please write parameters, Decision variables, Objective function and constraints for this case study.

Involved fixed costs based on the size of the warehouse and variable costs that depended on the quantity shipped SportStuff.com through the warehouse. Four potential locations for Sanjay Gupta founded SportStuff.com in 2004 with a warehouses were identified in Denver, Seattle, Atlanta, mission of supplying parents with more affordable sports and Philadelphia. Leased warehouses could be either equipment for their children. Parents complained about small (about 100,000 sq. ft.) or large (200,000 sq. ft.). having to discard expensive skates, skis, jackets, and Small Warehouses could handle a flow of up to 2 million shoes because children outgrew them rapidly. Sanjay's units per year, whereas large warehouses could handle a initial plan was for the company to purchase used equip flow of up to 4 million units per year. The current ware- ment and jackets from families and surplus equipment house in St. Louis was small. The fixed and variable from manufacturers and retailers and sell these over the costs of small and large warehouses in different loca- Internet. The idea was well received in the marketplace, tions are shown in Table 5-16. demand grew rapidly, and, by the end of 2004, the com Sanjay estimated that the inventory holding costs pany had sales of $0.8 million. By this time, a variety of at a warehouse (excluding warehouse expense) was new and used products were being sold, and the com about $600 V, where F is the number of units flowing pany received significant venture capital support. through the warehouse per year. This relationship is In June 2004, Sanjay leased part of a warehouse in based on the theoretical observation that the inventory the outskirts of St. Louis to manage the large amount of held at a facility (not across the network) is proportional product being sold. Suppliers sent their product to the to the square root of the throughput through the facility, warehouse. Customer orders were packed and shipped As a result, aggregating throughput through a few facili- by UPS from there. As demand grew, SportStuff.com ties reduces the inventory held as compared with disag- leased more space within the warehouse. By 2007, gregating throughput through many facilities. Thus, a SportStuff.com leased the entire warehouse and orders warehouse handling 1 million units per year incurred an were being shipped to customers all over the United inventory holding cost of $600,000 in the course of the States. Management divided the United States into six year. If your version of Excel has problems solving the TABLE 5-15 Regional Demand at SportStuff.com for 2007 Zone Demand in 2007 Zone Demand in 2007 Northwest 320,000 Lower Midwest 220,000 Southwest 200,000 Northeast 350,000 Upper Midwest 160,000 Southeast 175,000 TABLE 5-16 Location Seattle Denver St. Louis Fixed and Variable costs of Potential Warehouses Small Warehouse Large Warehouse Fixed Cost Variable Cost Fixed Cost Variable Cost (S/year) (S/Unit Flow) (S/year) (S/Unit Flow) 300,000 0. 20 5 00,000 0.20 250,000 0.20 420,000 0.20 220,000 0. 20 3 75,000 0.20 220,000 0. 20 3 75,000 0.20 240,000 0. 20 4 00,000 0.20 Philadelphia nonlinear objective function, use the following inventory costs: Range of 0-2 million 2-4 million 4-6 million More than 6 million Inventory Cost $250,000Y + 0.310F $530,000Y + 0.170F $678,000Y+0.133F $798,000Y 0.113 with UPS to handle all its outbound shipments. UPS charges were based on both the origin and the destina- tion of the shipment and are shown in Table 5-17. Man- agement estimated that inbound transportation costs for shipments from suppliers were likely to remain unchanged, no matter what warehouse configuration was selected If you can handle only a single linear inventory cost, you should use $475,000Y + 0.165F For each facility, Y = Tif the facility is used, 0 otherwise. SportStuff.com charged a flat fee of $3 per ship- ment sent to a customer. An average customer order con- tained four units. SportStuff.com, in turn, contracted Study Questions 1. What is the cost SportStufr.com incurs if all warehouses leased are in St. Louis? 