J. M. van den Akker

Integrated requirement selection and scheduling for the release planning of a software product

This paper investigates two integer linear programming models that integrate requirement scheduling into software release planning. 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, which can not only maximize revenues but also calculates an on-time-delivery project schedule simultaneously. Two simulations are presented 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.

Finding a robust assignment of flights to gates at Amsterdam Airport Schiphol

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.

Recoverable robustness by column generation

Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against common disturbances. Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming. Recently, a new approach has been developed that combines the best of these two: recoverable robustness. In this paper, we apply the technique of column generation to find solutions to recoverable robustness problems. We consider two types of solution approaches: separate recovery and combined recovery. We show our approach on two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and the cost of edges may increase.

Using column generation to solve parallel machine scheduling problems with minmax objective functions

In this paper we consider the parallel machine scheduling problem of minimizing an objective function of the minmax type, like maximum lateness, subject to release dates, deadlines, and/or generalized precedence constraints. We use a destructive strategy to compute a lower bound. Here we test the feasibility of a decision problem by applying column generation to compute a bound on the number of machines that we need to feasibly accommodate all jobs.After having derived the lower bound, we try to find a matching upper bound by identifying a feasible schedule with objective function value equal to this lower bound. Our computational results show that our lower bound is so strong that this is almost always possible. We are able to solve problems with up to 160 jobs and 10 machines in 10 minutes on average.

Column generation strategies and decomposition approaches for the two-stage stochastic multiple knapsack problem

We study the two-stage stochastic multiple knapsack problem.We use branch-and-price and compare two different decomposition approaches.The decomposition approaches performance is dependent on the number of knapsacks.Time improvements are made by investigating column generation strategies. Many problems can be formulated by variants of knapsack problems. However, such models are deterministic, while many real-life problems include some kind of uncertainty. Therefore, it is worthwhile to develop and test knapsack models that can deal with disturbances. In this paper, we consider a two-stage stochastic multiple knapsack problem. Here, we have a multiple knapsack problem together with a set of possible disturbances. For each disturbance, or scenario, we know its probability of occurrence and the resulting reduction in the sizes of the knapsacks. For each knapsack we decide in the first stage which items we take with us, and when a disturbance occurs we are allowed to remove items from the corresponding knapsack. Our goal is to find a solution where the expected revenue is maximized. We use branch-and-price to solve this problem. We present and compare two solution approaches: the separate recovery decomposition (SRD) and the combined recovery decomposition (CRD). We prove that the LP-relaxation of the CRD is stronger than the LP-relaxation of the SRD. Furthermore, we investigate numerous column generation strategies and methods to create additional columns outside the pricing problem. These strategies reduce the solution time significantly. To the best of our knowledge, there is no other paper that investigates such strategies so thoroughly.

Robust planning of airport platform buses

Most airports have two types of gates: gates with an air bridge to the terminal and remote stands. For flights at a remote stand, passengers are transported to and from the aircraft by platform buses. In this paper we investigate the problem of planning platform buses as it appears at Amsterdam Airport Schiphol. We focus on robust planning, i.e. we want to avoid that the bus planning is affected by flight delays and in this way invokes delays in other flights and ground-handling processes. We present a column generation algorithm for planning of platform buses that maximizes robustness. We also present a discrete-event simulation model to compare our algorithm to a first-come-first-served heuristic as is used in current practice. Our computational results with real-life data indicate that our algorithm significantly reduces the number of replanning steps and special recovery measures during the day of operation.

Optimizing Storage Placement in Electricity Distribution Networks

Decentralized power generation may lead to operational problems in electricity distribution networks, such as current overloads and too large voltages deviations. Storage systems can have a beneficial effect to alleviate these problems. However, these systems are relatively very expensive and have not been applied much in electricity grids in Europe. We present an optimization model which can be used to support the analysis of the operational benefits and investment cost of storage systems. It makes use of a simulated annealing approach to find good storage configurations, with a linear programming model to determine the load and optimal storage control, maintaining all the loadflow constraints. Our model seems to be an interesting approach to solving the storage location problems, and a promising approach to solve other investment problems.