Robert Gardner Runs a Small, Local-Only Delivery Service Robert Would Like Each Truck Equally Loaded, Both in Terms

question 29

Essay

Robert Gardner runs a small, local-only delivery service. His fleet consists of three smaller panel trucks. He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers. The box weights are: 210, 160, 320, 90, 110, 70, 410, 260, 170, 240, 80 and 180 for boxes 1 through 12, respectively. Since each truck differs each truck has different load capacities as given below:
$$\begin{array} { c c c c } \text { Truck } & \text { Weight Capacity } & \text { Box Capacity } & \text { Cast per pound } \\\hline 1 & \text { 800 pounds } & 5 & \$ 0.34 \\2 & 900 \text { pounds } & 6 & \$ 0.42 \\3 & 700 \text { pounds } & 4 & \$ 0.25\end{array}$$ Robert would like each truck equally loaded, both in terms of number of boxes and in terms of total weight, while minimizing his shipping costs. Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight.
Formulate the integer goal programming problem for Robert. (Hint: objective function involves decision and deviation variables.)

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Definitions:

Net Book Value

The value of an asset after accounting for depreciation and amortization, as recorded on a company's balance sheet.

Invested Capital

Funds invested by shareholders and debt holders in a company used for carrying out its operations and projects.

External Reporting

The process of providing information about a company's financial performance to outside parties, such as investors and regulators.

Imputed Interest Rate

The calculated interest rate used in situations where no actual interest rate is specified, often for the purpose of tax calculations or financial analyses.