The problem in Example 12.9 assumes that the heaviest demand occurs in the second (post-April) phase of selling. It also assumes that capacity is higher in the second production opportunity than in the first. Suppose the situation is reversed, so that the higher capacity and most of the demand occur in the first phase. Make some reasonable assumptions for the resulting input parameters, and then solve for the optimal production plan. Do you get qualitatively different results? Which situation would you rather face if you were Shirt Tails?

Example 12.9

PLANNING PRODUCTION OF BLOUSES AT SHIRTTAILS

ShirtTails is a clothing manufacturer that operates its own chain of discount retail stores. At the beginning of November 2011, ShirtTails is trying to plan its production of a new blouse that is worn primarily in the warmer months. Based on production constraints from other products, the company knows it has two opportunities to produce this blouse-in November 2011 and later in April 2012. The production capacity (for this blouse) is 1200 in November. In April, the capacity will increase to 2500. By April, demand for the blouses produced in November will be known. Using this information, ShirtTails will then be able to plan its production in April. The unit cost of producing a blouse is $12, and the selling price will be $14. These remain constant. There is a $1 holding cost per blouse still in inventory after the pre-April demand. By November 2012, any remaining blouses in inventory will be sold at a markdown price of $4. (This is because ShirtTails plans to introduce a new blouse the next year.) Demand for the blouses before April is not known with any certainty, but ShirtTails believes it should be somewhere between 100 and 1000. After April, the demand for blouses is expected to be anywhere from 3 to 7.5 times as large as the demand before April. What production plan should the company use to maximize the expected profit from these blouses?

Objective To develop an optimization model that specifies production quantities of blouses in two time periods, where the second production quantity can be based on demand information from the first period.