Question

Using Linear Programing to solve Make or Buy problem.

The Carson Stapler Manufacturing Company forecasts a 5000-unit demand for its Sure-Hold model during the next quarter. This stapler is assembled from three major components: base, staple cartridges, and handle. Until now Carson has manufactured all three components. However, the forecast of 5000 units is a new high in sales volume, and it is doubtful that the firm will have sufficient production capacity to make all the components. The company is considering contracting a local firm to produce at least some of the components. The production time requirements per unit are as follows:

	Production Time (hours)
Department	Base	Cartridge	Handle	Time Available (hours)
A	0.03	0.02	0.05	400
B	0.04	0.02	0.04	400
C	0.02	0.03	0.01	400

After considering the firm’s overhead, material, and labor costs, the accounting department has determined the unit manufacturing cost for each component. These data, along with the purchase price quotations by the contracting firm, are as follows:

Component	Manufacturing Cost	Purchase Cost
Base	$0.75	$0.95
Cartridge	$0.40	$0.55
Handle	$1.10	$1.40

Determine the make-or-buy decision for Carson that will meet the 5000-unit demand at a minimum total cost. How many units of each component should be made, and how many purchased?

1. Please clearly define the decision variables, objective function, and constraints in your Word Document submission.  
2. Please use Excel Solver to solve this problem and show your answer in the excel submission.  

Answer 1

The given problem can be solved using linear programming.

The objective function would be: To minimize total cost to meet 5000 units of demand

Let x1,x2 and x3 be the quantity of Base, Cartridge and Handle manufactured in house.

Let x4,x5 and x6 be the quantity of Base, Cartridge and Handle procured respectively.

So, the decision variables would be: x1,x2,x3,x4,x5 and x6.

Therefore, Total cost = (unit procurement cost * quantity procured)+ ( Unit manufacturing cost+ quantity manufactured)

Subject to the constraints as follows:

Demand Constraints:

• x1+x4<=5000
• x2+x5<=5000
• x3+x6<=5000

Production constraints:

• 0.03*x1 + 0.02*x2+0.05*x3 <= 400 ( Hours)
• 0.04*x1 + 0.02*x2+0.04*x3 <= 400 ( Hours)
• 0.02*x1 + 0.03*x2+0.01*x3 <= 400 ( Hours)

Thus the above problem is modelled in excel and solved using solver tool in excel.

The problem is modelled as follows:

Thus answering the questions based on above:

How many units of each component should be made, and how many purchased?

The above model is solved using solver and the above picture the output of what we got.

Thus, we have: