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Home Store is considering to build distribution centers (DCs) in five potential cities, Jacksonville, Atlanta, Columbia, Birmingham, and Gainesville, to serve four markets, NC, SC,

Home Store is considering to build distribution centers (DCs) in five potential cities, Jacksonville, Atlanta, Columbia, Birmingham, and Gainesville, to serve four markets, NC, SC, GA, and FL. The annual fixed costs of running each DC at the four potential regions are $700,000, $800,000, $650,000, $630,000, and $750, 000, respectively. Each DC can handle up to 30,000 tons of flow. Transportation costs per unit from each DC to each demand region and the annual demand of each market are given in the following table. Costs are given in terms of $1,000. Demands are given in terms of 1,000 tons. Home Store wants to minimize the total costs. Assume that Home Store plans to meet all demand.

Demand Regions Fixed Costs

NC SC GA FL

Jacksonville 95 90 89 88 700

Atlanta 90 85 80 85 800

Columbia 88 82 88 100 650

Birmingham 95 93 90 105 630

Gainsville 102 91 89 80 750

Demand 13 12 14 16

(a) Home Store wants to design a supply chain network in which each market is supplied by one distribution center, referred to as single-sourcing strategy. In practice, companies sometimes prefer this strategy because it lowers the complexity of coordinating the network and requires less investment in flexibility. Write down a network configuration model in the mathematical form. Detail the decision variables with a clear description of each, the objective function and the constraints. You are not required to use Excel to solve it. [Hints: You need to decide which DC to open and which DC to serve which market.]

(b) Because of increasing economic turbulences and other types of disruptions, Home Store wants to adopt a dual-sourcing strategy. That is, in addition to a dedicated distribution center, each market is also assigned a back-up distribution center. How does your model in (a) change? For simplicity, we assume that the probability of using a back-up distribution center is 10% (which is the same for all back-up DCs).

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