You are in charge of transportation of a product for company A. The company has three production facilities across the state of Georgia, and two cross-docks that receive product from each of the production facilities and then distribute it to three retail stores. Every production facility can send their product to either cross-dock, but cross-dock 1 can only satisfy the demand of retailers 1 and 2, while cross-dock 2 can satisfy the demand of retailers 2 and 3. Table 1 shows the production capacity of each production facility over the planning horizon of four weeks, and Table 2 shows the demand of each retailer for the planning horizon. Retailers demand must be met on time without backlogging.

The figure below shows the layout of the companys network:

Product is sent by truck between facilities with each pair of facilities having different capacities and transportation cost per unit of product. Table 3 show the capacity and cost for each facility pair in the network; these are the same for each week in the planning horizon.

Model this problem as a minimum cost network flow problem. In your network, nodes should represent facility-week combinations so you can track flows at different points in the horizon.

Period Facility Facility 4. 2 4 P1500 420 470 450 P2850 780 740 820 P3400 450 430 480 R1 420 490 420 470 R2710 820 720 790 R3620 340 500 490 Table 1: Production Capacity Table 2: Retailer Demand P1 R1 CD 1 P2 R2 CD 2 P3 R3 Capacity Cost Capacity Cost 500 280 600 300 650320 650 450 Arc Arc (P1,CD1) 400 250(CD1, R1) (P1,CD2)350 300(CD1, R2) (P2,CD1) 700 400(CD2, R2) (P2,CD2) 750 350(CD2, R3) (P3,CD1) 370 320 (P3,CD2) 400350 Table 3: Caption