HOMEWORK # 8: INTEGER LP. BINARY VARIABLES
The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck.
The company has recently contracted to supply gasoline distributors in southern Ohio, and
it has a $800,000 available to spend on the necessary expansion of its fleet of gasoline tank
trucks. Three models of gasoline tank trucks are available.
The company estimates that the monthly demand for the region will be 550,000 gallons of
gasoline. Because of the size and speed difference of the trucks, the number of deliveries or
round trips possible per month for each truck model will vary. Trip capacities are estimated
at 15 trips per month for the Super Tanker, 20 trips per month for the Regular Line, and 25
trips per month for the Econo-Tanker. Based on maintenance and driver availability, the firm
does not want to add more than 15 new vehicles to its fleet. In addition, the company has
decided to purchase at least three of the new Econo-Tankers for use on short-run, low demand
routes. As a final constraint, the company does not want more than half the new models to
Formulate a mathematical model to solve the problem assuming that the company wishes
to satisfy the gasoline demand with a minimum monthly operating cost.
Solve the problem in EXCEL.
Suppose that the demand was 480,000 gallons instead. Change the EXCEL values to find
the new solution. Note that, if you got the right answer, the number of ST and RL required
to minimize the operation costs is not an integer amount. Try to use rounding to find the best
feasible solution. Which of the four alternatives (round up/down each of the two non-integer
solutions) are feasible? Which is the best?
Use EXCEL to find the optimal integer solution. Discuss this new solution.
Spencer Enterprises is attempting to choose among a series of new investment alternatives.
The potential investment alternatives, the net present value of the future stream of returns,
the capital requirements, and the available capital funds over the next 3 years are summarized