Question

Company A is preparing its Production Plan for the next three months. In the table below you have the cost of production, demand and maximum production capacity for each month.

	Month 1	Month 2	Month 3
Production Cost per unit	$11	$17	$13
Demand	10,000	15,000	20,000
Max. Prod. Capacity	20,000	10,000	15,000

Company A’s warehouse can hold up to 10,000 units and it cost of carrying inventory is equal to 1% of production cost per unit in the ending inventory. Also, Company A has the option of renting a warehouse which can hold up to another 10,000 units for $6 per unit in the ending inventory. The company has no beginning inventory to start with and would like to end the three month period with zero ending inventory

Create LP Model ans Solve

Answer 1

We need to consider the production per month as the decision variable Pi The ending inventory can be denoted by IEi and beginning variable as IBi. Then our objective function is

Minimize Z where Z = 11P1 + 17P2 + 13P3 + 0.01*(11IE1 + 17IE2 + 13IE3)

Subject to constraints

P1 <= 20000

P2 <= 10000

P3 <= 15000

IEi = IB(i+1)

IB1+ P1 >= 10000

IB2 + P2 >= 15000

IB3 + P3 >= 20000

IB1 = 0

IE3 = 0

IEi >= 0

The model is shown below on excel

The formulas are shown below

The solver parameters are shown below

The result is shown below. The production plan should be 20000, 10000, 15000 and total cost of 586950