Its a pretty straightforward case - not traps - which require not much more than the application of the formulae and some common sense for the interpretation of the results.
CASE: Some applications of the transportation and transshipment models have nothing to do with the transportation of goods. An interesting class of problem that can be solved by this method involves production and inventory scheduling. We will illustrate this type of application by considering the problem faced by Contois Carpets Inc.
When CC installs new carpeting, one of the services offered is free removal of the existing carpet. The Steve Contois, the owner has observed that much of the carpeting removed is in good shape; he feels that if the carpet were cleaned and sanitized, it could be resold. As a result, Contois has invested in equipment that can be used to clean and sanitize the carpet prior to reselling it.
Contois would now like to develop a production and inventory schedule for the cleaning and sanitizing operation that will minimize the total production and operation cost for the next four quarters. Production capacities will be 600, 300, 500 and 400 yards. Production cost will vary by quarter. They are expected to be 2, 5, 3, and 3 $/yard. Demand is foreseen as 400, 500, 400 and 400 yards. The cost to carry inventory from one quarter to the next is a constant $ 0.25/yard.
QUESTION 1: Draw a network representation of the Contois Carpet problem. Hint: use four nodes each for the production and the demand during the four quarters. Connect them with arcs representing the flow from sources to sinks. "Transportation" along those arcs involves the corresponding production and carrying costs.
QUESTION: Solve for the optimal solution using the transportation algorithm
Graphic solution and explanations are provided.