Case 1.

Precision Machine Company (PMC) produces computer part labeled PC1 for computer manufacturers. The manufacturing process of PC1 is staged. At the first stage (Stage 1), PMC produces basic component. At the second stage (Stage 2), PMC brush up the basic component produced in Stage 1. Currently, PMC leases a general purpose machine (GPM) from an outside supplier at an annual rate of $4,000 per machine. Since GPM is a general purpose machine, it works relatively slow. Total service time (across two stages) averaged 35 seconds with a standard deviation of 24 seconds. The time between consecutive customer arrivals is exponentially distributed with an average of 37 seconds. The manufacturing cost of a component is $5,000. Holding cost of components is based on an annual interest rate of 10%. PMC is considering 2 new production options.

(1) Option 1: PMC leases a second GPM.

(2) Option 2: PMC returns GPM to the outside supplier and leases a new special purpose machine (SPM). SPM works sequentially from Stage 1 to Stage 2. The total service time in Stage 1 is 20 second with a standard deviation of 14 seconds, and the total service time in Stage 2 is 10 second with a standard deviation of 10 seconds. PMC leases SPM from an outside supplier at an annual rate of $7,000.

(a). Computes annual total cost (ATC) of Option 1. ATC = annual rental cost of machines +annual inventory holding cost.

(b) Computes ATC of Option 2.

(c) Determine the optimal option that minimizes ATC (including the original option (1 GPM case), Option 1 (2 GPM case), and Option 2 (1 SPM case)).