The variables Xi and Ii, by definition, must assume nonnegative values. On the other hand, the
variable 5i
can be positive when new temps are hired, negative when workers are fired, and zero
if no hiring or firing occurs. As a result, the variable must be unrestricted in sign,This is the first
instance in this chapter of using an unrestricted variable. As we willsee shortly,special substitution is needed to allow the implementation of hiring and firing in the model.
The objective is to minimize the sum ofthe cost of hiring and firing plus the cost of holding
inventory from one month to the next.The treatment ofthe inventory cost is similar to the one
given in Example 2.3-5-namely,