Question: A company needs an appropriate production plan for two products over the period of three months. Table below provides the demand range for each product and the total production capacity for

  

Question: A company needs an appropriate production plan for two products over the period of three months. Table below provides the demand range for each product and the total production capacity for each month. The table also provides the production rates (units per hour) for products A and B.
Month
1
2
3
Demand for A (units)
400-500
4800-5000
700-800
Demand for B (units)
900-1000
1000-1200
1150-1250
Capacity (hour)
3000
3600
2600
Production rate (A)
1.25
1.25
1
Production rate (B)
1
0.8
1.25
The company needs to satisfy all the demands. The production system is allowed to produce more and keep some inventory for the next period. However, the holding costs of $0.95 and
$0.75 per unit per month are charged for products A and B, respectively. The unit production costs for two products are $32 and $28 for A and B, respectively.
1- Develop a mathematical formulation to minimize the cost.
2- Find the optimal solution. To solve your model, assume that demands are uniformly distributed. Use Excel to find a random number for the demands (use = a + (b ? a) * RAND() or = RANDBETWEEN(a,b) to find a random number between a and b; for instance, demand of A in month 1 = 450 + (500? 450) * RAND()).
Note: Adequate explanations about the model and associated computer files should be provided.
3- Suppose that the production manager is allowed to modify the total production capacity for each month. What would be your cost-saving suggestion (based on the sensitivity analysis)? Find the optimal solution.
4- What is the maximum holding cost for product B which does not change the optimal solution you found in part C?
5- Write the associated dual problem for the original model (part A) and find the optimal solution.
6- Comment on the dual (shadow) prices generated in the sensitivity analysis of the dual model.

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