----------------------------------------------------------------------------- A v v i s o d i S e m i n a r i o ----------------------------------------------------------------------------- Lunedì 15 Dicembre, ore 12am ----------------------------------------------------------------------------- Stanza 34 Dipartimento di Scienze Statistiche Sapienza Università di Roma JOERG KALCSICS (Institute of Operations Research, Karlsruhe Institute of Technology) terrà un seminario dal titolo ON SALES & SERVICE DISTRICTING PROBLEMS tutti gli interessati sono invitati a partecipare. ----------------------------------------------------------------------------- Maggiori informazioni sui seminari presso il DSS sono consultabili a quest'indirizzo: http://goo.gl/Y6OQYm Saluti Pierpaolo Brutti --- ABSTRACT In sales districting, the task is to assign a given set of (prospective) customer accounts, each with a fixed market potential, to the individual members of the sales force such that each customer has a unique representative and each sales person faces equitable workload and has an equal income opportunity in terms of incentive pay, i.e., the districts should be balanced. Two other important planning criteria in sales districting are travel distances and clearly defined geographic areas of responsibility. The latter criterion is desired to avoid competition among the sales force and is typically termed as contiguity. Concerning travel distances, if a sales person visits each customer every day, then the travel time is proportional to the length of a TSP tour. However, the workload of districts is usually balanced over 2-4 weeks and some customers may have to be visited only once during this time whereas others require weekly service. Moreover, customers may have time windows, tours may include overnight stays, and so on, which makes the actual computation of the travel times impossible for large problems instances. Therefore, districting uses the concept of compactness as a proxy for travel distances. A district is said to be geographically compact if it is round-shaped and undistorted. The hope is that compact districts result in smaller travel times on a day-to-day basis than non-compact districts. A similar setting is encountered in service districting. In sales & service districting, customers are predominantly represented as points and although there exists a large body of literature, there is no consensus on a common compactness measure or suitable approaches to model contiguity of point sets. For example, all compactness measures are based on distances either between the center of a district and its basic units or between pairs of basic units of the same district. But even if they follow the same idea, the resulting districts may look considerably different. In this talk, we want to give an overview of different approaches to measure compactness and assess contiguity, and discuss their strengths and weaknesses when applied to practical problems. Moreover, we present a mathematical formulation to solve the districting problem optimally as well as an efficient geometric algorithm that is capable of coping with large practical problems.