江西财经大学 2005~2006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)In dynamic programming problem, when stage evaluation index is probability, then the f(Sk)=opt Iv(Sk, xk) fk+(Sk+)) recursive relationship is xk∈D Un+ (Sn+1)=1 (b) The key point of probabilistic dynamic programming differs from deterministic dynamic programming is the state at the next stage is not completely determined by the state and policy decision at the current (c)For non-linear programming, the local optimal solution is not generally a global optimal solution, but it Is true for convex programming (d) The model M/M/I means that in a queueing system, all interarrival times are distributed according to an exponential distribution, and all service times are distributed according to another exponential distribution and the number of servers is 1 (e) The birth-and-death equation for the following graph is An-P-+umPm=(+u)P λn-2 2 1 n n+1 u n- 2. Three Or teams adopt different methods to study a scientific research project. The probability of failure is 0.40, 0.60, 0.80 respectively. To decrease the probability of all three teams defeated, two scientists are allocated to these research teams, and after that, the failure probability of each teams is listed in following table Allocated scientists OR Team Team 2 ean 0 0.40 0.60 0.80 0.20 0.40 2 0.15 dynamic programming to solving this problem, the objective is to minimize the total failure probability of three teams (15 points Solution: Using network method to solving this problem, the network graph is1 江西财经大学 2005～2006 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) In dynamic programming problem, when stage evaluation index is probability, then the recursive relationship is ⎪⎩ ⎪ ⎨ ⎧ = = ⋅ + + + + ∈ ( ) 1 ( ) { ( , ) ( )} 1 1 1 1 n n k k k k k x D k k f S f S opt v s x f S k k (b) The key point of probabilistic dynamic programming differs from deterministic dynamic programming is the state at the next stage is not completely determined by the state and policy decision at the current stage. (c) For non-linear programming, the local optimal solution is not generally a global optimal solution, but it is true for convex programming. (d) The model M/M/1 means that in a queueing system, all interarrival times are distributed according to an exponential distribution, and all service times are distributed according to another exponential distribution, and the number of servers is 1. (e) The birth-and-death equation for the following graph is n Pn n Pn n n Pn ( ) λ −1 −1 + μ +1 +1 = λ + μ 2. Three OR teams adopt different methods to study a scientific research project. The probability of failure is 0.40，0.60，0.80 respectively. To decrease the probability of all three teams defeated, two scientists are allocated to these research teams, and after that, the failure probability of each teams is listed in following table Allocated scientists OR Team Team 1 Team 2 Team 3 0 0．40 0．60 0．80 1 0．20 0．40 0．50 2 0．15 0．20 0．30 Using dynamic programming to solving this problem, the objective is to minimize the total failure probability of three teams。（15 points）。 Solution: Using network method to solving this problem, the network graph is n-2 n-1 n n+1 λn-2 μn-1 λn-1 λn μn μn+1