Suppose that you have two possible locations to locate warehouses: city A and ci

Question

Suppose that you have two possible locations to locate warehouses: city A and city B. You can locate a warehouse in city A, or city B, or both cities. You have the following information about the possible warehouse locations: A warehouse in city A has a fixed monthly payment of 56,000 and a capacity of 5000 units. A warehouse in city B has a fixed monthly payment of 55,000 and a capacity of 6000 units. Once you locate a warehouse or warehouses, you will ship the product from these warehouses to the retailer stores you locate. There are also two possible locations to locate retailer stores: site 1 and site 2. You can locate at most 5 retailer stores at each one of these sites. You have the following information about the possible retailer store sites. A retailer store in site 1 has a fixed monthly payment of $2,000. The sale potential of a single retailer store in site 1 is 1000 units per month. A retailer store in site 2 has a fixed monthly payment of $2,500. The sale potential of a single retailer store in site 2 is 1500 units per month. Once you locate retailer stores, you have to ship the total sale potential at each site from the warehouses you have. For instance, if you locate 3 retailer stores in site 1, you need to ship exactly 3000 units to site 1 from the warehouses you have located. You can ship from any warehouse to any site. The costs of shipping one unit from the warehouse locations to the retailer store sites are given in the table below. city A city 13 site 1 55 SS site 2 510 56 Each unit is sold for 515 at any retailer store site and the sale potential of each retailer store will be the average number of items sold at the retailer store. As the manager of distribution network, you need to find where to locate the warehouses, how many retailer stores to locate at each potential site, and how to ship from the warehouses to the retailer store sites to satisfy the sale potentials at the sites. In doing so, you want to maximize the total monthly profit, which is equal to revenues from sales minus monthly warehouse and retailer store costs and shipping costs. Note that you cannot ship from a city if there is no warehouse in that city; and, the total amount you ship to a site will be determined by the number of retailer stores you locate on that site. a) (15 points) Mathematically formulate a mixed integer linear programming model for the above distribution planning problem by defining decision variables, objective function, and constraints. b) (15 points, 5 points each) Mathematically formulate the following restrictions as constraints independent of each other. i. If you locate a retailer store at a site, you have to locate at least 2. ii. Total number of retailer stores you locate should be less than or equal to 6. iii, You have to locate at least as many retailer stores in site 1 as in site 2.

Explanation / Answer

Value

t probability

0.95

0.1786

1.15

0.1341

1.20

0.1244

These values represent the t value for a given probability.

Probability

t value

0.20

1.341

0.15

1.517

0.10

1.753

Value

t probability

0.95

0.1786

1.15

0.1341

1.20

0.1244

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