Assignment Problem: J Peterman Catalog Co (JPC) is a major catalog sales company in greater Manhattan. To produce these catalog products, JPC employs the services of one of the largest contract manufacturers, Kramerica Company (KC). JPC is now considering changing the manner in which it interacts with KC.
To provide some background, the supply chain for catalog fashion apparel works approximately as follows: Because the lead times for acquiring fabric are very long, all fabric must be procured far in advance of the selling season when demand is still uncertain. By the time that garments are produced, there is much less demand uncertainty, but obviously the amount that can be produced is limited by the amount of fabric that was acquired. To keep things simple, we will assume that all production is make-to-order. That is, we will assume that units can be produced after they are demanded. We will also assume that production capacity is limited only by the availability of fabric.
We will consider a garment that JPC sells for $50 per unit. At the time that fabric must be procured, it is known that demand for the garment follows a normal distribution with a mean of 30,000 units and the standard deviation of 10,000. The cost of fabric is $15 per unit and the KC's additional cost of delivering a completed garment, e.g. cutting, sewing, packaging, shipping, etc., is $10 per unit. Any fabric that is not needed to satisfy demand can be sold off for $5 per unit. (Assume one unit of fabric is required to make one garment.) The following figure represents the time-line of demand and supply:
Under a new arrangement, JPC will buy the fabric. Then, when demand is observed, JPC will pay the KC $15 for each unit that they cut, sew, package, ship etc. in response to demand. Note that KC's profit margin under the new arrangement will be $5, exactly the same as under the traditional arrangement. JPC can also sell off any fabric that is not needed to satisfy demand for $5 per unit.
a) Under the new arrangement as described above, how many units of fabric should JPC procure to maximize its profits?
b) Compare the quantities under cases A (question 17) and B (question 18) above. Are they different or the same? Why?
c) What supply chain and operational issues might be of concern to JPC in making its decision about adopting the new arrangement like the one proposed above instead of the traditional arrangement described earlier?