运筹学作业题整理解决方案.doc

运 筹 学 作 业 整 理 1. 公交车调度安排 某市欲对其公交车的投放数量进行优化。通过调查发现，所需的最少公交车数随一天中的时间不同而变化，而且所需的最少公交车数在若干连续的4小时内可以被近似地看做一个常数，时间段与所需公交车数的关系如图1所示。为了进行日常维修，每辆公交车一天只能连续运行8小时。 图1 一天内不同时间段所需公交车数 请确定每一班运行公交车的数量，以满足最小需求约束，且使所运行的公交车总数最少。 2. Personnel Scheduling One AIR Company is adding more flights to and from its hub airport, and so it needs to hire additional customer service agents. However, it is not clear just how many more should be hired. Management recognizes the need for cost control while also consistently providing a satisfactory level of service to customers. Therefore, an OR team is studying how to scheduling the agents to provide satisfactory service with the smallest personnel cost. Based on the new schedule of flights, an analysis has been made of the minimum number of customer service agents that need to be on duty at different times of the day to provide a satisfactory level of service. The right most column of the flowing table shows the number agents needs for the time periods given in the first column. The other entries in this table reflect one of the provisions in the company’s current contract with the union that the represents the customer service agents. The provision is that each agent works an 8-hour shift 5 days per week. The five authorized eight-hour shifts are Shift 1: 6:00 AM to 2:00 PM Shift 2: 8:00 AM to 4:00 PM Shift 3: Noon to 8:00 PM Shift 4: 4:00 PM to midnight Shift 5: 10:00 PM to 6:00 AM. How many agents should be assigned to each shift? Please set up a LP model and solve it. 3. 已知某工厂计划生产I，II，III三种产品，各产品需要在A，B，C设备上加工，有关数据见表4-24。 表4-24 产品 设备IIIIII设备有效台时(月)A8210300B1058400C21310420单位产品利润(千元)322.9 请回答： （1）如何发挥设备能力，使生产盈利最大？ （2）若为了增加产量，可借用其他工厂的设备B，每月可借用60台时，租金为1.8万???，是否划算？ （3）若另有两种新产品IV，V，其中IV需用A设备12台时，B设备5台时，C设备10台时，单位产品盈利2.1千元；新产品V需用A设备4台时，B设备4台时，C设备12台时，单位产品盈利1.87千元。且A，B，C设备台时不增加，生产这两种新产品是否划算？ （4）对产品工艺重新进行设计，改进构造。改进后生产每件产品I，需用A设备9台时，B设备12台时，C设备4台时，单位产品盈利4.5千元，这对原计划有何影响？ 4.求下述线性规划问题目标函数的上界和下界。 5. 下表为用单纯形法计算时某一步的表格，已知该线性规