In the summer of 1988, Merton Truck Company (“Merton”) was struggling with financial performance. A manufacturer of two specialized trucks (model 101 and model 102), Merton was conflicted with how to manage production and improve financial results. The executive team offered many different options to improve performance, but many were conflicted. For example, the sales manager suggested cancelling all production of model 101 trucks, whereas the controller suggested increasing model 101 production and curtailing model 102 production. To determine the best course of action for the company, an in-depth analysis of their current practices and optimal position is required. Currently, Merton produces 1,000 of Model 101 trucks and 1,500 of Model 102 trucks. The company is constrained by monthly machine hours available in their production facilities for each activity (SEE EXHIBIT 1). The contribution margins for each model are $3,000 for Model 101, $5,000 for Model 102 (SEE EXHIBIT 2). Each model provides contribution margin, so increasing production in any capacity should increase overall profits. However, the decision on which product to increase production of has caused some internal conflict because of the allocation of shared resources. At the moment, the production facilities are maximizing the engine assembly capacity. This is a shared resource by both Model 101 production and Model 102 production. On one hand, Model 101 production has lower contribution margin ($3,000), but less engine assembly capacity utilization (1.0 machine hours per truck). On the other hand, model 102 production has higher contribution margin ($5,000), but greater engine assembly capacity utilization (2.0 machine hours per truck). To a lesser extent, metal stamping is another shared resource, however, the Merton is currently not maximizing utilization and both model 101 and model 102 require the same amount of machine hours for metal stamping (2.0 machine hours per truck). In order to maximize profits, Merton must optimize the production mix of its products. By optimizing production, the shared resources of engine assembly and metal stamping, in addition to the unique constraints to each model, will be allocated most efficiently. At current production levels, the company is earning $1.9 million in profit each month, after fixed overhead costs of $8.6 million per month are deducted (SEE EXHIBIT 3). However, Merton has the opportunity to increase profits by reducing model 102 production and producing more of model 101. This is because for the same amount of hours of engine assembly, the constrained resource, Merton can increase it’s total profit by $1,000 if it produces two model 101 trucks and sacrifices production of one model 102 truck. The optimal solution is for Merton trucks under the existing constraints, is to produce 2,000 model 101 trucks and 1,000 model 102 trucks, which increases monthly profits by $500,000 (SEE EXHIBIT 4). Considering that Engine assembly capacity is the bottleneck of production and assuming Merton can sell each of the trucks it produces, what is the capacity value for each additional machine hour of engine assembly? For each additional machine hour of engine assembly, Merton can also reduce model 101 production by one unit and reduce contribution margin by $3,000 to gain two hours of under-utilized engine assembly. The two hours of gained engine assembly can be translated into one additional model 102 unit produce for $5,000 of contribution margin, thereby increasing overall profit by $2,000 (SEE EXHIBIT 5). For the case of Merton, each additional engine assembly machine hour is worth $2,000 per month. As an additional example, if production engine assembly capacity increased to 4,100 machine hours, total profits would increase by $200,000 to $2.6 million (SEE EXHIBIT 6). However, the effect of additional engine assembly machine hours on profits does not extend into infinity. At some point there is a limit on how much additional benefit Merton can gain by increasing engine assembly capacity. This happens when another bottleneck in production is discovered. Maximizing the number of engine assembly machine hours yields a maximum optimal level of 4,500 machine hours (SEE EXHIBIT 7). At this level, we are constrained by two additional resources, metal stamping machine hours and model 102 assembly machine hours. This means that beyond 1 additional machine hour of engine assembly will not yield any additional benefit because other resources are constrained.

As another avenue to assess Merton’s capacity issue in the engine assembly line, the purchasing managers wanted to evaluate the option of renting capacity, furnishing all the necessary material and engine components and reimbursing an outside supplier for labor and overhead. This alternative was meant to resolve the engine capacity problem. As previously alluded, not having an engine assembly capacity as a constraint does not address the problem due to the other capacity constraints. As shown in Exhibit 8 the maximum available Engine assembly machine-hours constraint was removed in order to obtain the maximum allowable hours based on the remaining capacity constraints. As a result, the model resulted in maximum machine-hours per month for the engine assembly of 4,500 hours which is 500 additional hours that the engine assembly would run with no maximum cap but restricted by other constraints such as the metal stamping constraint. Therefore, these 500 hours available are the maximum labor Merton should rent from an outside firm to maximize its profit.
Finally, we noticed that the net profit increased by $1,000,000 (from $11 million to $12 million) from the optimal solution which results in $2000 per machine hour increase. That means that for each engine outsourced of the Mode M101, the contribution margin increases by $2000. Therefore, the maximum that the company should is $2000 per labor-hour outsource to assemble engines to a total maximum outsource of 500 hours.
Exhibit 1

Exhibit 2

Exhibit 3

Exhibit 4

Exhibit 5

Exhibit 6

Exhibit 7

Exhibit 8