Formulate an optimization problem to help the company find

Reference no: EM13550426

Three parallel rural routes connect two cities A and B. Traffic on these routes mainly consists of heavy trucks for a logging company, and passenger vehicle flow can be neglected. The performance functions of these three routes are: t1=50+0.2v1, t2=80+0.1v2, t3=120 + 0.05v3 t1, t2, t3 and are travel times in minutes; v1, v2, v3 are flows in number of trucks per day. There is a bridge along route 2. The structural design of the bridge allows a maximum of 1000 trucks per day. However, the bridge has been deteriorating in recent years due to the lack of proper maintenance. At the beginning of each logging season, the company will assess the condition of the bridge to determine the maximum trucks per day the bridge can safely handle. This season, the company discovers that the bridge can only handle 400 trucks per day. The company also estimates that it will generate a demand of 1500 trucks per day between the two cities in this logging season. The operating cost of each truck is $2 per minute.

1. Formulate an optimization problem to help the company find a routing strategy for this season in order to reduce its transportation operating cost.

2. Solve the problem and report the number of trucks on each route and the total operating cost of the logging company.

3. What is the loss in truck operating cost for the logging company compared to when the bridge was at its design loading capacity?

4. Derive the KKT condition of the problem formulated in part 1.

Reference no: EM13550426

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