Introduction

These notes convert the Premier Products case from a cost-based case to a throughput-based case. You should review the original Premier Products case. The information in the case is used to make this transformation. Five operating situations have been identified. In each situation the same throughput equation is maximized subject to the specific constraints for that situation using standard linear programming techniques. The objective is to find the mix of products that provides the most throughput for the company. Operating situations 1 and 2 have been worked out to illustrate the analytical process. You are to answer the questions for operating situations 3, 4 and 5.
 

Definition of throughput

Throughput for a specific product is calculated by taking the difference between the selling price of the product and the cost of all parts that must be purchased from external suppliers for the product. Throughput represents the money that the company gets to keep to pay the cost of all of its resources. The throughput for each of the products is its selling price minus its material cost.

Throughput equation

Maximize 83A + 33.5B + 49.5C + 44D

Assumptions

This analysis assumes that the variable overhead listed in Table A of the original case represents the cost of using a machine to produce the four products. It is also assumed that the cost of all machines is the same $20 per hour. For example, the variable overhead for product A is $15 per unit. If the $15 represents product A's use of a machine and the machine costs $20 per hour, then one unit of product A uses 3/4 (.75) of a machine hour [$15 per unit divided by $20 per hour]. Product B has a unit variable cost of $7.50 per unit. This works out to 3/8 (.375) of a machine hour for each unit of product B. Each unit of product C uses 1/4 of a machine hour, and one unit of product D uses 3/8 of a machine hour. In Table A the cost of direct labor for product A is given as $30 per unit. Because each unit of A requires 6 direct labor hours, this makes the rate $5 per hour. This rate is the same for products B, C, and D.

The original case states that 1,000 units of each product can be produced or a maximum amount of 2,000 units of A or B and a maximum of 2,000 units of C or D. This infers that labor and machines can only produce either A and B or C and D. The existing labor and machines cannot produce all four products. If 2000 units of A are produced and if each unit of A requires 6 labor hours, then the firm must have 12,000 direct labor hours available to work on products A and B. If the firm can produce 2000 units of C, then the firm must have 6,000 labor hours available for products C and D. [NOTE: These labor hour figures differ from those in the original case.] The maximum number of machine hours for products A and B is 1,500 because each unit of product A requires 3/4 of an hour and 2,000 units can be produced. The maximum number of machine hours for C and D is 750 machine hours because each unit of product D requires 3/8 of an hour and 2,000 units can be produced.
 

Operating situation 1

Because the labor and machines can only work on A and B or C and D, there are separate labor and machine constraints for each set of two products. The case says that the firm can produce any linear combination of products A and B up to a total of 2,000 units. This is labeled an internal constraint. There is a similar internal constraint for products C and D. There is also a market constraint, which drives the current resource configuration and limits production of any one product to 2,000 units. The decision rule is for the firm to make the most money it can given its resource limitations. Using the Lindo software, what is the constraint in this situation? In other words, what resource is preventing Premier from making more money?

Constraints:

(1) labor hours

6A + B < 12000

3C + 2D < 6000

(2) machine hours

.75A + .375B < 1500

.25C + .375D < 750

(3) internal capacity

A + B < 2000

C + D < 2000

(4) market

A < 2000

B < 2000

C < 2000

D < 2000

Throughput = $265,000 (A = C = 2000 units, B = D = 0 units)

The product mix calls for Premier to produce 2000 units of A and 2000 units of C. Total production costs are $175,000.

Direct labor (18,000 x $5 per hr)	$090,000
Machine hrs (2,000 hrs x $20 per hr)	$040,000
Fixed OH	$045,000
Total costs	$175,000

The firm's profit is $90,000 ($265,000 - $175,000).
 

Operating situation 2 (No internal capacity constraint)

Let's assume that the company removes the two internal constraints. These internal constraints can be thought of as a policy that has been in place for a while but no one knows why. Its purpose may have been valid in the past but now it impedes the ability of the company to use its resources most effectively. Can you think of an example of such a policy in your own organization? I bet you can. The labor, machine, and market constraints remain. The decision rule remains the same. The firm is trying to make the most money given its available resources. Using the Lindo software, which resource is the constraint in this situation?

Constraints:

(1) labor hours

6A + B < 12000

3C + 2D < 6000

(2) machine

.75A + .375B < 1500

.25C + .375D < 750

(3) market

A < 2000

B < 2000

C < 2000

D < 2000

Throughput = $278,200 (A = 2000, B = 0, C = 1200, D = 1200)

Throughput goes up again. Total costs are $180,000.

Direct labor (18,000 x $5 per hr)	$090,000
Machine hrs (2,250 hrs x $20 per hr)	$045,000
Fixed OH	$045,000
Total costs	$180,000

The profit is now $98,200 ($278,200 - $180,000) or $8,200 more than the last situation. This is amazing given that there were no additional resources expended and, therefore, no added costs incurred to gain this extra profit.
 

Operating situation 3 (Resource flexibility)

The firm would like its existing resources to be more flexible. The company would train its workers and would modify its machines so that they could work on all four products. The total available resources do not change, but the labor and machine constraints do change to reflect this new flexibility. The market constraints remain on all four products. What would the company's throughput be now with the new labor and machine constraints? Which resource is the constraint in this situation? How much profit would the firm make? How would you use the information in this situation to determine if the company should go ahead with the investment required to train its workers and to modify its machines?

Constraints:

(1) labor hours

(2) machine hours

(3) market

A < 2000

B < 2000

C < 2000

D < 2000
 

Operating situation 4 (Open up the market)

The firm decides to open up the market. There are potential customers who might increase the total quantity demanded for any or all of its products from 2,000 units to 4,000 units. Available resources are unchanged. In your opinion, would you go ahead with this decision? Explain your reasons.

Constraints:

(1) labor hours

(2) machine hours

(3) market
 

Operating situation 5 (No market constraint)

The firm wants to see how much money can be made if the markets for its products were wide open. In other words, there is now no market constraint at all for any of the products. The company can sell everything it produces. Available resources remain unchanged. Would you recommend the company take this action? Explain why or why not.

Constraints:

(1) labor hours

(2) machine hours