IEOR 3402: Assignment 3
Hand in solutions to the starred problems only.
You may work individually, or as a group of 2 students. (If you work as a group, please
submit one assignment per group.)
1. Nahmias, 3.7.
2. Nahmias, 3.12.
3. Nahmias, 3.32.
4. * Nahmias, 3.34. Assume that you must satisfy all demands without back-orders or lost
sales. You may use EXCEL or any other LP solver.
5. * In class, we have formulated the following linear program:
max X
T
t=1
r · St + h · It
s. t. St ? dt ?t = 1, . . . , T
Xt ? Ct ?t = 1, . . . , T
It ? It?1 + Xt ? St ?t = 2, . . . , T
I0 = 0
It
, St
, Xt ? 0 ?t = 1, . . . , T.
One of the underlying assumptions of this model was the any excess demand that cannot
be satisfied immediately will be lost (lost sales). Suppose instead that any excess demand
that cannot be satisfied immediately will be carried over to the next period (backlogging),
and any backordered unit will incur the cost of $b per period. Develop a linear program for
this problem by modifying the above formulation.
6. * You have just been made corporate vice president in charge of manufacturing for an
automotive components company and are directly in charge of assigning products to plants.
Among many other products, the firm makes automotive batteries in three grades: heavyduty,
standard, and economy. The unit net profits and maximum daily demands for these
products are given in the first table below. The firm has three locations where the batteries
can be produced. The maximum assembly capacities, for any mix of battery grades, are
given in the second table below. The number of batteries that can be produced at a location
is also limited by the amount of suitably formulated lead the location can produce. The lead
requirements for each grade of battery and the maximum lead production for each location
are also given in the following tables.
Unit Profit Max Demand Lead Requirement
Product ($/battery) (batteries/day) (lbs/battery)
Heavy-duty 12 700 21
Standard 10 900 17
Economy 7 450 14
1Plant Assembly Capacity Maximum Lead Production
Location (batteries/day) (lbs/day)
1 550 10,000
2 750 7,000
3 225 4,200
(a) Formulate a linear program that allocates production of the three grades among the
three locations in a manner that maximizes profit.
(b) Suppose company policy requires that the fraction of capacity (units scheduled/assembly
capacity) be the same at all locations. Show how to modify your LP to incorporate
this constraint.
(c) Suppose company policy dictates that at least 50 percent of the batteries produced
must be heavy-duty. Show how to modify your LP to incorporate this constraint.