Model Description Toms

MODEL DESCRIPTION

The problem: Merton’s financial performance during the first half year of 1988 was dissatisfying. Main reason was that Model 102 assembly and engine assembly production lines were not operating at full capacity. To improve the current inefficiency situation, a change in production lines was necessary. A few optional plans seemed difficult to evaluate and had further unclear influence on Merton’s financial position.

The solution approach: The potential outcomes in this report were generated by mathematical models and linear programming. Linear programming, a special case of mathematical programming, is used for the optimization of an objective function— in this case, maximizing annual profits. The mathematical model consists of variables, constraints, and an objective equation. After the mathematical model is built, we put data in Microsoft Excel spreadsheet, used Premium Solver function, and found the outcomes for each plan.

Variables: In the four alternative plans, there are twenty eight variables involved in total, all nonnegative. Nine variables represent machine-hours required per truck in all departments; eight variables represent standard costs of direct material and direct labor; four variables represent fixed overhead in all departments per month; six variables represent variable overhead per unit of Model 101 and Model 102, one variable represents profit that each Model 103 brings

Constraints: There are five constraints from two aspects. Four of the constraints limit the total amount of machine-hours spent every month: the available machine-hours spent in each department: engine assembly, metal stamping, model 101 assembly and model 102 assembly. The fifth constraint, which is solely used in plan 4, requires that the number of Model 101 produced is at least three times the number of Model 102.