In a supply chain, there are two companies (COMX, COMY). Both COMX and COMY have facilities to serve the same three customers. In order to increase the supply chain surplus, optimal distribution network design is desired. The decisions of how much to manufacture and ship a product, which manufacturing facilities to keep open or shut down will be given based on a linear optimization model. The tables below show the manufacturing and shipping cost from facility i to customer j, annual fixed cost of keeping facility i open, demand of customer j, capacity of manufacturing facility i.

COMX

Fromto	Customer 1	Customer 2	Customer 3	Capacity i	Fixed cost $
Facility 1	$20	$32	$13	100,000	1 Million
Facility 2	$10	$12	$11	50,000	2 Million
Demand j	15,000	30,000	45,000

COMY

Fromto	Customer 1	Customer 2	Customer 3	Capacity i	Fixed cost $
Facility 1	$15	$30	$18	70,000	1 Million
Facility 2	$15	$14	$17	90,000	1.5 Million
Facility 3	$15	$23	$20	60,000	2 Million
Demand j	30,000	50,000	100,000

1. Define decision variables including keeping a facility open or not explicitly which will optimize COMX and COMY distribution networks separately.
2. Formulate the objective function explicitly to minimize the total cost of COMY allowing shutdowns.
3. Formulate capacity related constraints explicitly if COMX and COMY are merged to serve three customers and facility 1 of both companies are not allowed to be shut down after the merge. Indicate how many constraints exist.
4. Formulate demand related constraints explicitly if COMX and COMY are merged to maximize the profit slowing not meeting demands which are not profitable.
5. Formulate the objective function explicitly if COMX and COMY are merged to maximize the profit allowing shutdowns and assuming the sales price for the product is $200.
6. How would you define decision variables and formulate constraints implying each customer of COMX has to use a single source to satisfy their demands?

Answer rating: 100% (QA)

a Decision variables are following Let Ai1 if facility i is kept open for COMA else ... View the full answer