Question

The Pineapple Company produces ice-cream at its factories in Kobe, Nagoya, and Sendai. These factories have not been able to keep up with demand for orders at Pineapple’s four warehouses in Tokyo, Osaka, Fukuoka, and Sapporo. As a result, the company has decided to build a new factory to expand its production capacity. The two locations being considered are Kumamoto and Hiroshima.

We are given information regarding the monthly demands at the four warehouses.

Warehouse	Monthly Demand (Litres)
Tokyo	15,000
Osaka	16,000
Fukuoka	16,000
Sapporo	15,000

We also know the production costs and monthly capacities at the existing factories. To help us decide where to build the fourth factory, we have estimated the production costs at the proposed factories.

Factory	Monthly Capacity (Litres)	Production Cost per litre
Kobe (existing)	16,000	$35
Nagoya (existing)	14,000	$37
Sendai (existing)	16,000	$39
Kumamoto (proposed)	-	$30 (estimated)
Hiroshima (proposed)	-	$32 (estimated)

In addition, the cost to transport ice-cream from the existing factories and the proposed factories to the warehouses are summarized below.

	Tokyo	Osaka	Fukuoka	Sapporo
Kobe	$50	$30	$50	$60
Nagoya	$40	$40	$50	$60
Sendai	$50	$50	$60	$40
Kumamoto (proposed)	$50 (estimated)	$50 (estimated)	$30 (estimated)	$60 (estimated)
Hiroshima (proposed)	$40 (estimated)	$30 (estimated)	$40 (estimated)	$50 (estimated)

Part a

What should be the proposed monthly capacity (L) at the new factory in order to keep up with the warehouse demands?

Part b

Based on the above information, what is the single measure/criteria we should use to decide on the location of the new factory? Please express your answer in words.

Part c

For each of the proposed new factory, we will formulate a separate LP model to compute the measure in part b. Let ?_?? be the quantity (litres) ship from factory ? to warehouse ?.

1. How many decision variables are required in each LP model?

2. Please complete the definitions of the decision variables (i.e. Let ?_?? be the quantity (litres) ship from factory ? to warehouse ?, where …?) for each of the two LP models.
3. Express the objective function in term of ?_??for either one of the two LP models.
4. Express the constraints in term of ?_??for either one of the two LP models.

Answer 1

1. Total demand on all four sites = 15000+16000+16000+15000 = 62000

Existing Production capacity = 16000+14000+16000 = 46000

short capacity = 62000 - 46000 = 16000

so, 16000 should be the proposed monthly capacity (L) at the new factory in order to keep up with the warehouse demands.

2. on the basis of information provided, proposed crietaria shoud be total Cost of producction and  cost of transport ice-cream from the existing factories and the proposed factories to the warehouses to transport ice-cream from the existing factories and the proposed factories to the warehouses

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