Inventory holding cost = 50(II + h + [3)
(Note that /4 =0 in the optimum solution.)The cost of hiring and firing is a bit more
involved. We know that in any optimum solution, at least 40 temps (= must be
hired at the start of March to meet the month's demand. However, rather than treating thissituation as a special case, we can let the optimization process take care of it automatically. Thus,
given that the costs of hiring and firing a temp are $200 and $400,respectively, we have
(C fI
") (NUmber of hired temps )
ost o' llnng
d f
' . = 200 at the start of
an mng March, April, May, and June
(
Number offired temps )
+ 400 at the start of
March, April, May, and June
To translate this equation mathematically,we will need to develop the constraints first.
The constraints ofthe model deal with inventory and hiring and firing. First we develop the
inventory constraints. Defining X, as the number oftemps available in month i and given that the
productivity of a temp is 10 units per month, the number of units produced in the same month is
lOXi'Thusthe inventory constraints are
lOx! = 400 + 1
1
(March)
I, + lOx2 = 600 + 1
2 (April)
1
2
+ lOx3 =400 + /3 (May)
13
+ 10x4 = 500 (June)
Next, we develop the constraints dealing with hiring and firing. First, note that the temp workforce starts with XI workers at the beginning of March. At the start ofApril, XI will be adjusted
(up or down) by 52 to generate X2'The same idea applies to x3 and X4' These observationslead to
the following equations
XI = 5
X2 = Xl + 52
x) = X2 + 53