A production department 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 (see Table). Union rules state that each full-time employee must work five consecutive days and then two days off. For example, if an employee works Monday to Friday, he/she will be off on Saturday and Sunday. Suppose that the production department wants to meet its daily requirements using only full-time employees. Formulate an LP that the production department can use to minimize the number of full time employees who must be hired. Day # of Full-Time Employees Required Monday 17 Tuesday 13 Wednesday 15 Thursday 19 Friday 14 Saturday 16 Sunday 11 a) Suppose that the number of workers needed on day i is di . Let wi be the actual number of workers on day i. Formulate an LP where the “cost” of having too many workers on day i is fi (wi – di). b) Suppose that the production department wants to minimize the maximum of the surpluses on each day (max (w1 – d1, w2 – d2,…, w7 – d7)). Formulate an LP. c) Suppose that the production department wants to ensure that at least 30% of the workers have Sunday off. Formulate a constraint for this case.
A production department 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 (see Table). Union rules state that each full-time employee must work five consecutive days and then two days off. For example, if an employee works Monday to Friday, he/she will be off on Saturday and Sunday. Suppose that the production department wants to meet its daily requirements using only full-time employees. Formulate an LP that the production department can use to minimize the number of full time employees who must be hired. Day # of Full-Time Employees Required Monday 17 Tuesday 13 Wednesday 15 Thursday 19 Friday 14 Saturday 16 Sunday 11 a) Suppose that the number of workers needed on day i is di . Let wi be the actual number of workers on day i. Formulate an LP where the “cost” of having too many workers on day i is fi (wi – di). b) Suppose that the production department wants to minimize the maximum of the surpluses on each day (max (w1 – d1, w2 – d2,…, w7 – d7)). Formulate an LP. c) Suppose that the production department wants to ensure that at least 30% of the workers have Sunday off. Formulate a constraint for this case.
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