Production Planning in an Uncertain Environment

Abstract

The decisions play an integral part in the life of humans. Human beings in a conscious state of mind or in a subconscious state of mind take numerous decisions in their day to day life, but unfortunately study reveals that many people are not so profound in taking good decisions. Also many times in group decision making the obtained decision is not suitable. This is so because different people have different alternatives according to their thinking and every decision maker has a different view regarding which alternative is better or not and out of several alternatives a single alternative is selected but it is very important to obtain good decisions especially when solving Production Planning Problem. The process of making plans in any corporation is referred to as the production planning. The Multi-Stage and Multi-Objective Production Planning problem refers to the problem of production planning having multiple stages and also having more than one objective function/goal. Such Production Planning problems are complex to handle due to the present of multiple stages and requirement of either one machine or more than one machine on each stage. However if there is not a balance in the relation of the input-output or if the machine fails to function (machine breakdown) at any of the stage occurs then the production target is disturbed to a great extent and the desired target of the production is not achieved. In the present work, a production Planning problem is solved in an uncertain environment. The objectives of the production planning problem are fuzzy in nature. The given data consists of the production rate/capacity, New machines installation cost, Inventory cost per 100 units in each stage that are fuzzy in nature and they are converted into crisp values. Lastly, LINGO 17 is used to solve this mixed integer programming production problem. The outline of the thesis is summarized below: Chapter 1 is the introductory chapter in which firstly the terms production, planning are defined and then process of production planning is demonstrated. Various production planning plans such as strategic plans, tactical plans and operational plans are illustrated in this chapter. Afterwards different techniques that are used in production planning are explained and the use of decision making in the process of production planning is demonstrated. A brief introduction to various approaches is given that are used to get the solution of the production planning problems. Chapter 2 consists of the preliminaries chapter which deals with the fuzzy set theory. There are many tools that are developed in mathematics in order to solve various problems of operation research. But no new tools and techniques are developed for the problems that are cumbersome in nature and possess no proper structure. In order to solve such problems Zadeh introduced the notion of fuzziness in 1965. Sometimes it becomes very difficult for the decision maker to determine the objectives and the constraints in an exact/precise manner. Hence such objectives/constraints are specified in fuzzy terms and a fuzzy linear programming is used to solve such problems. Some of the literature of the fuzzy set theory is given in this chapter. The basic definitions that are widely used in the fuzzy set theory are also explained. Defuzzification aims in determining a real value which corresponds to a fuzzy number. The various methods of defuzzification are presented. In the practical situation it is not always true that the decision making problem would consist of only numeric information. Sometimes it is a possibility that the decision making problems consists of both linguistic as well as the numerical information. Further, to handle linguistic data, a 2-tuple fuzzy linguistic representation model (Herrera and Martinez, 2000) has been presented. Chapter 3 deals with the various ordered weighted average (OWA) aggregation operators to aggregate goals and alternatives such as induced OWA and linguistic OWA etc. These operators are used in the decision making process in order to develop the aggregation method for combining the information. Some theorems of the OWA aggregation operator are also discussed in this chapter. Next the use of the linguistic quantifiers and the minimax disparity approach in identifying the OWA operators’ weights are discussed. Chapter 4 is the review of multi-stage multi-objective production planning problem of Gupta and Mohanty (2015) which is a mixed-integer programming problem. Further, to deal with subjective preference of decision maker, we have proposed the multi-stage multi-objective production planning problem at different orness levels. The objectives that are taken in the production planning problem are fuzzy in nature In order to achieve the desired production target a methodology is provided so that a balance is maintained in the I/O relation at every stage of the production process. The various complications faced by the firm and the objectives/goals are defined. Further, the solution of the resultant mixed-integer programming problem is obtained using LINGO 17.