[ 1.21 Suppose that the daily demand for product j is dj for j = 1,2. The demand
should be met from inventory, and the latter is replenished fiom production
whenever the inventory reaches zero. Here, the production time is assumed to be
insignificant. During each product run, Q, units can be produced at a fixed setup
cost of $kj and a variable cost of $cjQ, . Also, a variable inventory-holding cost
of $hj per unit per day is also incurred, based on the average inventory. Thus,
the total cost associated with product j during T days is $TdjkjlQj + Tcjdj +
TQjhj/2. Adequate storage area for handling the maximum inventory Q, has to
be reserved for each product j. Each unit of product j needs sj square feet of
storage space, and the total space available is S.
a.
b.
We wish to find optimal production quantities Ql and Q2 to minimize
the total cost. Construct a model for this problem.
Now suppose that shortages are permitted and that production need
not start when inventory reaches a level of zero. During the period
when inventory is zero, demand is not met and the sales are lost.
The loss per unit thus incurred is $C ,. On the other hand, if a sale
is made, the profit per unit is $Pj. Reformulate the mathematical
model.
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