It is essential for product software companies to decide which requirements should be included in the next release and to make an appropriate time plan of the development project. Compared to the extensive research done on requirement selection, very little research has been performed on time scheduling. In this paper, we introduce two integer linear programming models that integrate time scheduling into software release planning. Given the resource and precedence constraints, our first model provides a schedule for developing the requirements such that the project duration is minimized. Our second model combines requirement selection and scheduling, so that it not only maximizes revenues but also simultaneously calculates an on-time-delivery project schedule. Since requirement dependencies are essential for scheduling the development process, we present a more detailed analysis of these dependencies. Furthermore, we present two mechanisms that facilitate dynamic adaptation for over-estimation or underestimation of revenues or processing time, one of which includes the Scrum methodology. Finally, several simulations based on real-life data are performed. The results of these simulations indicate that requirement dependency can significantly influence the requirement selection and the corresponding project plan. Moreover, the model for combined requirement selection and scheduling outperforms the sequential selection and scheduling approach in terms of efficiency and on-time delivery.

We present a mathematical formalization of release planning with a corresponding optimization tool that supports product and project managers during release planning. The tool is based on integer linear programming and assumes that an optimal set of requirements is the set with maximal projected revenue against available resources. The input for the optimization is twofold. The first type of input data concerns the list of candidate requirements, estimated revenues, and resources needed. Second, managerial steering mechanisms enable what-if analysis in the optimization environment. Experiments based on real-life data made a sound case for the applicability of our approach.

Column generation has proved to be an effective technique for solving the linear programming relaxation ofhuge set covering or set partitioning problems, and column generation approaches have led to state-of-the-art so-called branch-and-price algorithms for various archetypical combinatorial optimization problems. We use a combination of column generation and Lagrangean relaxation to tackle a single-machine common due date problem, where Lagrangean relaxation is exploited for early termination of the column generation algorithm and for speeding up the pricing algorithm. We show that the Lagrangean lower bound dominates the lower bound that can be derived from the column generation algorithm when applied to the standard linear programming formulation, but we also show how the linear programming formulation can be adapted such that the corresponding lower bound is equal to the Lagrangean lower bound. Our comprehensive computational study shows that the combined algorithm is by far superior to two existing purely column generation algorithms: it solves instances with up to 125 jobs to optimality, while a purely column generation algorithm can solve instances with up to only 60 jobs.

We consider the single-machine scheduling problem of minimizing the number of late jobs. We omit here one of the standard assumptions in scheduling theory, which is that the processing times are deterministic. In this scheduling environment, the completion times will be stochastic variables as well. Instead of looking at the expected number of on time jobs, we present a new model to deal with the stochastic completion times, which is based on using a chance constraint to define whether a job is on time or late: a job is on time if the probability that it is completed by the deterministic due date is at least equal to a certain given minimum success probability. We have studied this problem for four classes of stochastic processing times. The jobs in the first three classes have processing times that follow: (i) A gamma distribution with shape parameter p j and scale parameter β, where β is common to all jobs; (ii) A negative binomial distribution with parameters p j and r, where r is the same for each job; (iii) A normal distribution with parameters p j and σ 2 j . The jobs in the fourth class have equally disturbed processing times, that is, the processing times consist of a deterministic part and a random component that is independently, identically distributed for each job. We show that the first two cases have a common characteristic that makes it possible to solve these problems in O(n log n) -mail: slam@cs.uu.nl tion that the due dates and the minimum success probabilities are agreeable. We show that under this assumption the third problem is N P-hard in the ordinary sense, whereas the fourth problem is solvable by Moore and Hodgson's algorithm.We further indicate how the problem of maximizing the expected number of on time jobs (with respect to the standard definition) can be tackled if we add the constraint that the on time jobs are sequenced in a given order and when we require that the probability that a job is on time amounts to at least some given lower bound.

In this paper we consider the train unit shunting problem extended with service task scheduling. This problem originates from Dutch Railways, which is the main railway operator in the Netherlands. Its urgency stems from the upcoming expansion of the rolling stock fleet needed to handle the ever-increasing number of passengers. The problem consists of matching train units arriving on a shunting yard to departing trains, scheduling service tasks such as cleaning and maintenance on the available resources, and parking the trains on the available tracks such that the shunting yard can operate conflict-free. These different aspects lead to a computationally extremely difficult problem, which combines several well-known NP-hard problems. In this paper, we present the first solution method covering all aspects of the shunting and scheduling problem. We describe a partial order schedule representation that captures the full problem, and we present a local search algorithm that utilizes the partial ordering. The proposed solution method is compared with an existing mixed integer linear program in a computational study on realistic instances provided by Dutch Railways. We show that our local search algorithm is the first method to solve real-world problem instances of the complete shunting and scheduling problem. It even outperforms current algorithms when the train unit shunting problem is considered in isolation, that is, without service tasks. Although our method was developed for the case of the Dutch Railways, it is applicable to any shunting yard or service location, irrespective of its layout, that uses self-propelling train units and that does not have to handle passing trains.