Model 6: Warehousing

A company needs to lease warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these 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 (by adding a new lease and/or having an old lease expire) at least once but not every month.

The space requirement (in thousands of square feet) and the leasing costs (in hundreds of dollars) for the various leasing periods are as follows:

Month Required
period (months)
Cost ($) per 1,000
sq ft leased
1 30 1 650
2 20 2 1,000
3 40 3 1,350
4 10 4 1,600
5 50 5 1,900

The objective is to minimize the total leasing cost for meeting the space requirement. Formulate the linear programming model for this problem.