Bikes.com is a web-based company that sells bicyles on the Internet. Its distinctive feature is that...

  

Transcribed Image Text:

Bikes.com is a web-based company that sells bicyles on the Internet. Its distinctive feature is that it allows customers to customize the design when they order and then to receive quick delivery. Bikes.com gives customers choices for frame size (34, 36, 38), suspensions (standard or heavy duty), and gear speeds (5,10,15). As a result, customers can order 1 of 18 possible combinations (3 2 3) which are presented in Table 1. 2223 9 10 11 12 72 2 2222 22 13 8212 721L 6123 512 2 1 1 41215 3113 12 Model A 1 2 1 1 B C 1 Orders 4 5 0 1 7 0 4 8 13 B3LL5 1 0 Table 1: Bikes.com product portfolio 14 15 16 17 18 13 3126 3 2 3 3 3 1 4 0 1 235 22 The company shorthand refers to frame size as option A (A1 is the 34 inch model, A2 is the 36 inch model, and A3 is the 38-inch model). Similarly, the standard suspension is option B1, and the heavy-duty suspension is B2. The gear speeds are C1 (50), C2 (10) and C3 (15). Rather than stock 18 different types of bicycles, Bikes.com holds inventories of the eight major components, and then assembles the bikes once a customer order comes in. Orders are taken Mondays through Wednesdays, assemblies are done on Thursdays and shipments go out on Fridays. Thus, at the close of business on Wednesday, Bikes.com has an inventory of components and a list of orders and its task is to decide what demands to meet to maximize profit. Tables 1 and 2 describe customers orders for this week and the inventory status at the end of Wednesday. Component A1 A2 A3 B1 B2 C1 C2 C3 Inventory 59 87 93 15 97 76 54 42 Table 2: Bikes.com components inventory The profitability varies by model type, as shown in Table 3. Model 1 2 3 4 5 6 Profit 45 55 70 65 75 7 8 9 10 90 47 57 72 67 11 12 13 14 15 16 17 18 77 92 50 60 75 70 80 95 Table 3: Bikes.com product profits 1. Write a mathematical model to maximize the profit that can be achieved from this week's orders. 2. Implement this model in GAMS to obtain an optimal solution. Bikes.com is a web-based company that sells bicyles on the Internet. Its distinctive feature is that it allows customers to customize the design when they order and then to receive quick delivery. Bikes.com gives customers choices for frame size (34, 36, 38), suspensions (standard or heavy duty), and gear speeds (5,10,15). As a result, customers can order 1 of 18 possible combinations (3 2 3) which are presented in Table 1. 2223 9 10 11 12 72 2 2222 22 13 8212 721L 6123 512 2 1 1 41215 3113 12 Model A 1 2 1 1 B C 1 Orders 4 5 0 1 7 0 4 8 13 B3LL5 1 0 Table 1: Bikes.com product portfolio 14 15 16 17 18 13 3126 3 2 3 3 3 1 4 0 1 235 22 The company shorthand refers to frame size as option A (A1 is the 34 inch model, A2 is the 36 inch model, and A3 is the 38-inch model). Similarly, the standard suspension is option B1, and the heavy-duty suspension is B2. The gear speeds are C1 (50), C2 (10) and C3 (15). Rather than stock 18 different types of bicycles, Bikes.com holds inventories of the eight major components, and then assembles the bikes once a customer order comes in. Orders are taken Mondays through Wednesdays, assemblies are done on Thursdays and shipments go out on Fridays. Thus, at the close of business on Wednesday, Bikes.com has an inventory of components and a list of orders and its task is to decide what demands to meet to maximize profit. Tables 1 and 2 describe customers orders for this week and the inventory status at the end of Wednesday. Component A1 A2 A3 B1 B2 C1 C2 C3 Inventory 59 87 93 15 97 76 54 42 Table 2: Bikes.com components inventory The profitability varies by model type, as shown in Table 3. Model 1 2 3 4 5 6 Profit 45 55 70 65 75 7 8 9 10 90 47 57 72 67 11 12 13 14 15 16 17 18 77 92 50 60 75 70 80 95 Table 3: Bikes.com product profits 1. Write a mathematical model to maximize the profit that can be achieved from this week's orders. 2. Implement this model in GAMS to obtain an optimal solution.