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copied!<p>OK - even though you have an answer, let me take a shot. </p> <p>Let's take the general problem: 7 days x 3 shifts = 21 different shifts to fill There are 7 possible employee schedules expressed as days on (1) & days off (0)</p> <p>MTWTFSS 0011111 1001111 1100111 1110011 1111001 1111100 0111110</p> <p>We want to minimize the number of scheduled employees that matches the number of required hours. </p> <p>I have a matrix of number of employees of each type per shift and that number is an integer variable. My optimization model is:</p> <p>Min (number of employees)</p> <p>Subject to: sum of (# of emp sched * employee schedule) <strong>=</strong> staff required for each shift</p> <p>and </p> <p>number of employees scheduled is integer </p> <p>You can change the = sign in the first constraint to a >=. Then you'll get a feasible solution with extra staff. You can solve this in Excel with the basic SOLVER addin. </p> <p>Let's say I need four employees for each day on a shift but I'm willing to tolerate extra staff. </p> <p>A solution using the schedules above is: </p> <p>Number of staff by schedule type: 0,2,0,2,0,2,0</p> <p>Schedule types 0011111,1001111,1100111,1110011,1111001,1111100,0111110</p> <p>(In other words 2 with schedules 1001111, 2 with schedules 1111001, and 2 more with schedules 1111100)</p> <p>This results in one day (Monday) with two extra staff and 4 employees on all the other days. </p> <p>Of course, this isn't a unique solution. There are at least 6 other solutions with two extra staff members. Constraint programming would be a better and much faster approach since there will often be many feasible schedules.</p>

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