SCM 366

RedBrand Assignment 2

This assignment is a slight modification to The RedBrand Company Assignment 1. In this problem, RedBrand has shipping options that were not previously available, but it also faces shipping limits on each from-to path (that is there are arc capacities). In addition to the previous shipping options, the company can also ship between plants, between customers and between warehouses. The cost matrix has been updated to reflect these additional options. Capacity at the plants and demand at each customer have not changed from Assignment 1. However, there is an arc capacity of 200 units from any source to any sink. That is to say, From/To flows cannot exceed 200.

Plant	Supply Capacity
I	200
II	300
III	100

Customer	Demand Required
I	400
II	180

Shipping Costs ($ per unit shipped) from Sources to Sinks (--- indicates impossible shipment)

From	Plant I	Plant II	Plant III	Warehouse 1	Warehouse 2	Customer I	Customer II
Plant I	---	5	3	5	5	20	20
Plant II	9	---	9	1	1	8	15
Plant III	0.4	8	---	1	0.5	10	12
Warehouse 1	---	---	---	---	1.2	2	12
Warehouse 2	---	---	---	0.8	---	2	12
Customer I	---	---	---	---	---	---	1
Customer II	---	---	---	---	---	7	---

For example, the supply capacity (i.e., most that can be shipped) from Plant I is 200. Customer II demands at least 180 units. The cost to ship one unit from Plant II to Customer II is $15. The warehouses are transshipment points. No more than 200 units can be shipped from one location to anotherthe arc shipping limit. The --- in the cost matrix indicates an impossible shipping path.

Find the minimum cost-shipping plan that satisfies all customer demands. Your solution should show the minimum total cost and the flows from sources to sinks. (Hint: this is a transshipment problem).