Operation Research By Anitha Chandran Chitra.R Radha.R Sudhit Sethi

Question 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 the Table below. 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 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. DaysNo of full time employees required Day 1 - Monday 17 Day 2 - Tuesday 13 Day 3 - Wednesday 15 Day 4 - Thursday 19 Day 5 - Friday 14 Day 6 - Saturday 16 Day 7 - Sunday 11

Solution Decision variables: x1 - number of full time employees working from Monday to Friday x2 - number of full time employees working from Tuesday to Saturday x3 - number of full time employees working from Wednesday to Sunday x4 - number of full time employees working from Thursday to Monday x5 - number of full time employees working from Friday to Tuesday x6 - number of full time employees working from Saturday to Wednesday x7 - number of full time employees working from Sunday to Thursday

Objective Objective : To minimize the number of full-time employees that must be hired. Objective Function : Min Z = x1+ x2 + x3 + x4 + x5 + x6 + x7

Constraints Each full-time employee must work five consecutive days and then receive two days off. x1+x4+x5+x6+x7 = 17 x2+x5+x6+x7+x1 = 13 x3+x6+x7+x1+x2 = 15 x4+x7+x1+x2+x3 = 19 x1+x2+x3+x4+x5 = 14 x6+x7+x2+x3+x4 = 16 x7+x3+x4+x5+x6 = 11 Non – Negativity Constraints : x1, x2, x3, x4, x5, x6, x7>=0