A manufacturing facility produces 5 products.
Production scheduling is done on an hourly basis. Demand for
the products for the next hour is shown below in the column
labeled Required Production.
The facility has 10 cells, each capable of producing
at some subset of the products. The last column shows the production
rate for the products in the production cells. Note that the
rates are the same for all cells capable of producing a given
product.
|
Products
|
Required
Production
|
Production Rate/hour
|
|
1
|
12
|
10
|
|
2
|
17
|
8
|
|
3
|
18
|
12
|
|
4
|
15
|
10
|
|
5
|
8
|
6
|
The table below shows cell capability. A blank
means that a cell can produce the product while an X indicates
that it cannot.
We want to determine an hourly production schedule
that specifies which cells to open and what products should
be produced in the open cells. The goal to open as few cells
as possible, however, we must open enough cells to make the
desired quantities.
A cell can produce more than one product in
an hour and the amounts produced do not have to be integer.
Construct a model that can be solved for each
hour. Solve the problem for the numbers provided.
|
