Consider a company manufacturing N unique types of products (A_1, ..., A_N), tha

Question

Consider a company manufacturing N unique types of products (A_1, ..., A_N), that are fabricated and assembled in K different workstations (W_1, ..., W_K). For each product n = 1, ..., N, the demand is D_n which is sold at the unit price P_n the cost of raw material is c_n, and requires t_k^n minutes of the k^th workstation. Assume that the company works 8 hours per day and 5 days per week (thus the total number of available minutes is 60 times 8 times 5 = 2400 minutes). Assume that the overall labors cost and overhead cost equals $E. Suppose that the workstation k* is the bottleneck. Between the two decision rules for product mix, Traditional Method and Bottleneck Method, which one is more beneficial, under any of the following assumptions: Assume that the time at the bottleneck station k* for all products are equal, i.e., t_k*^1 = t_k*^N Provide one set of values for the parameters P_n, C_n, t_n, D_n in which the payoff of the Traditional Method is higher than the payoff of the Bottleneck Method. Provide one set of values for the parameters P_n, C_n, t_n, D_n in which the payoff of the Bottleneck Method is higher than the payoff of the Traditional Method. Provide one set of values for the parameters P_n, C_n, t_n, D_n in which the payoff of the Bottleneck Method is equal to the payoff of the Traditional Method.

Explanation / Answer

The requirements necessary for the demand forecasting result are as follows

Machine A: 80 × 10 + 60 × 10 + 40 × 5 + 20 × 5 = 1700 2400

Machine B: 80 × 15 + 60 × 10 + 40 × 10 + 20 × 10 = 2300 2400

Machine C: 80 × 15 + 60 × 10 + 40 × 15 + 20 × 10 = 2500 2400 Bottleneck

Machine D: 80 × 5 + 60 × 10 + 40 × 10 + 20 × 10 = 1600 2400

The contribution margin per bottleneck minute is:

A1(200 - 40 - 40)/15 = $8/min

A2 (150 - 30 - 30)/10 = $9/min

A3 (100 - 20 - 20)/15 = $4/min

A4 (75 - 10 - 10)/5 = $11/min

The best product mix is 65A,75B,40C

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