Green Lot-Sizing

The lot-sizing problem concerns a manufacturer that needs to solve a production planning problem. The producer must decide at which points in time to set up a production process, and when he/she does, how much to produce. There is a trade-off bet

Economic lot-sizing with remanufacturing: complexity and efficient formulations

Within the framework of reverse logistics, the classic economic lot-sizing problem has been extended with a remanufacturing option. In this extended problem, known quantities of used products are returned from customers in each period. These returned products can be remanufactured, so that they are as good as new. Customer demand can then be fulfilled both from newly produced and remanufactured items. In each period, we can choose to set up a process to remanufacture returned products or produce new items. These processes can have separate or joint set-up costs. In this paper, we show that both variants are NP-hard. Furthermore, we propose and compare several alternative MIP formulations of both problems. Because ‘natural’ lot-sizing formulations provide weak lower bounds, we propose tighter formulations, namely shortest path formulations, a partial shortest path formulation and an adaptation of the (l, S, WW)-inequalities for the classic problem with Wagner-Whitin costs. We test their efficiency on a large number of test data sets and find that, for both problem variants, a (partial) shortest path type formulation performs better than the natural formulation, in terms of both the LP relaxation and MIP computation times. Moreover, this improvement can be substantial

The Economic Lot-Sizing Problem with an Emission Constraint

We consider a generalisation of the lot-sizing problem that includes an emission constraint. Besides the usual financial costs, there are emissions associated with production, keeping inventory and setting up the production process. Because the constraint on the emissions can be seen as a constraint on an alternative cost function, there is also a clear link with bi-objective optimisation. We show that lot-sizing with an emission constraint is NP-hard and propose several solution methods. First, we present a Lagrangian heuristic to provide a feasible solution and lower bound for the problem. For costs and emissions for which the zero inventory property is satisfied, we give a pseudo-polynomial algorithm, which can also be used to identify the complete Pareto frontier of the bi-objectiv

Stochastic Improvement of Cyclic Railway Timetables

Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can cope with the stochastic disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijn”. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable