Question 1: (50 points)

While the shipping cost may be lower between certain plants and distribution centers, Meko has established shipping routes between every plant and every warehouse. This is in case of unforeseen problems such as a forced shutdown at a plant, unanticipated swings in regional demands, or poor weather along some routes.

From-To	Ha Noi	Da Nang	HCMC	Can Tho
Hai Duong	250	420	380	280
Dong Nai	1280	990	1440	1520
Binh Duong	1550	1420	1660	1730

Table 1 - Shipping Costs per 1000 units in $

Plant	Anticipated Production (1000s)
Hai Duong	45
Dong Nai	120
Binh Duong	95

Table 2 - The production quantities at the factories in the next month (in thousands of units)

Warehouse	Shipment quantity (1000s)
Ha Noi	80
Da Nang	78
HCMC	47
Can Tho	55

Table 3 - The amounts shipped to each warehouse

The goal is to determine a pattern of shipping that minimizes the total transportation cost from plants to warehouses.

1. Develop mathematical model for this case (with Index Set, Parameters, Decision Variables, Objective Function & Constraint set).
2. Use optimization tools (e.g., Excel Solver/CPLEX/Lingo) to find the optimal pattern of shipping that minimize the total transportation cost from plants to warehouses (an Excel file or CPLEX/Lingo code should be included).
3. From above optimal shipping pattern, conclude the minimized total transportation cost.

• Answer: