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Unformatted text preview: ISyE 323 Lecture #5 Prof. Jeff Linderoth September 17, 2009 ISyE Lecture #5 Outline Outline Production Planning Example ((not) Section 3.4) General Algebraic Modeling Personnel Scheduling Yummy A Blending Problem ISyE Lecture #5 2 ISyE Lecture #5 Personnel Scheduling Outline Production Planning Example ((not) Section 3.4) Background Model Steps Final Model General Algebraic Modeling Personnel Scheduling Yummy A Blending Problem ISyE Lecture #5 3 ISyE Lecture #5 Personnel Scheduling Problem Statement I Union Airways needs to schedule customer service agents at checkin desks and gates. I A 24hour day is divided into 5 (overlapping) 8hour shifts: 1. 6:00 AM 2:00 PM 2. 8:00 AM 4:00 PM 3. 12:00 PM 8:00 PM 4. 4:00 PM 12:00 AM 5. 10:00 PM 6:00 AM I Agents pay is different for different shifts I The airline knows how many workers are required for each portion of the day. I The goal is to find the schedule of workers to cover the requirements at minimum cost. ISyE Lecture #5 4 ISyE Lecture #5 Personnel Scheduling Shifts and Requirements The requirements for each time period, the shifts that cover them, and the pay for each shift, are given by: Shift Minimum Number of Time Period 1 2 3 4 5 Agents Needed 6 AM8 AM 48 8 AM10 AM 79 10 AM12 PM 65 12 PM2 PM 87 2 PM 4 PM 64 4 PM 6 PM 73 6 PM 8 PM 82 8 PM 10 PM 43 10 PM12 AM 52 12 AM6 AM 15 Cost/day/agent $170 $160 $175 $180 $195 ISyE Lecture #5 5 ISyE Lecture #5 Personnel Scheduling Decision Variables and Objective Function I Let x j = the number of agents assigned to shift j , j = 1 ,..., 5 I Is divisibility assumption satisfied? I The objective function is given by Z = 170 x 1 + 160 x 2 + 175 x 3 + 180 x 4 + 195 x 5 . We want to minimize Z . ISyE Lecture #5 6 ISyE Lecture #5 Personnel Scheduling Functional Constraints I The number of agents on duty during each time period must be greater than or equal to the required number. I For example, from 2 PM4 PM, we need at least 64 workers. I Since shifts 2 and 3 both cover the 2 PM4 PM time slot, we know x 2 + x 3 64 I NB: these constraints come from the data table just like in previous examples if we treat the s as 1s ISyE Lecture #5 7 ISyE Lecture #5 Personnel Scheduling The LP minimize Z = 170 x 1 + 160 x 2 + 175 x 3 + 180 x 4 + 195 x 5 subject to x 1 48 (68 AM) x 1 + x 2 79 (810 AM) x 1 + x 2 65 (10 AM12 PM) x 1 + x 2 + x 3 87 (12 PM2 PM) x 2 + x 3 64 (2 PM4 PM) x 3 + x 4 73 (4 PM6 PM) x 3 + x 4 82 (6 PM8 PM) x 4 43 (8 PM10 PM) x 4 + x 5 52 (10 PM12 AM) x 5 15 (12 AM6 AM) x j j = 1 ,..., 5 Some of these constraints are redundant which are they?...
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This note was uploaded on 11/18/2009 for the course ISYE 323 taught by Professor Jeff during the Spring '09 term at University of Wisconsin Colleges Online.
 Spring '09
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