JP Merchant, a firm that produces car components for m clients, has already p warehouses located in Spain to distribute its products. The logistics manager of the firm, after complaints from the clients due to the late delivery of the products, wants to open new warehouses so as to deliver its products within T hours. In other words, he wants to know where to locate the new warehouses and its number so as to deliver in maximum of T hours to ALL the clients (total coverage). The existing warehouses have to be considered, since they are all operational. The manager is considering n new potential locations for the new warehouses, and he knows the time between each client i and each potential and existing warehouse j, defined by tij. Formulate a binary linear problem that minimizes the number of new warehouses to address this issue.
After solving the problem, the logistics manager is not satisfied with the solution, since some of the existing warehouses have bad locations, which implies that he needs many warehouses to achieve the goal of serving all clients within T hours. So he wants to modify the problem. Now he wants to know what is the minimum number of warehouses to solve the problem of total coverage, but considering that some of the existing warehouses can be closed.