Company ABC has a production line that produces a product from
two raw materials. To make a unit of product, one unit of raw
material A is processed in machine A, and one unit of raw material
B is processed in machine B. The outputs of these two machines
are combined at machine C to produce the finished good. The production
process is shown in the figure. Note that the finished product
contains one unit each of raw materials A and B.
Due to variability, the capacities of the machines change from
time to time. The capacities of the machines (expressed in units
per day) together with the demands and unit profits for the
next six days are shown in the table. The profits include both
revenue and raw material costs, but do not include the inventory
costs.
Data for the Problem
Day
Machine A Capacity
(Units/Day)
Machine B Capacity
(Units/Day)
Machine C Capacity
(Units/Day)
Finished Goods Demand
(Units)
Finished Goods
Unit Profit
($/Unit)
1
100
90
60
50
100
2
80
100
100
80
110
3
100
90
150
70
100
4
90
100
90
260
90
5
100
90
100
70
105
6
90
100
50
60
110
You are to find the amounts each machine should
process for the next six days. Because demand may exceed
capacity at any time, the owner is willing to build inventory.
The cost of storing inventory for one day at A is $1 per
unit, the cost at B is $2 per unit, and the cost at C is
$4 per unit. The maximum inventory that can be carried at
each of the machines is 10 units. The goal is to maximize
net profit less inventory cost. The demand in a day is an
upper bound to sales. If it is impossible to meet demand,
sales may be lost.
Use a network model to solve this problem. Use side constraints
if necessary.
Operations Research Models and Methods
Internet
by Paul A. Jensen
Copyright 2001 - All rights reserved
