Design a delivery plan that minimizes cost

Status: Closed
Prize: $25
Entries Received: 7
Winner: vrts

Winner

Contest Brief

Our firm delivers goods to 4 towns, and we need a delivery plan which minimizes the total delivery costs. In this plan, we need a delivery route that starts from our headquarter town and returns to it after reaching all 4 towns.

For privacy reason, we will not give the actual names of the towns. For this project, we call our headquarter town H, and the other 4 destination towns A, B, C, and D. We need a delivery plan that shows how we should delivery starting from H and go to all the five towns (A, B, C, D) and at last return to H. For example, a possible delivery plan can be H -> A -> B -> C -> D -> H, which means we first leave the Headquarter and go to A, and then leave A and go to B, and then leave B and go to C, and then leave C and go to D, and at last leave D and return to the Headquarter.

We don't know exactly the delivery costs, but we have data on them in previous months (shown below). The data below mean, for example, the first row means the delivery cost from Headquarter (H) to town A was $100 in last December, was $120 in last November, and was $115 in last October. We need a delivery plan for the coming February but we don't know what the costs in February will be. So please use the information provided below to make some prediction for the costs in February and then design a delivery plan for us. We want a delivery plan that has a low cost in total.

From H to A (from A to H the same): $100 (December), $120 (November), $115 (October)
From H to B (from B to H the same): $80 (December), $90 (November), $100 (October)
From H to C (from C to H the same): $50 (December), $45 (November), $60 (October)
From H to D (from D to H the same): $130 (December), $120 (November), $110 (October)
From A to B (from B to A the same): $50 (December), $70 (November), $100 (October)
From A to C (from C to A the same): $80 (December), $105 (November), $95 (October)
From A to D (from D to A the same): $150 (December), $200 (November), $165 (October)
From B to C (from C to B the same): $70 (December), $70 (November), $75 (October)
From B to D (from D to B the same): $200 (December), $160 (November), $185 (October)
From C to D (from D to C the same): $60 (December), $70 (November), $55 (October)
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Due to some schedule conflict, we will probably not be responding to the clarification board while the project is open, but we will select the best plan when the contest is closed. Please submit a pdf file that describes the delivery plan and also the calculated total cost.