1. GOAL PROGRAMMING FOR AGGREGATE PLANNING BY :- SAURABH SHARMA 214112031 1

2. CONTENTS Introduction Goal programming Establishing goals and assessing resources Goals for aggregate output Solved examples(with excel) Softwares References 2

3. INTRODUCTION In real world decision making situations, it may not be feasibile to reduce all the goals of an organization to a single objective. Also single goal can be aimed and priority is selected for multiple goals. The solution represents an attempt to optimize the goals according to priorities. Rather than only focussing on maximizing profit or minimizing cost,the organization may simultaneously be interested in maintaining a stable workforce, increasing its share of market, etc. 3

4. Goal Programming It deals with decision problems involving conflicting objectives. The basic idea of the technique is to convert the multiobjective problem into one or more problems with one objective each. The quality of the final solution is influenced by the decision maker’s ranking of the different objectives Goal programming seeks an efficient solution that attempts to meet all the goals of the problem 4

5. ESTABLISHING GOALS AND ASSESSING RESOURCES The operations manager usually finds it convenient to plan at different levels of abstraction. At one extreme is the broad overall level; planning on this level considers total output capabilities of all existing production resources without regard to specific products that could be produced. Second level of abstraction is how much of each individual product should be produced and in what sequence. Aggregate output planning deals with the first, and broader of these two levels of abstraction. 5

6. GOALS FOR AGGREGATE OUTPUT Aggregate plans are developed with particular goals in mind. For a specific time frame or planning horizon, estimates of the aggregate demand for goods and services are made. “The goal is to develop a plan that will satisfy or meet demand, within the limits of available resources, at the least cost to the organization”. Such other goals as maintaining stable workforce levels, constant inventory may also be planned for. 6

7. QUE> A company produces two types of air coolers (1) a ‘Dial setting’ model and (2) ‘Touch sensing’ model. It is currently experiencing very strong demand for its air coolers and can sell all of these two types, it can produce. The company makes a profit of Rs 1000 on the ‘Dial setting’ model and RS 1200 on the ‘Touch sensing’. The production capacities and processing times are as shown: Processing hoursper air cooler Type of air coolerComponent subassembly Final assembly and testing Dial setting72 Touch setting53 Hours available per day 9060 Suppose now management of company is faced with multiple conflicting goals becasuse of one of its labour 7

8. unions. Because of this fallout occurs on total hours, the hours available for component subassembly can be at most 60 hours per day, and the hours available for final assembly and testing can be atmost 40 hours per day. Thus for this situation management decides to rank its set of goals as:- GoalPriority 1Utilize at most 60 hrs per day in comp. subassembly and 40 hrs in final assembly P1 2Produce to make a daily profit at least Rs 20000P2 3Produce to achieve daily sales of atleast 12 touch sensing air coolers P3 4Produce to achieve daily sales of atleast 5 dial sensing air coolers P4 The company now wishes to determine the product mix that would most nearly achieve the four priority ranked goals 8

9. Index :- –i = dial setting model –j = touch setting model Parameters:- –Xi = no. of components of “Dial setting” manufactured –Xj = no. of components of “Touch sensing” manufacture –P1 = Utilize at the most 60 hrs per day in comp subassembly and 40 hrs per day in final testing. –P2 = Produce to make a daily profit of atleast 20000 –P3 = Produce to achieve daily sales of atleast 12 touch sensing air coolers –P4 = Produce to achieve daily sales of atleast 5 dial sensing air coolers 9

10. For this problem, let us first define the following deviational variables: d1+ = overachievement of target daily profit. d1- = under------------------------------------------ d2+ = overachievement of target daily sales of touch setting air coolers. d2- = under-----------------------------------------------------. d3+ = overachievement of target daily sales of dial setting air coolers. d3- = under------------------------------------------------------------. d4+ = overachievement of target daily hours for component subassembly. d4- = under----------------------------------------------------------. d5+= overachievement of target daily hours for final assembly and testing d5- = under----------------------------------------------------------. 10

11. The goal programming model for this new problem situation is:- Objective function:- Minimize Z = (p1d4+) + (p1d5+) + (p2d1-) + ( p3d2-) + (p4d3-) Subject to:- 1000Xi+1200Xj-(d1+) + (d1-) = 20000 Xj – (d2+) + (d2-) = 12 Xi – (d3+) + (d3-) = 5 7 Xi + 5 Xj – (d4+) + (d4-) = 60 2 Xi + 3 Xj – (d5+) + (d5-) = 40 11

12. Que:- An electronics company produces two types of television sets, color and black-and-white. The production of a color set requires 10 hours of skilled and 100 hours of unskilled labor. The production of a black- and-white set requires 5 hours of skilled and 150 hours of unskilled labor. The company has 100 hours of skilled labor and 1,500 hours of unskilled labor normally available per month for the production of television sets. The maximum number black-and-white and color sets that can be sold each month are 45 and 70, respectively. The profit margin from the sale of a color set is $20, whereas it is $15 from a black-and-white set. The company has set the following goals: 1. Avoid the over utilization of skilled labor since it is hard to obtain in the labor market. 2. Minimize the under utilization of unskilled labor. 3. Meet the demand as much as possible. 4. Limit over utilization of unskilled labor to 100 hours.Formulate the above as a goal programming problem. 12

13. ANS Note that since the demand goal stated "meet the demand as much as possible" production deviation either above or below demand is considered undesirable for both types of televisions. Also note that all apparent "hard" constraints are superceded by goal constraints. Index:- t = time period Parameters:- C ʈ = Quantity of color televisions produced B ʈ = Quantity of black and white televisions produced Deviational variable:- ds+ = Overachievement of skilled labor utilization target ds- = Underachievement of skilled labor utilization target du+ = Overachievement of unskilled labor utilization target du- = Underachievement of unskilled labor utilization target 13

14. dc+ = Overachievement of color television demand target dc- = Underachievement of color television demand target db+ = Overachievement of black and white television demand target db- = Underachievement of black and white television demand target do+ = Overachievement of unskilled labor overutilization target do- = Underachievement of unskilled labor overutilization target Objective function:- Minimize Z = ds+ + du- + dc+ + dc- + db+ + db- + do+ 14

15. Subjected to:- 10 C ʈ + 5 B ʈ - ds+ + ds- = 100 (Skilled use goal) 100 C ʈ + 150 B ʈ - du+ + du- = 1,500 (Unskilled use goal) C ʈ - dc+ + dc- = 70 (Color demand goal) B ʈ - db+ + db- =45 (B&W demand goal) du+ - do+ + do- = 100 (Unskilled overuse goal) where: C ʈ, B ʈ, ds+, ds-, du+, du-, dc+, dc-, db+, db-, do+, do- > 0 and C ʈ, B ʈ are integer 15

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18. Softwares MS Excell module Matlab Goalpro LiPS(Linear integral programming software) LINGO 18

19. REFERENCES Everett E Adam Jr.,Ronald J Ebert, “Production and operation management”, 1978. Martand Telsung, “Industrial Engg and production management”, S chand, 2010. R Paneerselvam, “Production and Operation Management”, second edition. HAMDY A TAHA, “Operation Research”, prentice hall. 19

20. Thank You 20