At Lummins Engine Corporation, production employees work 10 hours per day, four days per week. Each...

At Lummins Engine Corporation, production employees work 10 hours per day, four days per week. Each day of the week, at least the following number of employees must be working: Monday through Friday, seven employees; Saturday and Sunday, three employees. Lummins has set the following goals, listed in order ofpriority: ■ Goal 1: Meet employee requirements with 11 workers. ■ Goal 2: The average number of weekend days off per employee should be at least 1.5 days. ■ Goal 3: The average number of consecutive days off an employee gets during the week should not exceed 2.8 days. Use goal programming to determine how to schedule Lummins employees.

Expert Solution

First solving for Goal 1

As for goal 1, there are no restriction on weekends off or consecutive offs so solving like a normal linear progaming problem with work schedule of 4 working days and 3 consecutive days -

Below is the solution we get using solver -

So goal 1 is met.

Now we can think about meeting goal 2 (note: for goal 2 we will have an additonal constraint that is number of employees to be 11) -

We will need to change the work schedule as follows so that to have weekend days off of at least 1.5 to all employees:

Monday	1	1	1	1	0	0	0
Tuesday	0	1	1	1	1	0	0
Wednesday	0	0.5	1	1	1	0.5	0
Thursday	0	0.5	1	1	1	0	0.5
Friday	1	0	0.5	1	1	0.5	0
Saturday	1	1	0	0.5	1	0	0.5
Sunday	1	1	1	0	0.5	0	0.5

solving using solver we do not get feasible solution -

Please rate my answer...!!

orchestra answered 2 years ago

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