NTEGER PROGRAMMING An international textile company aims to open distribution centers in four cities around Europe: London, Dusseldorf, Valencia, and Helsinki. Each distribution center may ship 89 units per week if it is opened. The weekly fixed cost of keeping each distribution center open is €680 for London, €570 for Dusseldorf, €445 for Valencia, and €515 for Helsinki. According to historical sales of the company in Europe, they have divided Europe into 3 different districts. District 1 requires 78 units per week, District 2 requires 99 units per week, and District 3 requires 67 units per week. The costs (including production and shipping costs) of sending one unit from a distribution center to a district are shown in the following table. The company wants to meet the weekly demands of the districts at minimum cost, subject to the preceding information and the following restrictions: Formulate an IP that can be used to minimize the weekly costs of meeting the demands of the districts. The transshipped amounts are integer values. (a) Clearly define your decision variables and any parameter you introduce. (b) Write down the objective function. (c) Write down the constraint which represents “Each distribution center may ship 89 units per week if it is opened.” (There will be 4 constraints in this option). (d) Write down the constraint which represents the demand satisfaction. .” (There will be 3 constraints in this option). (e) Write down the constraint which represents “The London and the Helsinki distribution centers cannot be opened at the same time.” (There will be 1 constraint in this option). (f) Write down the constraint which represents “At most two distribution centers can beopened.” (There will be 1 constraint in this option). (g) Write down the constraint which represents “If the London distribution center is opened,then the Valencia distribution center must be opened.” (h) Write down the constraint which represents “Either the Dusseldorf or the Valenciadistribution centers must be opened, but not both. (i) Write down the sign restrictions of your decision variables. (Clearly provide the rangesof the indexes).
INTEGER PROGRAMMING
An international textile company aims to open distribution centers in four cities around Europe: London, Dusseldorf, Valencia, and Helsinki. Each distribution center may ship 89 units per week if it is opened. The weekly fixed cost of keeping each distribution center open is €680 for
London, €570 for Dusseldorf, €445 for Valencia, and €515 for Helsinki. According to historical sales of the company in Europe, they have divided Europe into 3 different districts. District 1 requires 78 units per week, District 2 requires 99 units per week, and District 3 requires 67 units per week. The costs (including production and shipping costs) of sending one
unit from a distribution center to a district are shown in the following table.
The company wants to meet the weekly demands of the districts at minimum cost, subject to the preceding information and the following restrictions:
Formulate an IP that can be used to minimize the weekly costs of meeting the demands of the districts. The transshipped amounts are integer values.
(a) Clearly define your decision variables and any parameter you introduce.
(b) Write down the objective function.
(c) Write down the constraint which represents “Each distribution center may ship 89 units per week if it is opened.” (There will be 4 constraints in this option).
(d) Write down the constraint which represents the demand satisfaction. .” (There will be 3 constraints in this option).
(e) Write down the constraint which represents “The London and the Helsinki distribution centers cannot be opened at the same time.” (There will be 1 constraint in this option).
(f) Write down the constraint which represents “At most two distribution centers can beopened.” (There will be 1 constraint in this option).
(g) Write down the constraint which represents “If the London distribution center is opened,then the Valencia distribution center must be opened.”
(h) Write down the constraint which represents “Either the Dusseldorf or the Valenciadistribution centers must be opened, but not both.
(i) Write down the sign restrictions of your decision variables. (Clearly provide the rangesof the indexes).
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