Using mixed integer programming to design employee rosters
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Using mixed integer programming to design employee rosters N Beaumont Monash University, Australia This paper describes the problem of rostering a workforce so as to optimise a weighted sum of three criteria while satisfying several constraints. The rostering entailed deciding on a pattern of working days and breaks over a period of (typically) one year. Demand had to meet 24 hours each day and 365 days each year. It was possible to formulate this problem as a mixed integer program and, with some experimentation, solve it using an `off the shelf' linear programming package. The results obtained are compared with rosters the client now uses. Keywords: manpower planning; mixed integer programming; workforce scheduling
Introduction The client for which this research was done employed staff who drove to and serviced customers. The demand varied with day of week and (especially) time of day, and had to be met 24 hours each day and 365 days each year. Weekends and public holidays had no special status and there was no discernible seasonal variation in demand. Queuing was undesirable albeit inevitable but its cost had not been quanti®ed by the client. The identity of the client and the kind of work done is con®dential but analogous activities are repair people travelling between and servicing faulty lifts and police travelling between and dealing with incidents. The workforce comprised the client's own employees (paid by the week) and self employed contractors who were available on call and paid a ®xed amount per call. Only the former were rostered. Employees got no extra pay for working on weekends or public holidays. The `cycle' problem (as this rostering problem was called by client) required ®nding a pattern of days off (known as rostered days off or RDOs) and working days (days on) which satis®ed the criteria agreed between the employees and management and had the desirable features (see Formulation). The system had to be able to design cycles of any length. The most commonly used cycle comprised 48 working weeks and 4 weeks leave. It was assumed that one four week holiday would be taken but the cycles generated allowed this to be split into separate 2 week holidays thus making leave arrangements more ¯exible. Staff cycle
Correspondence: Dr N Beaumont, Faculty of Business and Economics, Monash University, PO Box 197, Caul®eld East, Victoria 3124, Australia. E-mail: [email protected]
through the cycle, moving from week 48 to week 1 (usually after annual leave). For example, if 104 people were employed, then two staff would be working each week of a 48 week cycle so 96 would be working and 8 would be on leave. It was possible to use different cycles simultaneously. At one time 48, 20 and 1 week cycles were being used (the last means that the employee works the same days each week) but management wanted to move to a single cycle. It is possible for two different cycles of the same length to be used simultaneously. Ne
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