A note on solutions to the maximal expected covering location problem

Abstract

The maximal expected covering location problem (MEXCLP) and its adjusted counterpart (AMEXCLP) compute expected coverage arising only from unqueued calls, whereas the interactive use of the hypercube queueing model (HQM) considers both unqueued and queued calls in this computation. In this note we show that the three models are not strictly comparable because of the structural differences in their objective functions and that, when using HQM, it is important to state clearly the factor being used to express traveling time in terms of service time units. Scope and purpose The maximal expected covering location problem (MEXCLP) addresses, under three simplifying assumptions, the problem of optimally locating servers so as to maximize the expected coverage of demand, considering the possibility of server unavailability when a call enters the service system. These simplifying assumptions were later relaxed by Batta et al. (Transport. Sci. 23 (1989) 277) through the use of an adjusted model (AMEXCLP) and the interactive use of the hypercube queueing model (HQM); these authors compared the expected coverage computed using the three corresponding objective functions. In the present note we address two points in this previous work which, in our opinion, deserve a more detailed discussion: (i) the models are not strictly comparable because of structural differences in their objective functions; (ii) when using HQM it is important to state clearly the factor being used to express traveling time in terms of service time units.