The influence of time windows on the costs of urban freight distribution services in city logistics applications

In freight distribution services a required quality level may have a relevant effect on transportation costs. For this reason an evaluation tool is useful to compare different service settings and support the decision, on the base of quantitative indicators. This paper proposes a method for cost evaluation in this context and presents an application to a case study concerning a freight distribution service, which operates on a wide road network having a city centre, a peripheral urban area and a peri-urban rural zone. A simulation method is proposed to obtain real-life scenarios in order to test the method and its indicators. The performance of each indicator has been evaluated in an experimental context to produce realistic test cases, using a trip planning tool and a demand generator. First, the behaviour of the indicators is analysed with regard to the time windows width planned for the service. Then, their ability in estimating the total transportation cost to satisfy all the requests, under different time period profiles, is shown. The results confirm the ability of the set of indicators to predict with a good approximation the transportation costs and therefore to be used in supporting the service quality planning decision

A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page