Question:
Alberta Wheat Pool (AWP, now part of Agricore United) sells chemicals and seeds to Alberta farmers and buys their grains. The chemicals are sold at several elevators, which are located near the farms. Before the 1990s, each elevator manager (approximately 300) independently made decisions about the amount of chemicals needed during the coming year. Because the elevator manager was evaluated only based on sales, he ordered the maximum probable amount. Excess chemicals were transported back to a heated regional warehouse. in the early 1990s, AWP changed the performance measure of elevator managers in order to cut the cost of excess transportation and holding cost over the winter. A position was created: Coordinator of Regional Finance and Accounting to assist with coordination across° levators. A tool used was the single-period inventory model, which was to assist elevator managers make better decisions. To illustrate, consider the ordering of a particular herbicide by a specific elevator. Each unit weighs 50 kg. The selling price is $56.93 per unit, and the purchase cost (including the transportation cost) is $45.54. Any excess herbicide is transported to the Calgary Warehouse at the cost of $1.09 per unit. The holding cost rate is 10 percent of unit cost per year, charged only for half a year (approximate length of winter). It is estimated that 10 percent of shortage will be lost. The rest will incur $2.19 per unit in expediting cost from the Calgary warehouse. The elevator manager estimates that the demand for this herbicide can take values 100, 400, and 1,500 units with probabilities of .1, .5, and .4, respectively. What is the best order quantity?