You can use the enumeration method or formulate it as a Linear Integer Program (LIP) and use the POM software to solve the LIP model.

Problem #3. (a Case study) The Ajax manufacturing company produces a special type of containers used in farming operations. At present, the company ships the product, to all customers, from the finished product storage at their manufacturing plant. Table I Provides information on the geographical location and average yearly demand for each customer. To expand and improve delivery operations, the company has decided to build 2-medium size warehouses in Midwestern region of the country. Based on a detail location analysis, they have selected the following 3 alternative locations for the warehouses. 1)- Findlay Ohio, 2)- Hermitage Pennsylvania, and 3)- alliance, Ohio. The capacity of the warehouses will be determined based on the location of the warehouse and their service areas. The approximate cost of building each warehouse and operating it is estimated as follows: Location Findlay Ohio Alliance Oho Hermitage PA yearly (in $Mil.) 1.32 1.15 1.51 Table 1 provides information on the location of customers, grouping the customers into 4 regions, and the average demand per customer (determined from the last 8 years shipping data.). Assume, average shipping cost/unit $0.04 per mile What is needed: Assuming the 4 cities in the 2nd column of Table 1 are the regional distribution centers (RDC) for the 4 regions. 1)- Determine aggregate mean and standard deviation of demand for each RDC and for the total shipment per year. (As discussed in this chapter). 2)- Suppose the company has imposed the following restrictions on shipments a)- A Warehouse in Findlay is not allowed to ship to Pittsburgh due to log travel time. Similarly, no flow between a warehouse in Hermitage and Toledo is allowed. b)- A warehouse in Alliance, OH can ship to any of the 4 RDC. Use the numeration procedure and determine the location of the two warehouses 3). It is said that, warehouse capacity must roughly be equal to 20% of yearly shipment. Using this assumption, and the fact that average apace allowed per unit of this product is 15 ft?, Determine storage capacities in ft2 for the two warehouses. 4)-If we determine to install telephone connection between the warehouses and the 4 RDC, what the minimum cost of the system if AT&T charges $1.2 per miles of connection Table 1. Geographical distribution of units sold (2011-2019) General Area City representing the region Average demand/year (RDC) 36000 Toledo 31000 Detroit MI Toledo OH Northwest Indiana Findlay, OH 12000 19000 Columbus, OH Mansfield, OH Zanesville, OH Columbus 9500 24000 40500 Pittsburgh PA New castle PA Morgantown WV Steubenville. OH Pittsburg 13000 18000 26500 18800 Erie PA Cleveland, OH Jamestown PA Cleveland 23500 18200 33000 Problem #3. (a Case study) The Ajax manufacturing company produces a special type of containers used in farming operations. At present, the company ships the product, to all customers, from the finished product storage at their manufacturing plant. Table I Provides information on the geographical location and average yearly demand for each customer. To expand and improve delivery operations, the company has decided to build 2-medium size warehouses in Midwestern region of the country. Based on a detail location analysis, they have selected the following 3 alternative locations for the warehouses. 1)- Findlay Ohio, 2)- Hermitage Pennsylvania, and 3)- alliance, Ohio. The capacity of the warehouses will be determined based on the location of the warehouse and their service areas. The approximate cost of building each warehouse and operating it is estimated as follows: Location Findlay Ohio Alliance Oho Hermitage PA yearly (in $Mil.) 1.32 1.15 1.51 Table 1 provides information on the location of customers, grouping the customers into 4 regions, and the average demand per customer (determined from the last 8 years shipping data.). Assume, average shipping cost/unit $0.04 per mile What is needed: Assuming the 4 cities in the 2nd column of Table 1 are the regional distribution centers (RDC) for the 4 regions. 1)- Determine aggregate mean and standard deviation of demand for each RDC and for the total shipment per year. (As discussed in this chapter). 2)- Suppose the company has imposed the following restrictions on shipments a)- A Warehouse in Findlay is not allowed to ship to Pittsburgh due to log travel time. Similarly, no flow between a warehouse in Hermitage and Toledo is allowed. b)- A warehouse in Alliance, OH can ship to any of the 4 RDC. Use the numeration procedure and determine the location of the two warehouses 3). It is said that, warehouse capacity must roughly be equal to 20% of yearly shipment. Using this assumption, and the fact that average apace allowed per unit of this product is 15 ft?, Determine storage capacities in ft2 for the two warehouses. 4)-If we determine to install telephone connection between the warehouses and the 4 RDC, what the minimum cost of the system if AT&T charges $1.2 per miles of connection Table 1. Geographical distribution of units sold (2011-2019) General Area City representing the region Average demand/year (RDC) 36000 Toledo 31000 Detroit MI Toledo OH Northwest Indiana Findlay, OH 12000 19000 Columbus, OH Mansfield, OH Zanesville, OH Columbus 9500 24000 40500 Pittsburgh PA New castle PA Morgantown WV Steubenville. OH Pittsburg 13000 18000 26500 18800 Erie PA Cleveland, OH Jamestown PA Cleveland 23500 18200 33000