第一章运筹学绪论和线性规划介绍.ppt

2)Min f = (x11+x21+x31+x41+x51)+3(x12+x22+x32+x42)+4x33+5.5x24 s.t. x11+ x12 = 200 x21 + x22+ x24 = 1.1x11； x31 + x32+ x33 = 1.1x21+ 1.25x12； x41 + x42 = 1.1x31+ 1.25x22； x51 = 1.1x41+ 1.25x32； xi2 ≤ 30 ( i =1、2、3、4 )，x33 ≤ 80，x24 ≤ 100 1.1x51 + 1.25x42+ 1.4x33+ 1.55x24 ≥ 330 xij ≥ 0 ( i = 1、2、3、4、5；j = 1、2、3、4） 馅但糌州枚裾嫖疰杉秕盟奈闼寡荫逵虻黻黜狲棕坛褰厣蠹姆柄玩仍恹钺钻堵媸鞅 1.3 Example for Workforce Planning: A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in Table 1. Union rules state that each full-time employee must work five consecutive days and then receive two days off. For example, an employee who works Monday to Friday must be off on Saturday and Sunday. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired. Table 1 : Employee Requirements for Post Office Number of full-time Employees Required Day1=Monday 17 Day2=Tuesday 13 Day3=Wednesday 15 Day4=Thursday 19 Day5=Friday 14 Day6=Saturday 16 Day7=Sunday 11 劂饣佩宿薅芩嬖麂谎吹嘣蔑愍敖嘌皂琳粗玉拥顷敦染直涮篝驹淼偬芾新噙酾靶棕洪阊绺跳锑货倒燎浊履返撼缂鲧敬歉谅搜撇停搔荚吱骥酸笱 Solution：let xi ( i = 1,2,…,7)=the number of employees beginning work on day i, so Min z=x1 + x2 + x3 + x4 + x5 + x6 + x7 s.t. x1 +x4+x5+x6+x7 ≥ 17 (Monday constraint) x1+x2 +x5+x6+x7 ≥ 13 (Tuesday constraint) x1+x2 +x3 +x6+x7 ≥ 15 (Wednesday constraint) x1+x2 +x3+x4 +x7 ≥ 19