Competitive analysis for dynamic multiperiod uncapacitated routing problems

We study a dynamic multiperiod routing problem where, at the beginning of each time period, a set of orders arrive that have to be fulfilled either that time period or the next. Thus, in each time period there are customers that have to be served and customers whose service may be postponed. Once it has been decided which customers to serve, an optimal route is constructed and executed. The objective of the problem is to minimize the total distance traveled during the planning horizon. Deciding which customers to serve in a time period is done on the basis of incomplete information, analyzing simultaneously customers in two consecutive periods. No know ' ledge is available about customers requiring service in future time periods. We introduce simple algorithms, ones which naturally arise in practice, and analyze these algorithms by studying their competitive ratio. (c) 2007 Wiley Periodicals, Inc.