Using linear programming to simulate service engineers
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Using linear programming to simulate service engineers S Powell* London School of Economics This paper describes the use of a network ¯ow model to simulate a proposed spatial allocation of engineers to service requests. The model involves generating a pattern of demand and then determining an allocation of engineers to jobs which maximises the number of jobs immediately serviced. Within the maximum number of jobs the allocation pattern which minimises the amount of travelling is determined. The results obtained were compared with the allocation rules then in use. Keywords: linear programming; simulation; manpower planning
Introduction The client for whom this work was done is a software house which itself has a client, a service organisation, that employs engineers who repair equipment. Historically the service organisation allocates a small prede®ned geographical region to each of its service engineers. Customers make calls to a centre, which then checks in whose region the customer is and alerts the relevant engineer. The engineer travels to the job and there undertakes the servicing. The jobs are allocated on a daily basis and there is an upper limit on the number than can be allocated to an engineer for a day's work. Thus when a service request arrives it is allocated to the appropriate engineer for the next day if the number allocated to that day does not exceed the limit, otherwise to the ®rst available day in which the job limit is not exceeded. The geographical borders are rigid. Even if another customer requires attention two doors away, an engineer is not allowed to service the call if the customer falls within another engineer's region. Thus it is possible for a job to be not serviced the next day because the engineer of the area is fully occupied, while the engineer in a nearby area is underoccupied. The service organisation wanted to move to automated scheduling and had turned to the software house to provide a computer-based scheduling system. The software house believed that the service organisation would bene®t from removing the arti®cial boundaries, and that scheduling groups of engineers more ¯exibly across wider geographical borders would make more effective use of their time. *Correspondence: London School of Economics, Houghton Street, London WC2A 2AE, UK.
However the software house was unable to `prove' or otherwise convince the service organisation of this. So the software house was looking for a convincing argument, demonstration, or proof to assure its client that its beliefs were well founded. In addition it was open to suggestions about the structure of a scheduling algorithm. The aim of the software house manager was to be given the contract to develop the engineer scheduling systemÐhe considered that he was more likely to be successful if he could demonstrate to the service organisation that the current engineers could be used more ef®ciently. The author was asked to a
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