A company sells many products online. The company needs substantial warehouse space for storing products. Plans are being made for leasing warehouse storage space over the next 5 months. Just how much space will be required in each of these months is unknown. Since the space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis.
On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased at least once but not every month.

The space requirement and the leasing costs for the various leasing periods are as follows:

Month Required Space Leasing Period Cost per
(sq ft) (months) (sq ft leased)
1 30,000 1 $65
2 20,000 2 $100
3 40,000 3 $135
4 10,000 4 $160
5 50,000 5 $190

The objective is to minimize the total leasing cost for meeting the space requirements.
Formulate a LP model for this problem.

a) Variable Definition. Let Xij be the space in a number of square feet leased from the beginning of month i to the end of month j.
What are the possible values of I, and j, respectfully? Write down all the decision variables.

b) Write down the LP formulation

Answer rating: 100% (QA)

First we will conceptualise the problem Let x ij amount of space leased in i month for a period of j ... View the full answer