Off-The-Wall Drugs has three distribution centers in a region from which it supplies four stores. Each distribution center stocks all of the supplies that are sold at each of the stores. When orders come in, the individual items being requested by the stores are packaged at the distribution centers into standard boxes and then shipped from the distribution center to the store requesting the material. Thus, under these assumptions, we can treat demand as being in terms of boxes requested by the stores.
While each distribution center stocks all of the items in inventory at each of the stores, each distribution center has a limited packaging capability (measured in terms of boxes per week). These capacities are as follows:
The weekly demands of the stores are as follows:
The unit costs of shipping a box between each of the distribution centers and the stores are as follows:
(a) Find the optimal distribution strategy for Off-The-Wall Drugs (i.e., determine which distribution centers should ship how much each week to which stores). Solve the problem as a transportation problem, showing your solution (including dual variables and reduced costs) in the tableau format used in this chapter.
(b) What would the change in the objective function be if we increased the demand at store A by one unit? How would the flows change in response to this increase in demand?
(c) What would the change in the objective function be if we increased the supply at distribution center 1 by one unit? How would the flows change in response to this increase in supply?
(d) What would the change in the objective function be if we increased the supply at distribution center 2 by one unit? How would the flows change in response to this increase in supply?
(e) What would the change in the objective function be if we increased the supply at distribution center 3 by one unit? How would the flows change in response to this increase in supply?
Note: For parts (b) through (e) of this exercise, you should be able to answer the questions without having to resolve the problem.