Tactical fixed job scheduling with spread-time constraints

We address the tactical fixed job scheduling problem with spread-time constraints. In such a problem, there are a fixed number of classes of machines and a fixed number of groups of jobs. Jobs of the same group can only be processed by machines of a given set of classes. All jobs have their fixed start and end times. Each machine is associated with a cost according to its machine class. Machines have spread-time constraints, with which each machine is only available for L consecutive time units from the start time of the earliest job assigned to it. The objective is to minimize the total cost of the machines used to process all the jobs. For this strongly NP-hard problem, we develop a branch-and-price algorithm, which solves instances with up to 300 jobs, as compared with CPLEX, which cannot solve instances of 100 jobs. We further investigate the influence of machine flexibility by computational experiments. Our results show that limited machine flexibility is sufficient in most situations

A Combinatorial Optimization Approach to Accessibility Services in International Airports

In this PhD thesis we study a specific variant of the well known Fixed Job Scheduling Problem, namely the Tactical Fixed Job Scheduling Problem with Spread-Time constraints. In this problem it is required to schedule a number of jobs on non identical machines that differ from each other for the set of jobs they can perform and that have constraints on the length of their duty. After providing an extensive literature review of the Fixed Job Scheduling and of its main variants, the original contribution is presented. We illustrate some lower bounds for the optimal value of the problem and display the first heuristic algorithm for solving it. We also study a specific case of interest connected with the assistance of passengers with special needs in large scale international airports