Migros is one of the leading companies in the retailing industry, offering a wide range of products on its stores all around the country. Recently, the company decided to expand its operations; and begin opening stores in a new country. In this country, there are k districts, which all have their respective demands. Migros wants to ensure that all demand is covered to be able to reach all of its potential customers; with the minimum cost possible. To cover these demands, Migros has 4 different store type options, 5M, 3M, 2M and Jet, with their respective capacities.By incurring an additional fixed personnel cost, it is possible to extend the service capacity of each store up to 110% of its normal capacity. Each type of store can be built only once to a particular district. Each store has an initial cost to build. Also, stores can cover the demands for the districts in addition to the district they are in as long as they are in their reach. Moreover, each store type (5M, 3M etc.) has different coverage distances simply because people might be more lenient to travel larger distances for a 5M than for a Jet. However, each unit demand covered by a store from another district adds a cost proportional to the distance between the store and the district. To build a consistent brand image, Migros wants to have the same set of stores located at districts of similar demand behaviors. In addition, Migros wants to make 5M stores reachable to everyone, so they want to build a 5M to a district if no neighbouring district has one. However, the company does not want to build two 5M stores in two neighboring districts either. Additionally, Migros wants to ensure that the total numbers of 3M and Jet stores are kept close for marketing purposes.

(a) Model the problem Migros faces as a Linear or Integer Programming Model 

(b) In addition to the opening stores, Migros needs to open 4 warehouses in total to support its stores, and each store must be supported by one warehouse. Every day, one truck goes from a warehouse to each district it supports. Write an LP model to minimize the maximum distance traveled for a single delivery. (Model this part separately from the main model in (a), you can add new parameters or variables).

(c) Finally, Migros considers trying an experimental quality standard, they would like to try to put a limit to the number of districts each store type can serve. However, they would like to know how this additional constraint would affect the cost. How would your model change? (You don’t need to rewrite whole model, it is enough to just provide the additional constraint to the model in (a))