Case Problem 3: Production Strategy

Shelby Shelving is a small company that manufactures two types of shelves for grocery stores. Model S is the standard model and model LX is a heavy-duty version. Shelves are manufactured in three major steps: stamping, forming, and assembly. In the stamping stage, a large machine is used to stamp standard sheets of metal into appropriate sizes. In the forming stage, another machine bends the metal into shape. Assembly involves joining the parts with a combination of soldering and riveting. Since different amount of solder and rivets are used for assembly, they have different workstations.

Model S shelves are sold for $350 and model LX shelves are sold for $405. Shelbys operation is fairly small in the industry, and management believes it cannot raise prices beyond these levels because of the competition. However, the marketing department believes that Shelby can sell as much as it can produce at these prices. Within a given month, Shelby has 1,200 hours of stamping, 1,200 hours of forming and 1,000 hours of assembly available.

Each model S shelf requires 0.3 hours for stamping, 0.25 hours for forming, and 0.5 hours for assembly. Each model S shelf costs $80 per hour to stamp, $120 per hour to form, and $165 per hour to assemble. The cost of materials for model S is $175 per unit.

Each model LX self requires 0.3 hours for stamping, 0.25 hours for forming, and 0.6 hours for assembly. Each model LX shelf costs $80 per hour to stamp, $120 per hour to form, and $165 per hour to assemble. The cost of materials for model LX is $210 per unit.

The president feels that the company should focus of making more of model LX. To that end, he wants the company to have at least 60% of the production dedicated to model LX shelves.

Managerial Report

Analyze the production problem at Shelby Shelving, develop a linear program, and prepare a report for the president presenting you findings and recommendations.

1) What is the recommended number of model S and model LX shelves to produce?

2) How does the requirement that the number of units of model LX produced be at least 60% of the total production affect profits?

3) Based on your findings for problems 1 and 2, where should efforts be expended in order to increase profits? Give at least one specific example, explain, and justify.

No specific length is required, but the Managerial Report must cover the items listed below.

This is to be written as a report being submitted to a higher level of management and may be viewed by the client. Avoid conversational language, but also avoid stilted language.

Cover page with all applicable information.

Statement of Purpose of the Report. What is the purpose of this report? What problem is being addressed?

Presentation of data. Since this comes from the handout, data does not need to be collected. But what is the factual information given in this problem. What are the uncontrollable inputs? What are the controllable inputs?

Compose problem statement into a comprehensive mathematical model.

Give the linear program you have developed. Explain the objective function and the constraints. Show how these address the purpose of the report.

Propose and justify optimal solution in context of the problem statement.

Provide the complete solution to the linear program. Note that this will be the response to question #1 of the Case Problem. Include Excel output to support answer.

Perform sensitivity analysis of the optimal solution. Questions #2, and #3 of the Case Problem each consider alternatives to the original problem. Respond to each of these questions with a short analysis of the differences and the implications of these differences in terms of the problem statement. For which of these does the solution change? Include Excel outputs to support answers.

Communicate the solution to an appropriate audience. This report is for the President of the company. Make sure your explanations are appropriate, professional, and do a good job explaining the outcomes to someone who may not be mathematically minded. Include a response to question #3 of the Case Problem.