Truck Leasing Problem Essay

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Winnie Cheng
ESE 204
Truck Leasing Strategy

Reep Construction recently won a contract for the excavation and site preparation of a new rest area on the Pennsylvania Turnpike. The main problem is that the firm wants to minimize cost of meeting the monthly trucking requirements for this project but also follows a no-layoff policy.

The constraints of the problem are as follows:

The job requires four months to complete, with 10, 12, 14 and 8 trucks needed in months 1 through 4, respectively.

The firm signed a long-term lease with PennState Leasing last year for trucks where one of these trucks will be available for use on the new project in month 1, two for month 2, three for month 3 and one for month 4. The long-term leasing
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This plan would lead to a minimal cost of $151,660.

The costs are split up amongst the type of trucks in this way: Type of Truck | Cost | Long-term trucks (7) | 2000*7 = 14000 | S13 (3) | 11675*3 = 35025 | S14 (6) | 14160*6 = 84960 | S23 (1) | 11675 | S31 (1) | 6000 | Total Cost | 151660 |

The reduced cost for S11, S41, S12, S22, and S32 is above zero because in the solution these values are zero, so increasing the “final value” of these trucks or leasing one of any of these trucks would lead to an increase in cost of 3515, 3515, 3725, 210 and 915, respectively. This also means that the cost would have to decrease by those respective numbers in order for the optimal solution to include those variables.

The shadow prices for each of the constraints show how much the objective function would get better or worse by if the right hand side was increased by one unit. For instance if the total number of trucks needed for month 1 increased from 10 to 11, the cost would get better by $2485 or decrease by $2485 (since the shadow price is the negative of the dual price). The positive dual values for the long-term trucks show that using the long-term trucks instead of the short-term trucks actually
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