Implications of the assumptions on which the p-median problem are based when distribution network design

In a previous work, a real distribution network is optimized with a heterogeneous fleet minimizing the costs involved, which decision variables are: location, allocation, routing and inventory. To optimize the distribution network a methodology of three phases was proposed: location, allocation, routing and routing-inventory. In each phase models and algorithms to their optimization were proposed, specifically the phases one and two are detailed. In phase one, the p-median was used in order to localize the distribution centres and in phase two, i.e. the customer allocation to the distribution centres, cheaper costs were used in addition to the real characteristics of non-urban road network. In this optimization process a finding of great importance was found: the solution spaces to be evaluated of the p-median problem applied to a real problem is not exponential but rather the opposite, the solution space is finite numerals as well as the number of possible allocations carried out by each of the allocated distribution centre. In this work is shown empirically that the number of scenarios to be evaluated for the localization of the distribution centres and the customer allocation them is not exponential.