Shelby Shelving

Executive Summary:

Shelby Shelving, a small company that manufactures two types of shelf models (Model S and LX) for grocery stores, is concerned with its overall profitability. In order to remedy the problem, the plant’s engineer suggested that the current production of Model S should be cut back. However, the controller disagrees and believes that the actual problem was the model S assembly department trying to absorb a large overhead with a small production volume.

Model:

A constrained optimization model was developed to address Shelby Shelving’s problem.

• The decision variables are the number of units that Shelby Shelving should produce for Model S and Model LX respectively.
• The resource constraints include the monthly assembly capacity for Model S and Model LX as well as the number of hours that are allocated to stamping and forming for both models. This is also detailed in the following table:

[pic 1]

• The profit function is identified by considering the factors including selling price, costs associated with direct materials and direct labor, and variable overhead costs for both models. Variable profit contribution = selling price – direct materials – direct labor – variable overhead. The gross profit generated from the two models (S and LX) is calculated as the sum product of variable profit contribution and the number of units that should be produced for each model type. The net profit is then calculated as gross profit minus fixed cost, which is found by adding costs from stamping, forming, and assembly. This is also detailed in the following table:

[pic 2]

Analysis:

1. By maximizing net profit and changing the decision variables subject to the constraints listed above, the optimal number of shelves that Shelby should produce is 1900 for Model S and 650 for Model LX. The corresponding monthly profit is $268,250. The corresponding allocation for Model S is 570 hours of stamping and 475 hours of forming, and for Model LX is 195 hours of stamping and 325 hours of forming. The bottlenecks are the binding constraints, which are monthly assembly capacity used by Model S and number of hours used in the stamping department.
2. Based on the calculations above, it can be concluded that Model S has a higher contribution margin than Model LX. Therefore, resources should be allocated to produce the maximum number of Model S possible. This also shows that the engineers assumption is wrong since he wanted to decrease the monthly production of Model S in order to minimize loss per unit. However, if his strategy was executed, then the total cost of Model S will increase and overall profit will decrease.
3. From the Sensitivity Report, Shelby Shelving should expand its forming department by 58.333 hours (given by “allowable increase”). The shadow price shows that one unit increase in the forming department will generate a profit of $490. Thus, if additional capacity is added to the forming department at cost of $200 per hour, it will yield a net profit of $490 – $200 = $290 per hour.
4. The change would not affect Shelby’s production plan because the contribution margin for Model S will still be higher than that of Model LX even after the $100 hike in material cost. Thus, Shelby should still continue to maximize the production of Model S. It should be also noted that the company is currently producing at the maximum capacity of 1900 units for Model S.
5. If the selling price of Model LX can be raised to $2400 per unit, then the following would happen:

[pic 3]

        Because the variable profit contribution of Model LX will increase to $545 per unit, which is higher than that of Model S, Shelby Shelving should increase the production of Model LX and decrease the production of Model S.

Summary:

Based on the results from the constrained optimization model, it can be concluded that Shelby Shelving should continue to produce at the maximum capacity possible for Model S, which is 1900 units. It follows that the optimal number of production for Model LX is 650 units.