Armco, Inc., is a manufacturing company that has a contract to supply a customer with parts from April through September. However, Armco does not have enough storage space to store the parts during this period, so it needs to lease extra warehouse space during the 6-month period. Following are Armco’s space requirements:
Month Required Space (ft2)
April ............47,000
May .............35,000
June .............52,000
July .............27,000
August ...........19,000
September ...........15,000
The rental agent Armco is dealing with has provided it with the following cost schedule for warehouse space. This schedule shows that the longer the space is rented the cheaper it is. For example, if Armco rents space for all six months, it costs $1.00/ft2 per month, whereas if it rents the same space for only one month, it costs $1.70/ft2 per month.
Rental Period (months) $/ft2/mo
6 ...............1.00
5 ...............1.05
4 ...............1.10
3 ...............1.20
2 ...............1.40
1 ...............1.70
Armco can rent any amount of warehouse space on a monthly basis at any time for any number of (whole) months. Armco wants to determine the least costly rental agreement that will exactly meet its space needs each month and avoid any unused space.
a. Formulate and solve a linear programming model for this problem.
b. Suppose that Armco decided to relax its restriction that is rent exactly the space it needs every month such that it would rent excess space if it were cheaper. How would this affect the optimal solution?