5chapter5-4文档.ppt

* 5.4 Inventory Model:Gasoline and Consumer Demand * Suppose you are asked to determine how often and how much gasoline should be delivered to the various stations. Each time gasoline is delivered, a cost of d dollars is incurred, which is in addition to the cost of gasoline and is independent of the amount delivered. We assume that, in the short run, the demand and price of gasoline are constant for each station, yielding a constant total revenue as long as the station does not run out of gasoline. * Because total profit is total revenue minus total cost, and total revenue is constant by assumption, total profit can be maximized by minimizing total cost. Thus, we identify the following problem: Minimize the average daily cost of delivering and storing sufficient gasoline at each station to meet consumer demand. * After discussing the relative importance of the various factors determining the average daily cost, we develop the following model: average daily cost = f(storage costs, delivery costs, demand rate). It is reasonable to assume the cost per unit stored would be constant over the range of values under consideration. Similarly, the delivery cost is assumed constant per delivery, independent of the amount delivered, over the range of values under consideration. * We will construct in Chapter 12 an analytic model for the average daily cost and use it to compute an optimal time between deliveries and an optimal delivery quantity: where T * = optimal time between deliveries in days; Q * = optimal delivery quantity of gasoline in gallons; r = demand rate in gallons per day; d = delivery cost in dollars per delivery; s = storage cost per gallon per day. * The derivation of the formula The store costs = Q = rT, the total costs = the average cost per gallon where = is valid when that is and * Suppose we decide to check our submodel for constant demand rate by inspecting the sales for the past 1000 days at a