Static workforce scheduling problem Paper production company SE 303 Lab Static workforce scheduling problem Paper production company
Static Workforce Scheduling Number of full time employees on different days of the week. Each employee must work five consecutive days and then receive two days off. The schedule must meet the requirements by minimizing the total number of full time employees.
Solution LP Formulation: Min. z = x1+ x2 + x3 + x4 + x5 + x6 + x7 subject to x1 + x4 + x5 + x6 + x7 ³ 17 x1+ x2 + x5 + x6 + x7 ³ 13 x1+ x2 + x3 + x6 + x7 ³ 15 x1+ x2 + x3 + x4 + x7 ³ 19 x1+ x2 + x3 + x4 + x5 ³ 14 x2 + x3 + x4 + x5 + x6 ³ 16 x3 + x4 + x5 + x6 + x7 ³ 11 x1, x2, x3, x4, x5, x6, x7 ³ 0
Paper Company Different paper products Production constraints Packaging Availability
Paper Products Three basic products: pads of paper, 5-packs of paper, and 20-packs of paper. The pad of paper consists of single pad of 25 sheets of lined paper. The 5-pack consists of 5 pads of paper, together with a small notebook. The 20-pack of paper consists of 20 pads of paper, together with a large notebook.
Production Constraints The small and large notebooks are not sold separately. Production of each pad of paper requires 1 minute of paper-machine time, 1 minute of supervisory time, and $0.10 in direct costs. Production of each small notebook takes 2 minutes of paper-machine time, 45 seconds of supervisory time, and $0.20 in direct cost. Production of each large notebook takes 3 minutes of paper machine time, 30 seconds of supervisory time and $0.30 in direct costs.
Packaging and Availability Constraints To package the 5-pack takes 1 minute of packager’s time and 1 minute of supervisory time. To package 20-pack takes 3 minutes of packager’s time and 2 minutes of supervisory time. The amount of available paper-machine time, supervisory time, and packager’s time are constants b1, b2, and b3, respectively.
Costs Any of the three products can be sold to retailers in any quantity at the prices $0.30, $1.60, and $7.00, respectively.
Solution