

Network Flow Programming Models 


Distribution and Worker Assignment 

A company has three plants: P1, P2 and P3, and two customers:
C1 and C2. You are to construct and solve a network flow model
to make several decisions for the company. Details of the
situation are listed below for a one month period.
 C1 has a firm demand for 1000 units of product, while C2
has a demand for 600 units. These demands must be satisfied.
 The cost of transferring a unit of product from plant i
to customer j is c(i, j) These costs are shown
in the table.
c(i,j)

1

2

1

10

15

2

14

20

3

25

22

 Each plant can manufacture no more that 500 units of product
during regular time. Not including labor cost, the cost of
manufacture at P1 is $100 per unit, at P2 the cost is $110
per unit, and at P3 the cost is $120 per unit.
 At each plant an additional 100 units can be manufactured
on overtime. The overtime cost, again not including labor,
is 1.5 times the regular time cost.
 The company has two sources of labor: skilled labor indicated
by W1 and semiskilled by W2. There are 100 skilled laborers
available and 200 semiskilled laborers. Skilled laborers
are paid $2000 per month and semiskilled laborers are paid
$1700 per month. Not all workers available need be hired.
 Each skilled laborer will produce 12 units of product per
month, while each semiskilled laborer will produce 10 units
per month.
 The company must transport workers to the plants. The cost
of transporting a worker to P1 is $300 per month, to P2 the
cost is $250, and to P3 the cost is $275.
 The network model is to minimize total cost.

