A national grain trader procures wheat in standard bags of 50 kg from several farmers and sends the wheat bags to different retail outlets.

The supply from the different farmers are given in the following table:

Farmer Supply (bags)

FT 1 100 FT 2 150 FT 3 200 FT 4 125 FT 5 145 The demand of each retail outlets is:

Retailer Demand (bags)

RT 1 90 RT 2 135 RT 3 170 RT 4 190 RT 5 135 Wheat bags are cross-docked from the inbound truck to outbound truck and not stored in the traders’ facilities. Unloading and loading of the bags depend on the inbound and outbound truck size; thus, some trucks require more time than others. The following table shows the labor minutes needed to unload a bag from an inbound truck and load the bag on the outbound truck.
Truck to Retailer (time, in minutes)
Truck from Farmer RT 1 RT 2 RT 3 RT 4 RT 5 FT 1 3 4 4 4 4 FT 2 4 3 4 4 4 FT 3 4 4 3 4 3 FT 4 3 4 4 3 4 FT 5 4 5 4 4 3 Determine the optimal unloading–loading pattern that will minimize the total labor minutes used using computer.