Operations Management: Processes and Supply Chains, 12th Edition

Solved Problem 1

Peachy Keen, Inc., makes mohair sweaters, blouses with Peter Pan collars, pedal pushers, poodle skirts, and other popular clothing styles of the 1950s. The average demand for mohair sweaters is 100 per week. Peachy’s production facility has the capacity to sew 400 sweaters per week. Setup cost is $351. The value of finished goods inventory is $40 per sweater. The annual per-unit inventory holding cost is 20 percent of the item’s value.

1. What is the economic production lot size (ELS)?

2. What is the average time between orders (TBO)?

3. What is the total of the annual holding cost and setup cost?

Solution

1. The production lot size that minimizes total cost is

   $$\begin{array}{ccc}\hfill \text{ELS}& =\hfill & \sqrt{\frac{2DS}{h}}\sqrt{\frac{p}{p-d}}=\sqrt{\frac{2(100\times 52)(\$351)}{0.20(\$40)}}\sqrt{\frac{400}{(400-100)}}\hfill \\ =\hfill & \sqrt{456,300}\sqrt{\frac{4}{3}}=\mathrm{780\; ...}\hfill \end{array}$$