Raa, Taughts
Lecture Notes
1
MSc in Operational Research Operational Research Techniques II Lecture 6
GOAL PROGRAMMING
INTRODUCTION In many important real-world decision-making situations, it may not be feasible, or desirable to reduce all the goals of an organization into b. single objective. For example, instead of focusing only on optimizing profits, the organization may simultaneously be interested in maintaining a stable work force, increasing its share of market and limiting price increases. Goal programming is an extension of linear or nonlinear programming involving an objective function with multiple objectives. While developing a goal programming model, the decision variables of the model are to be defined first. Then the managerial goals related to the problems are to be listed down and ranked in order of priority. Since it may be very difficult to rank these goals on a cardinal scale, an ordinal ranking is usually applied to each of the goals. It may not always be possible to fully achieve every goal specified by the decision-maker. Thus, goal programming is often referred to as a lexicographic procedure in which the various goals are satisfied in order of their relative importance. Example 1 An office equipment manufacturer produces two kinds of products: computer covers and floppy boxes. Production of either a computer cover or a floppy box requires 1 hour of production capacity in the plant. The plant has a maximum production capacity of 10 hours per day. Because of the limited sales capacity, the maximum number of computer covers and floppy boxes that can be sold are 6 and 8 per day, respectively. The gross margin from the sale of a computer cover is Rs. 80, and Rs. 40 for a floppy box. The overtime hour should not exceed 2 hours/day. The plant manager has set the following goals arranged in order of importance. 1. To avoid any underutilization of production capacity. 2. To limit the overtime hours to 2 hours. 3. To sell as many computer covers and
1
MSc in Operational Research Operational Research Techniques II Lecture 6
GOAL PROGRAMMING
INTRODUCTION In many important real-world decision-making situations, it may not be feasible, or desirable to reduce all the goals of an organization into b. single objective. For example, instead of focusing only on optimizing profits, the organization may simultaneously be interested in maintaining a stable work force, increasing its share of market and limiting price increases. Goal programming is an extension of linear or nonlinear programming involving an objective function with multiple objectives. While developing a goal programming model, the decision variables of the model are to be defined first. Then the managerial goals related to the problems are to be listed down and ranked in order of priority. Since it may be very difficult to rank these goals on a cardinal scale, an ordinal ranking is usually applied to each of the goals. It may not always be possible to fully achieve every goal specified by the decision-maker. Thus, goal programming is often referred to as a lexicographic procedure in which the various goals are satisfied in order of their relative importance. Example 1 An office equipment manufacturer produces two kinds of products: computer covers and floppy boxes. Production of either a computer cover or a floppy box requires 1 hour of production capacity in the plant. The plant has a maximum production capacity of 10 hours per day. Because of the limited sales capacity, the maximum number of computer covers and floppy boxes that can be sold are 6 and 8 per day, respectively. The gross margin from the sale of a computer cover is Rs. 80, and Rs. 40 for a floppy box. The overtime hour should not exceed 2 hours/day. The plant manager has set the following goals arranged in order of importance. 1. To avoid any underutilization of production capacity. 2. To limit the overtime hours to 2 hours. 3. To sell as many computer covers and