2. What supply chain notwork configuration do you recom- mend for SportStuff.com? Why? 3. How would your recommendation change if transportation costs were twice those shown in Table 5.177 TABLE 5-17 Seattle Denver St. Louis Atlanta Philadelphia UPS Charges per Shipment (Four Units) Northwest Southwest Upper Midwest $2.00 $2.50 $3.50 $2.50 $2.50 $2.50 $3.50 $3.50 $2.50 $4.00 $4.00 $3.00 $4.50 $5.00 $3.00 Lower Midwest $4.00 $3.00 $2.50 $2.50 $3.50 Northeast $5.00 $4.00 $3.00 $3.00 $2.50 Southeast $5.50 $4.50 $3.50 $2.50 Involved fixed costs based on the size of the warehouse and variable costs that depended on the quantity shipped SportStuff.com through the warehouse. Four potential locations for Sanjay Gupta founded SportStuff.com in 2004 with a warehouses were identified in Denver, Seattle, Atlanta, mission of supplying parents with more affordable sports and Philadelphia. Leased warehouses could be either equipment for their children. Parents complained about small (about 100,000 sq. ft.) or large (200,000 sq. ft.). having to discard expensive skates, skis, jackets, and Small Warehouses could handle a flow of up to 2 million shoes because children outgrew them rapidly. Sanjay's units per year, whereas large warehouses could handle a initial plan was for the company to purchase used equip flow of up to 4 million units per year. The current ware- ment and jackets from families and surplus equipment house in St. Louis was small. The fixed and variable from manufacturers and retailers and sell these over the costs of small and large warehouses in different loca- Internet. The idea was well received in the marketplace, tions are shown in Table 5-16. demand grew rapidly, and, by the end of 2004, the com Sanjay estimated that the inventory holding costs pany had sales of $0.8 million. By this time, a variety of at a warehouse (excluding warehouse expense) was new and used products were being sold, and the com about $600 V, where F is the number of units flowing pany received significant venture capital support. through the warehouse per year. This relationship is In June 2004, Sanjay leased part of a warehouse in based on the theoretical observation that the inventory the outskirts of St. Louis to manage the large amount of held at a facility (not across the network) is proportional product being sold. Suppliers sent their product to the to the square root of the throughput through the facility, warehouse. Customer orders were packed and shipped As a result, aggregating throughput through a few facili- by UPS from there. As demand grew, SportStuff.com ties reduces the inventory held as compared with disag- leased more space within the warehouse. By 2007, gregating throughput through many facilities. Thus, a SportStuff.com leased the entire warehouse and orders warehouse handling 1 million units per year incurred an were being shipped to customers all over the United inventory holding cost of $600,000 in the course of the States. Management divided the United States into six year. If your version of Excel has problems solving the TABLE 5-15 Regional Demand at SportStuff.com for 2007 Zone Demand in 2007 Zone Demand in 2007 Northwest 320,000 Lower Midwest 220,000 Southwest 200,000 Northeast 350,000 Upper Midwest 160,000 Southeast 175,000 TABLE 5-16 Location Seattle Denver St. Louis Fixed and Variable costs of Potential Warehouses Small Warehouse Large Warehouse Fixed Cost Variable Cost Fixed Cost Variable Cost (S/year) (S/Unit Flow) (S/year) (S/Unit Flow) 300,000 0. 20 5 00,000 0.20 250,000 0.20 420,000 0.20 220,000 0. 20 3 75,000 0.20 220,000 0. 20 3 75,000 0.20 240,000 0. 20 4 00,000 0.20 Philadelphia nonlinear objective function, use the following inventory costs: Range of 0-2 million 2-4 million 4-6 million More than 6 million Inventory Cost $250,000Y + 0.310F $530,000Y + 0.170F $678,000Y+0.133F $798,000Y 0.113 with UPS to handle all its outbound shipments. UPS charges were based on both the origin and the destina- tion of the shipment and are shown in Table 5-17. Man- agement estimated that inbound transportation costs for shipments from suppliers were likely to remain unchanged, no matter what warehouse configuration was selected If you can handle only a single linear inventory cost, you should use $475,000Y + 0.165F For each facility, Y = Tif the facility is used, 0 otherwise. SportStuff.com charged a flat fee of $3 per ship- ment sent to a customer. An average customer order con- tained four units. SportStuff.com, in turn, contracted Study Questions 1. What is the cost SportStufr.com incurs if all warehouses leased are in St. Louis? 2. What supply chain notwork configuration do you recom- mend for SportStuff.com? Why? 3. How would your recommendation change if transportation costs were twice those shown in Table 5.177 TABLE 5-17 Seattle Denver St. Louis Atlanta Philadelphia UPS Charges per Shipment (Four Units) Northwest Southwest Upper Midwest $2.00 $2.50 $3.50 $2.50 $2.50 $2.50 $3.50 $3.50 $2.50 $4.00 $4.00 $3.00 $4.50 $5.00 $3.00 Lower Midwest $4.00 $3.00 $2.50 $2.50 $3.50 Northeast $5.00 $4.00 $3.00 $3.00 $2.50 Southeast $5.50 $4.50 $3.50 $2.50