A company currently ships its product from 5 plants to 4 warehouses. It is considering closing
one or more plants to reduce cost. What plant(s) should the company close, in order to
minimize transportation and fixed costs?
Transportation Costs (per 1000 products)
	Plant 1	Plant 2	Plant 3	Plant 4	Plant 5
Warehouse 1	$4,000	$2,000	$3,000	$2,500	$4,500
Warehouse 2	$2,500	$2,600	$3,400	$3,000	$4,000
Warehouse 3	$1,200	$1,800	$2,600	$4,100	$3,000
Warehouse 4	$2,200	$2,600	$3,100	$3,700	$3,200
Open/close decision variables
	Plant 1	Plant 2	Plant 3	Plant 4	Plant 5
Decision	0	0	0	0	0
Number of products to ship (per 1000)
	Plant 1	Plant 2	Plant 3	Plant 4	Plant 5	Total	Demand
Warehouse 1	0	0	0	0	0	0	15
Warehouse 2	0	0	0	0	0	0	18
Warehouse 3	0	0	0	0	0	0	14
Warehouse 4	0	0	0	0	0	0	20
Total	0	0	0	0	0
Capacity	0	0	0	0	0
Distr. Cost	$0	$0	$0	$0	$0
Fixed Cost	$0	$0	$0	$0	$0
Total Cost	$0	$0	$0	$0	$0	$0
Problem
A company currently ships products from 5 plants to 4 warehouses. The company is considering the option of
closing down one or more plants. This would increase distribution cost but perhaps lower overall cost. What
plants, if any, should the company close?
Solution
1) The variables are the decisions to open or close the plants, and the number of products that should be
shipped from the plants that are open to the warehouses. In worksheet Facility these are given the names
Open_or_close and Products_shipped.
2) The logical constraints are
	Products_shipped >= 0 via the Assume Non-Negative option
	Open_or_close = binary
The products made can not exceed the capacity of the plants and the number shipped should meet the
demand. This gives
	Products_made <= Capacity
	Total_shipped >= Demand
3) The objective is to minimize cost. This is given the name Total_cost on the worksheet.
Remarks
It is often possible to increase the capacity of a plant. This could be worked into the model with additional 0-1
or binary integer variables. The Solver would find out if it would be profitable to extend the capacity of a plant.
It could also be interesting to see if it would be profitable to open another warehouse. An example of this can
be found, in somewhat modified form, in the capacity planning model in the Finance Examples workbook.