江西财经大学 2004~2005学年第一学期期末考试试卷 试卷代码:03275A卷 课时:80 课程名称:运筹学Ⅱ(英) 适用对象:管理科学专业 1. Fill in the blanks (10 points) (a)If the objective value is maximum sales revenue, then in dynamic programming, the basic f(Sk=max(v(Sk, xg)+R (Ski)) equation IS MM(Sn+))=0 (b) The dynamic programming is divided into two types, they are: deterministic dynamic programming and probabilistic dynamic programming. (c) The integer programming is divided into three types, they are pure integer programming. mixed integer programming and binary integer programming. ( d )For M/M/I model, the expected number of customers in queueing system isL=d The expected queue length is L (-2) The waiting time in system for each individual customer is w The waiting time in queue for each individual customer is w (-2) 2. A company is planning its advertising strategy for next year for its three major products Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice-president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales (in appropriate units) for the different advertising expenditures Advertising expenditure Product 7 10 2481 36935 Use dynamic programming to solve this problem. (15 points)1 江西财经大学 2004～2005 学年第一学期期末考试试卷 试卷代码：03275A 卷 课时：80 课程名称：运筹学Ⅱ（英） 适用对象：管理科学专业 1. Fill in the blanks. (10 points) (a) If the objective value is maximum sales revenue, then in dynamic programming, the basic equation is ⎪⎩ ⎪ ⎨ ⎧ = = + + + + + ∈ ( ) 0 ( ) { ( , ) ( )} 1 1 max 1 1 n n k k k k k x D k k f S f S v s x f S k k (b) The dynamic programming is divided into two types, they are: deterministic dynamic programming and probabilistic dynamic programming. (c) The integer programming is divided into three types, they are :pure integer programming, mixed integer programming and binary integer programming. (d) For M/M/1 model, the expected number of customers in queueing system is μ λ λ − L = The expected queue length is ( ) 2 μ μ λ λ − Lq = The waiting time in system for each individual customer is μ − λ = 1 W The waiting time in queue for each individual customer is μ(μ λ) λ − Wq = 2. A company is planning its advertising strategy for next year for its three major products. Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice-president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales (in appropriate units) for the different advertising expenditures: Product Advertising expenditure 1 2 3 1 2 3 4 7 10 14 17 4 8 11 14 6 9 13 15 Use dynamic programming to solve this problem. (15 points)