mistake, and at last Eq. (4) expresses that non of the variables are negative.2PREFACE TO DYNAMIC PROGRAMMINGDynamic programming is a method often used for a series of continuous and dependant decisions to make. Dynamic programming is called dynamic, because its all problems must be solved step by step to get response, and the acceptable solutions must just be considered in each stage. Dynamic programming system has a generality in operation research discussions that is applied in solving programs such as linear and non-linear programming and non-linear programming with correct variables. But it's not economical to apply it when dimensions of the problem are so big, because to solve such a program will be consuming a lot of time and also needs much attention. Model making and solving the problems in production planning are the uses of this method which in various periods, has a variety in costs, different sources and also changes in requests.The issues stated in dynamic production programming are entirely divided into two groups. Issues which have limitation in production capacity and without any limitation in production capacity, an efficient and acceptable solution has not been presented yet for the second state.3EXPRESSING THE CONDITIONS OF ANISSUEThis paper is a case study for creating a production programming system at z company that produces different detergents. This company':- f/il products are made in the form of three various formulas, ano then the products are packed and delivered to customer in different forms and sizes. It is a continuous production system and is formed of three sections: preparing raw material (paste production), producing detergent power and packaging.Before this research done, the company was encountered with so many troubles that we can mention some of the most important ones as follows. The customer's dissatisfaction not delivering in time, the frequencies of changes in production formula, high amount and volume of storing the final products produced. Therefore, after the investigation and research done about the condition over this issue, limitation and goal were considered as follows.3.1Minimizing deviation of customer's requirementsDelivering the products in time resulting the customers satisfaction has the most important priority for such an organization, so a decision was made for the sales department to transfer the customers requirement to the programming department, according to plurality of customers and varieties of their requests and needs, it was also decided for sales department to inform programming department about the importance degree of supplying the needed products.3.2Maximizing the profitThe goal of such an organization is to account the profit of each product and to maximize it on the basis of production planning.3.3Minimizing the frequencies of changes in formulaproductionBefore creating a production planning system, the production department had to change the formula frequently for the sake of not paying any attention to balanced production lines and limitation not to have raw material.The company had to pay much for these changes and minimizing these costs is one of the goals in production planning system. Changing the formula includes the waste of useful time for production and destroyed materials which differ, according tothe kind of changes in formula.3.4Minimizing the inventory of final productsSometimes, selling the products may not be performed at the specific time and doesn't match the primary schedule of sales department. And this is why the company has to use space outside the store (open space) to keep the products concerning the limited capacity of final storage.This may also increase the products, destruction and more further make problems to the lack of space for transportation, therefore considering the possession of required space to store each kind of product, and to present a suitable production planning in order to minimize space used outside the store (open space) will be another goal of this planning.3.5Balancing the production sections with regard torate in productionBalancing the production rate among the three sections: Inventory of raw material (paste production), detergent power production, and packaging are also the goals of this production planning system.3.6Limitation in inventory of raw materialEach kind of the production needs a specific kind and rate of raw material, so according to the commons shared among some of the raw material, its necessary <c consider the limitation in inventory of raw materi'si.4APPLING DYNAMIC DECISION MAKING INPROBLEMMinimizing charges of changes in production formula causes dynamic state of the problem, since the same as knapsack problem we have to determine which products with each formula must be assigned in production planning to maximize the company's profits according to the costs of change in formula and the present limitations. As known to all, solving the problems in dynamic production planning, particularly the ones with a limitation in production capacity have long and boring calculation, so, in order to keep away from these calculations, we present an innovative of creating a zero-one model to omit the dynamic state, and we will explain it more as follows.5MAKING A MODEL FOR A PROBLEM INFORM OF GOAL PLANNINGThe conditions over this issue is so that its goal are not as important as each other, and this is why goal programming technique is used to formulate it.S.l To satisfy the customer (first priority)Function, minimizes the goal of customer's requirements by considering the announced priority by sales department as followsmin tldD-s.t. TK9Xf+dD-=Dt(5)Xt,dD->0(6)i = 1,2,3,-.h j = 1,2,3,- -.mwhere WitWeight (importance degree), customers requirement of detergent power in formula /' packaging jnThe number of different kinds of formulas indetergent power productionmThe number of different kinds in packaging detergent power for each formulaTKjjThe number of cartons needed for producing onekilogram of detergent powder in formula / packaging j© 19 4-2 07 hin A a mic urnalElectr i P i hi gHh re. etJAHAN A, et al: Heuristic modeling for a dynamic and goal programming in production 112 planning of continuous manufacturing systemsXyThe amount of detergent power production (kg)5.2in formula / packaging;dDu-The amount of decrease in production regarding the customers need in formula;' packaging;D-The number of customers requirements form formula ;' packaging/Maximizing profit and minimizing the costs of changes for production formula (second priority)min (-dB)n ms.t. XZ Vff - CflYfi - CflYfi. -/-i y-iSEmpty space at storedS*Used space outside the store in cubic meter as astore5.4 Limitations<R.(16)Eq. (16) indicates raw material limitations. Eqs. (17)-(19) indicate the restrictions of production capacity in the section of preparing raw materials, detergent powder production and packaging.(7)(8)(9)(10)(11)(12)(13)where Rk A4,-Cll.Yll.-CnYn-dB = 01> + 1><1YrXj,=0Y,Yfi.=0It*!*! <W-i )TJKAlLD, (Yfi. + Y,) XIJtdB>0 / = l,2,3,-,» ; = 1,2,3,-,/*where dBPure profitbyThe rate of profit for each '/ri!o/jran; of detergentpower using torr/iulit /' packaging jfThe present formula used in productionCyCharge of change in production from i into;YyTo change the production formulation or notchannging it from ;' into ;' (zero-one variable) Regarding Eq. (7) maximizes function of goal profit and minimizes the charge to change formulation, it is comprehensive in Eq. (8) considering Fig. 1, we can just move from the present formula towards two other formulas, and Eqs. (9),(10) indicate change in direction of formulation. Eqs. (11),(12) determine if change in formulation is not beneficial, products won't be produced entirely.(17)UPAyXPA(18)ZZTPyXTPi-l l-(19)ZYJBtXt<TB- Available amount of rav. material *-The amount of ussa raw material /' in packaging;to produce one kilogram of detergent powderPA;,-Tho amotut of us?ri paste to produce one kilogram cf detergent powder from formula /' inpackaging ;PATotal time devoted to paste production department at the period of time programmedTPit-Time spent to produce a kilogram of detergent powder from formula i in packaging;TP-Total time devoted to the detergent powder production department at the period of time pro-gammedTB-Time spent to pack a kilogram of detergent powder from formula i in packaging;TB-Total time devoted to detergent powder packing department at the period of time programmed Finally the model can be expressed asI n mZ= />/>»/»:*>/>P2(-dB),P3(dS*)Fig. 1 Indication of present formula change direction into formulas i and V5.3 Minimizing use of space outside the store as a store (last priority)minfdS*)s.t. ZZSJK¥X,-dS*=S(14)which is subject to Eqs.(l)-(19). 6 MODEL RESULTSTables 1-4 indicate the sample input data in the model and Table S indicates the results gotten through solving the problem to apply algorithm GRG with LINGO software.Table 1 Sample input datacustomer's deman