运筹学与供应链管理-第4讲(ppt56)-运筹学(编辑修改稿)

运筹学与供应链管理-第4讲(ppt56)-运筹学(编辑修改稿)内容摘要：

ory Control with Uncertain Demand Example 2: 01234560 2 4 6 8 10 12 14 16 18 20 22Inventory Control with Uncertain Demand Example 2: Estimate the probability that the number of copies of the Journal sold in any week. The probability that demand is 10 is estimated to be 2/52 = , and the probability that the demand is 15 is 5/52 = . Cumulative probabilities can also be estimated in a similar way. The probability that there are nine or fewer copies of the Journal sold in any week is (1 + 0 + 0 + 0 + 3 + 1 + 2 + 2 + 4 + 6) / 52 = 19 / 52 = . Inventory Control with Uncertain Demand We generally approximate the demand history using a continuous distribution. By far, the most popular distribution for inventory applications is the normal. A normal distribution is determined by two parameters: the mean and the variance 2Inventory Control with Uncertain Demand These can be estimated from a history of demand by the sample mean and the sample variance . D 2sniiDnD11 nii DDns12211Inventory Control with Uncertain Demand The normal density function is given by the formula We substitute as the estimator for and as the estimator for .     xxxf f o r 21e x p21 2D  sInventory Control with Uncertain Demand 00 2 4 6 8 10 12 14 16 18 20 2224 24 26Optimization Criterion In general, optimization in production problems means finding a control rule that achieves minimum cost. However, when demand is random, the cost incurred is itself random, and it is no longer obvious what the optimization criterion should be. Virtually all of the stochastic optimization techniques applied to inventory control assume that the goal is to minimize expected costs. The Newsboy Model (Continuous Demands) The demand is approximately normally distributed with mean and standard deviation . Each copy is purchased for 25 cents and sold for 75 cents, and he is paid 10 cents for each unsold copy by his supplier. One obvious solution is approximately 12 copies. Suppose Mac purchases a copy that he doesn39。 t sell. His outofpocket expense is 25 cents  10 cents = 15 cents. Suppose on the other hand, he is unable to meet the demand of a customer. In that case, he loses 75 cents  25 cents = 50 cents profit. The Newsboy Model (Continuous Demands) Notation: = Cost per unit of positive inventory remaining at the end of the period (known as the overage cost). = Cost per unit of unsatisfied demand. This can be thought of as a cost per unit of negative ending inventory (known as the underage cost). The demand is a continuous nonnegative random variable with density function and cumulative distribution function . The decision variable is the number of units to be purchased at the beginning of the period. ocucD xf xFQThe Newsboy Model (Continuous Demands) Determining the optimal policy: The cost function The optimal solution equation  uoucccQF*            QuQo dxxfQxcdxxfxQcQG 0The Newsboy Model (Continuous Demands) Determining the optimal policy: 02468101210 6 2 1000 200 300 400(Thousands)G(Q)OQ*QThe Newsboy Model (Continuous Demands) Example 2 (continued): Norma。