Lot-sizing in a serial distribution system with capacitated in-system production flow

In this paper, we focus on an N-stage serial production-distribution system with limited production capacity at the first stage. Our objective in such a system is to find inventory management policies that minimize the global logistic cost, including transportation and holding costs. We use myopic heuristics based on the breakdown of the system into local systems. One of these systems is a 2-stage system, and the second is a 3-stage system. They both can be solved with a very good performance guarantee. The successive optimizations of such systems provide quite good policies for the global system as asserted by the experimental results at the end of the paper.

Using graph concepts to assess the feasibility of a sequenced air traffic flow with low conflict rate

In this paper, we propose to study feasibility issues of a new air traffic paradigm. In this paradigm, aircraft are following immaterial moving points in such a way that no conflict (or at most few) occurs between aircraft. We provide lower and upper bounds on the maximum density of a solution. In particular, we characterize the density of the solution according to the colorability of an auxiliary graph, modelling the potential conflicts between moving points.Transportation Graph theory Air traffic management

Approximating bounded job start scheduling with application in Royal Mail deliveries under uncertainty

Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the "bounded job start scheduling problem". Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound g=m and p_j<m, respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. Finally, we exploit machine augmentation and lexicographic optimization, which is useful for P||Cmax under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in good trade-offs in terms of makespan and number of used machines. We substantiate this approach numerically using Royal Mail data

Operator non-availability periods

In the scheduling literature, the notion of machine non availability periods is well known, for instance for maintenance. In our case of planning chemical experiments, we have special periods (the week-ends, holidays, vacations) where the chemists are not available. However, human intervention by the chemists is required to handle the starting and termination of the experiments. This gives rise to a new type of scheduling problems, namely problems of finding schedules that respect the operator non availability periods. These problems are analyzed on a single machine with the makespan as criterion. Properties are described and performance ratios are given for list scheduling and other polynomial-time algorithms