Question 2: (Dynamic Production Planning)

LP model formulation and computer solution

Model Formulation

Definition of Decision/ Helper variables:

Development of Objective Function:

Development of constraints: Formulas

Non-negativity constraints:

Computer solution

Decision/Helper variables section:

O.F. Section:

Constraints:

Solver:

Problem statement:

The Carroll Corporation manufactures water heaters for the home and light industrial markets. Carroll is presently trying to plan its production and inventory levels for the next six months. Because of seasonal fluctuation in utility and raw material costs, the per unit cost of producing water heaters varies from month to month as does the demand for water heaters. Production capacity also varies from costs, demands, and production capacity Carrolls management expects to face over the next six months.

Table 2: Monthly production costs, demands, and production capacity

Month

1 2 3 4 5 6

Unit Production Cost $240 $250 $265 $285 $280 $260

Demand 1,000 4,500 6,000 5,500 3,500 4,000

Production Capacity 4,000 3,500 4,000 4,500 4,000 3,500

Given the size of Carrolls warehouse, a maximum of 6000 units can be held in inventory at the end of any month. The owner of the company likes to keep at least1, 500 units in inventory as safety stock to meet unexpected demand contingencies. To keep stable workforce, the company wants to produce at no less than one half of its maximum production capacity each month. Carrolls controller estimates the cost of carrying a unit in any month is equal to 1.5% of the unit production cost of the in the same month. There are currently 2,750 units in inventory. Carroll wants to identify the production and inventory plan for the next six months that will meet the expected demand each month while minimizing production and inventory costs.