|
|
 |
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 semi-skilled by W2. There are 100 skilled laborers
available and 200 semi-skilled 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 semi-skilled 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.
|
|
