Parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times. If preemption is not allowed, then most problems are not only NP-hard, but also very hard from a practical point of view. In this paper, we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions. Characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule. To that end, we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables, n covering constraints, and a single side constraint. We show that the linear programming relaxation can be solved e ciently by column generation because the pricing problem is solvable in pseudo-polynomial time. We display this approach on the problem of minimizing total weighted completion time on m identical machines. Our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral. Moreover, they show that our branch-and-bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm.

Time-indexed formulations for machine scheduling problems have received a great deal of attention; not only do the linear programming relaxations provide strong lower bounds, but they are good guides for approximation algorithms as well. Unfortunately, time-indexed formulations have one major disadvantage—their size. Even for relatively small instances the number of constraints and the number of variables can be large. In this paper, we discuss how Dantzig-Wolfe decomposition techniques can be applied to alleviate, at least partly, the difficulties associated with the size of time-indexed formulations. In addition, we show that the application of these techniques still allows the use of cut generation techniques.

The vehicle scheduling problem (VSP) is a traditional problem in public transport. One of the main assumptions is that buses can be operated the whole day without any interruption for refueling etc. Recently, new technological innovations have led to the introduction of electric vehicles (EVs). For these new vehicles, we cannot ignore the need of refueling during the day, as the range of an electric bus is severely limited, because of the capacity of the batteries. In this paper, we study the electric VSP (e-VSP), where we use EVs with a limited range. During the day the batteries can be charged; in this paper we assume that a battery cannot be replaced/substituted. We present two models that differ in the level of detail resembling the actual processes. In our first model, we assume a linear charging process, work with a constant price of electricity during the day, and do not take the effect of the depth-of-discharge on the lifetime of the battery into account. Our second model resembles practice much better: we allow any type of charging process, work with the actual electricity prices, and take the depreciation cost of the battery into account. To keep this model tractable, however, we approximate the exact value of the charge by discretizing it. The refined model can be solved to optimality using integer linear programming for instances of small/medium size, and therefore, we describe two other solution methods based on column generation 123Public Transp (2017) 9:155-176 DOI 10.1007/s12469-017-0164-0 that find good, but not necessarily optimal, solutions for large instances. We have tested our algorithms on real-world instances.

Recent studies have reported a significant increase of proteinuria in kidney transplant recipients who were switched from a calcineurin inhibitor (CI) to sirolimus. This has (partly) been ascribed to the hemodynamic renal effects of CI withdrawal. We have evaluated the evolution of proteinuria in renal transplant recipients who underwent conversion from azathioprine to sirolimus. In a randomized, prospective, multicenter study called RESCUE (Recurrent cutanEous Squamous cell Carcinoma Under RapamunE) the efficacy and safety is investigated of conversion to sirolimus in stable renal transplant recipients with a cutaneus squamous cell carcinoma (SCC). In our center 25 patients have been included in this study of which 13 patients were randomized to continue their current immunosuppressive treatment and 12 to conversion to sirolimus. After a mean follow-up of 360 days mean proteinuria increased from 0.37+/-0.34 to 1.81+/-1.73 g/24 h after conversion to sirolimus (P<0.005). In the control group there was no change in proteinuria. A significant increase of proteinuria was observed in all seven patients with proteinuria before conversion, whereas proteinuria remained absent in all patients without previous proteinuria. Two of the patients with proteinuria were converted from cyclosporine and five were converted from azathioprine to sirolimus. Sirolimus was discontinued in five patients with proteinuria, and in all of them proteinuria declined to baseline values. Our study demonstrates that conversion from azathioprine to sirolimus after kidney transplantation may cause a reversible increase of proteinuria. Sirolimus-induced proteinuria therefore cannot be ascribed to the hemodynamic renal effects of withdrawal of CI.

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This paper integrates requirement scheduling issues into software release planning. Two integer linear programming models are presented-the first model can schedule the development of the requirements for the new release exactly in time so that the project span is minimized and the resource and precedence constraints are satisfied. The second model is for combined requirement selection and scheduling and it can not only maximize revenue but also calculates an on-time-delivery project schedule simultaneously. We also run two simulations to examine the influence of precedence constraints and compare the differences of the traditional prioritization models and the two new ones. The simulation results suggest that requirement dependency can significantly influence the project plan and the combined model for requirement selection and scheduling is better in the sense of efficiency and on-time delivery.

In this paper we investigate the gate assignment problem as it appears at Amsterdam Airport Schiphol (AAS). Currently, the gate planners spend many hours on adjusting the automatically generated planning during the day of operation to make it proof against small deviations from the schedule. To alleviate this problem, we aim at finding a robust solution, given the planned arrivals and departures for the next day.We present a completely new integer linear programming formulation that is based on so-called gate plans. Each gate plan consists of a subset of the flights that can be assigned to a single gate of the corresponding type; gates with identical characteristics are aggregated in gate types. The gate assignment problem then boils down to selecting the best subset of gate plans such that each flight belongs to one selected gate plan, and such that the number of selected gate plans for a certain type of gate is equal to the number of gates of this type. In the first phase, we solve the LP-relaxation through column generation, and we describe specific features to find a very good solution to the ILP quickly. This solution is then handed to the planners at AAS in order to assign gate plans to physical gates. This consists of a number of relatively small problems that can be solved by hand and in which additional operational constraints can be incorporated. We also present the possibility of directly assigning flights to physical gates using the column generation formulation, where we then take into account other criteria as well.Computational results with real-life data provided by AAS are promising and indicate that the algorithm is able to solve real-life instances within rather small running times.

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