Improved Lower Bounds for the Proportional Lot Sizing and Scheduling Problem

Where standard MIP--solvers fail to compute optimum objective function values for certain MIP--model formulations, lower bounds may be used as a point of reference for evaluating heuristics. In this paper, we compute lower bounds for the multi--level proportional lot sizing and scheduling problem with multiple machines (PLSP--MM). Four approaches are compared: Solving LP--relaxations of two different model formulations, solving a relaxed MIP--model formulation optimally, and solving a Lagrangean relaxation. Keywords: Multi--level lot sizing, scheduling, lower bounds, PLSP 1 Introduction The problem we are focussing at, can be described as follows: Several items are to be produced in order to meet some known (or estimated) dynamic demand without backlogs and stockouts. Precedence relations among these items define an acyclic gozinto--structure of the general type. In contrast to many authors who allow demand for end items only, now, demand may occur for all items including component ..

Stability Measures for Rolling Schedules with Applications to Capacity Expansion Planning, Master Production Scheduling, and Lot Sizing

rolling horizon nervousness rescheduling capacity expansion master production scheduling lot sizing

An option-based revenue management procedure for strategic airline alliances

An airline has to decide whether to accept an incoming customer request for a seat in the airplane or to reject it in hope that another customer will request the seat later at a higher price. Capacity control, as one of the instruments of revenue management, gives a solution to this decision problem. In the presence of strategic alliances capacity control changes. For the case of two airlines in the alliance and a single flight leg we propose an option-based capacity control process. The determination of booking limits for capacity control is done with real options. A simulation model is introduced to evaluate the booking process of the partner airlines within the strategic alliance, considering the option-based procedure. In an iterative process the booking limits are improved with simulation-based optimization. The results of the option-based procedure will be compared with the results of the simulation-based optimization, the results of a first-come-first-served (FCFS) approach and ex post optimal solutions.Revenue management Strategic alliances Capacity control Real options Simulation-based optimization Stochastic approximation

A basic mathematical model for evacuation problems in urban areas

Real life situations like floods, hurricanes or chemical accidents may cause the evacuation of a certain area to rescue the affected population. To enable a fast and a safe evacuation a basic mixed-integer evacuation model has been developed that provides a reorganization of the traffic routing of a certain area for the case of an evacuation. This basic problem of evacuation minimizes the evacuation-time while prohibiting conflicts within intersections. Our evacuation model is a dynamic network flow problem with additional variables for the number and direction of used lanes and with additional complicating constraints. Because of the size of the time-expanded network, the computational effort required by standard software is already very high for tiny instances. To deal with realistic instances we propose a heuristic approach.Evacuation LP-based heuristic Mathematical programming