The Transportation Model Dialog allows several variations on the simple transportation model. The check boxes Include Minimums, Include Maximums and Include Multipliers cause the Add-in to build tables that allow the entry of minimum transportation flows, maximum transportation flows, and arc gain factors respectively. The Integer Flows box, adds the requirement that the solution maintain integer flows.
The matrices for the example with arbitrary values of lower bound upper bound and gains are shown below. Lower bounds represent minimum shippments along certain routes, while upper bounds represent shipping capacities. When the gain factors are other than one, the amount shipped on a link is not the same as the amount received. The multipliers shown below represent a loss, perhaps due to spoilage.
When the shipping and receiving bounds are integer and the flow multipliers are all 1, we can be sure that the solution to the transportation problem will be integer. When this is not true, however, the flow solution may not be integer. The flow solution shown in the green area is certainly not integer. The Integer check box is provided to add the constraint that the flows be integer. The integer problem is much more challenging for the computer than when integrality is required. The Excel Solver will take many minutes to find an integer solution, if one exists, while the solution algorithm only requires a second or two when integrality is not required.