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Off-Cue Marketing is looking to expand its footprint into a region dominated by a host of other full-service convenience stores

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Off-Cue Marketing Expansion Project

Off-Cue Marketing is looking to expand its footprint into a region dominated by a host of other full-service convenience stores (like 7-11, QuikTrip, Pump-N-Puke, etc.).  

The region has been broken down into abstract ‘hex squares’, where decisions will be made whether to locate a store in each region (named A through OO – a total of 41 regions). Note that you can locate a store in a region or chose to NOT locate a store in that region.   One store max. 

Here is a picture, including four ‘border areas’ (B1-B4) that are relevant to our decisions.  

 

 

Each region is defined by its COST (to build a store), it’s MVALUE (market value), and the level of competition (COMP) that it faces in the region.  The data is shown at the back of the problem write-up.

Stores need to be located such that the following requirements are true:

a) Costs cannot exceed 5000 units. 

b) Each region must be ‘covered’ by at least 1 store, but no more than 3 stores. “Coverage”? 

a. Consider locating a store in Region I. It ‘covers’ itself (I), and the regions that border it (D,E,M,N,R).  

c) Each border (B1-B4) must have exactly one store in a region that ‘touches’ the border.  Note that regions A, E,BB and NN count for TWO regions based upon their location. 

d) Stores must be placed in regions such that the average COMP value must be less than or equal to 4.25. 

e) Your model should place stores such that it maximizes the total market value while meeting the constraints discussed. 

Create a correct Integer Linear Programming model to decide which regions should have OffCue Stores.  Summarize your solution by pictorially showing where stores should be located (this will also be a good check for you). 

 

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