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A PRODUCTION AND INVENTORY APPLICATION 333

11 The distribution system for the Herman Company consists of three plants, two warehouses
and four customers. Plant capacities and shipping costs (E) from each plant to each
warehouse are:

Warehouse

Plant 1 2 Capacity
1 4 7 450
2 8 5 600
3 5 6 380

Customer demand and shipping costs per unit (in E) from each warehouse to each
customer are:

Customer
Warehouse 1 2 3 4

1 6 4 8 4
2 3 6 7 7
Demand 300 300 300 400

a. Develop a network model of this problem.
b. Find the optimal shipping plan.
c. Suppose that shipments between the two warehouses are permitted at E2 per unit and
that direct shipments can be made from plant 3 to customer 4 at a cost of E7 per unit.
Find the optimal shipping plan.
12 A rental car company has an imbalance of cars at seven of its locations. The following
network shows the locations of concern (the nodes) and the cost to move a car between
locations. A positive number by a node indicates an excess supply at the node, and a
negative number indicates an excess demand.

+5 –3
30
2 4
27
45
20 15 7 +6
30
–8 1 25 5 +2
25 28 12
20
3 6
35
+3 –5

a. Develop a model for restoring the proper balance at the locations.
b. Solve the model formulated in part (a) to determine how the cars should be redistributed
among the locations.

13 Naples Fishing Supply manufactures a variety of fishing equipment, which it sells
throughout Europe. For the next three months, Naples estimates demand for a particular
product at 150, 250 and 300 units, respectively. Naples can supply this demand by

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