5f p1 05f p1 f f f f f demand by hour p2 p2 p3

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Unformatted text preview: ctive: Minimize total daily labor cost = $100 F + $32 ( P1 + P2 + P3 + P4 + P5) subject to: F + P1 F + P1 0.5F + P1 0.5F + P1 F F F F F Demand by hour + P2 + P2 + P3 + P2 + P3 + P2 + P3 + P3 + P4 + P4 + P5 + P4 + P5 + P4 + P5 + P5 ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≤ 10 12 14 16 18 17 15 10 12 9:00 - 10:00 10:00 - 11:00 11:00 - 12:00 12:00 - 13:00 13:00 - 14:00 14:00 - 15:00 15:00 - 16:00 16:00 - 17:00 Available full-time tellers 19 LP Formulation for Employee Scheduling Constraints (continued): • Part-time working hours cannot exceed 50% daily required total hours, which is the sum of tellers in each hour. 4( P + P2 + P3 + P4 + P5 ) ≤ 0.50(10 + 12 + 14 + 16 + 18 + 17 + 15 + 10) 1 After simplifying, 4 P1 + 4 P2 + 4 P3 + 4 P4 + 4 P5 ≤ 56 F , P1 , P2 , P3 , P4 , P5 ≥ 0 20 Optimal Solution Employ 10 full-time tellers, and – 2 part-time tellers start at 10 A.M. – 7 part-time tellers start at 11 A.M. – 5 part-time tellers start at noon. at a total cost of $1448 per day. • There are several alternate optimal solutions. (See the spreadsheet model in worksheet “tellers” in file “Learning Kit.x...
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