Se está descargando tu SlideShare. ×

Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Cargando en…3
×

1 de 12 Anuncio

# Goal Programming.pptx

Goal Programming Application

Goal Programming Application

Anuncio
Anuncio

Anuncio

### Goal Programming.pptx

1. 1. Goal Programming of Bauxite Mines Company
2. 2. Problem Statement The Bauxite Mines Company owns three different mines which are Mine 1, Mine 2, and Mine 3, which produces ore that after being crushed, is graded into three classes: Low, Medium, and High grades. KGF Smelting plant has offered a contract to smelt the obtained ore whose requirement per week is in such a way: • Low Grade: 12 tonnes • Medium Grade: 8 tonnes • High Grade: 24 tonnes
3. 3. The three mines have different operating characteristics as detailed below: Now the Bauxite Mines company is in a state of decision-making whether to accept the contract which is offered by the KGF smelting company or make changes to the existing contract to make profits…?
4. 4. Goal Programming Decision Variables: A= No: of Days per week Mine 1 is operated B= No: of Days per week Mine 2 is operated C= No: of Days per week Mine 3 is operated Objective Function: Min 180A+108B+72C Functional Constraints: 5A+B+C >= 12 2A+B+C >= 8 5A+3B+2C >= 24 A<=5 B<=5 C<=5 A, B, C >=0 *Note: Assuming Mine 1, Mine 2, and Mine 3 operate only for 5 days a week.
5. 5. Objective function Value
6. 6. Here we observed that A = 0.7, B = 3.5, C = 5 thereby we are getting the objective function value as 864 (in lakhs)
7. 7. ● But the problem arising here while considering the optimal solution is the excess production of medium grade i.e., 1.9 tons in a week. ● Initially, the problem is in minimizing the cost and now a new problem has arisen to reduce the excess grade production in our optimal solution because the company cannot handle excess as such. ● where excess ore might be obtained as just referring to medium-grade ore a moment’s thought will reveal if we can reduce or cut down the medium-grade production through our current solution. we might find an excess of another grade of ore. Hence, we need to consider all grades and their excess rather than just medium grades.
8. 8. Goal Programming Formulation *As programmed earlier through the optimal solution we inferred that the total production cost incurred was 864 Lakhs whereas the company is also trying to cut down the production further. Hence, the company chose to limit the production cost to 810 Lakhs. Now we have two objectives:  minimize cost – our previously calculated minimum cost was 864L (per week). The company is now interested in decreasing the production cost that they incur. Therefore, the company is now limiting the production cost to a maximum of 810 Lakhs.  Excess Production of Ore – Referring to three grades of the ore for which the respective goals are the amounts that we need to produce are 12, 8, and 24 tonsrespectively.
9. 9. Bauxite mines company sells grade wise as low-grade 20 lakh/ton, Medium grade 60 lakh/ton, and High grade 20 lakh/ton. As per selling the allotted weights are designed as: Hence for our Bauxite Mines problem where we wish to reconcile our conflictingobjectives, we have the equations: 180A+ 108B+72C = 810 + E+ - E- 5A+B+C = 12 + L+ - L- 2A+B+C= 8 + M+ - M- 5A+3B+2C = 24 + H+ - H- A  5 B  5 C  A,B,C,E+,E-,H+,H-,M+,M-,L+,L-  0 These equations are, given our variables, equations that must be satisfied.
10. 10. To proceed this we are going with weighted goal approaches:  to attach weights to each of the variables associated with upward/downward deviation and then to solve a single problem whose objective is to minimize this weighted deviation sum. T approach is sometimes known as weighted goal programming Weighted Goal Programming:(Objective) Minimize E+ + 20L+ + 20L- + 60M+ +60M- + 20H+ +20H- + Subject to 180A+ 108B+72C - E+ + E- = 810 5A+B+C - L++ L- = 12 2A+B+C- M++M- = 8 5A+3B+2C- H++ H- = 24 A  5 B  5 C  A, B, C, E+, E-, H+, H-, M+, M-, L+, L-  0
11. 11. Solution
12. 12. • The production cost obtained from the solution of goal programming is 804 Lakhs and the goal which the company asked to reduce (810 lakhs) is achieved and the days to be operated by mine 1, mine 2, Mine 3 is 1.333,5,0.333 days in a week • As per the contract, the company wanted to produce a Low of 12 tons, a Medium of 8 tons, High of 24 tons but the company can achieve the capacity of Low-12 tons, Medium-8 tons, and High-22.333 tons. • By linear programming 1.9 tons of medium grade get wasted so indirectly, it incurs the loss of 1.9*60=138 lakhs and the cost incurred is 864 lakhs. Total profit observed as 1200-864=336 lakhs for production of Low-12 tons, Medium-8 tons, High-24 tons • By Weighted pre-emptive goal programming, the total cost incurred is 804 lakhs for the production of Low 12 tons, Medium-8 tons, and High-22.33 tons, and total profit observed as 1166.6-804=362 lakhs, Which is a profitable condition for the company compared to producing Low-12 tons, Medium-8, and Hia22.33 tons. So, Bauxite mines company make a contract with KGF smelting company for the quantities of Low 12 tons, Medium-8 tons, High-22.333 tons instead of 12,8,24 tons Recommendation