/A standard and has been opened read-only to prevent Major#2 Fall 2015: Salama S
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/A standard and has been opened read-only to prevent Major#2 Fall 2015: Salama Supermarkets is in the process of expansion in the estern area of Saudi Arabia. During the next year, Ibrahim is planning to constdet new stores that will serve 10 geographically dispersed communities experience indicates that a community must be within 25 kilometres of a store to attract customers. In addition, the population of a community plays an important role in where a store is located, in the sense that bigger communities generate more participating customers. The following tables provide the populations as well as the distances (in km) between the communities: distance from communicty i to community j (km) 20 40 35 17 24 30 8 33 12 23 68 40 30 20 19 70 40 36702245302180 0,000 15,000 28,000 40 23 35 68 36 17 40 7 70 2430228023 50 20 4 24 70 12 8 1030 20 414 2 33 70 21 40 13 50 40 2 70 24 20 410 30,000 23 7040 13 40 12 14 50 50 30,000 26 30 20,000 15,000 60,000 10 12 40 80 10 40 50 30 50 22 Formulate an ILP that can find the least number of stores (and their corresponding locations) to be constructed, taking into account the distance restriction and the concentration of populations e here to searchExplanation / Answer
ILP formulation
Decision variables: Let Xj be a binary variable such that Xj = 1 indicates that a store is constructed in community j, if Xj = 0 , then store is not constructed in community j
Objective: Min X1+X2+X3+X4+x5+x6+X7+X8+X9+X10
s.t.
X1+X5+X6+X10 >= 1 (communities 1,5,6,10 are within 25 km of comm 1. So at least 1 store should be there)
X1+X2+X3+X7+X8 >= 1 (communities 1,2,3,7,8 are within 25 km of comm 2. So at least 1 store should be there)
X2+X3+X6+X9 >= 1 (communities 2,3,6,9 are within 25 km of comm 3. So at least 1 store should be there)
X4+X7+X8+X10 >= 1 (communities 4,7,8,10 are within 25 km of comm 4. So at least 1 store should be there)
X1+X5+X6+X9 >= 1 (communities 1,5,6,9 are within 25 km of comm 5. So at least 1 store should be there)
X1+X3+X5+X6+X7+X8 >= 1 (communities 1,3,5,6,7,8 are within 25 km of comm 6. So at least 1 store should be there)
X2+X4+X6+X7 >= 1 (communities 2,4,6,7 are within 25 km of comm 7. So at least 1 store should be there)
X2+X4+X6+X8+X9 >= 1 (communities 2,4,6,8,9 are within 25 km of comm 8. So at least 1 store should be there)
X3+X5+X8+X9+X10 >= 1 (communities 3,5,8,9,10 are within 25 km of comm 9. So at least 1 store should be there)
X1+X4+X9+X10 >= 1 (communities 1,4,9,10 are within 25 km of comm 10. So at least 1 store should be there)
X1, X2, X3, X4, X5, X6, X7, X8, X9, X10 = 0,1
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