Stefan Creemers

Scheduling Markovian PERT networks to maximize the net present value

We examine project scheduling with net present value objective and exponential activity durations, using a continuous-time Markov decision chain. On the basis of a judicious partitioning of the state space, we achieve a significant performance improvement as compared to the existing algorithms.

The Optimal Allocation of Server Time Slots Over Different Classes of Patients

We present a model for assigning server time slots to different classes of patients. The objective is to minimize the total expected weighted waiting time of a patient (where different patient classes may be assigned different weights). A bulk service queueing model is used to obtain the expected waiting time of a patient of a particular class, given a feasible allocation of service time slots. Using the output of the bulk service queueing models as the input of an optimization procedure, the optimal allocation scheme may be identified. For problems with a large number of patient classes and/or a large number of feasible allocation schemes, a step-wise heuristic is developed. A common example of such a system is the allocation of operating room time slots over different medical disciplines in a hospital.

Queueing models for appointment-driven systems

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue (also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decision making concerning server capacity (e.g. how often, when and for how long should a server be online). We develop a new model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.

New strategies for stochastic resource-constrained project scheduling

We study the stochastic resource-constrained project scheduling problem or SRCPSP, where project activities have stochastic durations. A solution is a scheduling policy, and we propose a new class of policies that is a generalization of most of the classes described in the literature. A policy in this new class makes a number of a priori decisions in a preprocessing phase, while the remaining scheduling decisions are made online. A two-phase local search algorithm is proposed to optimize within the class. Our computational results show that the algorithm has been efficiently tuned toward finding high-quality solutions and that it outperforms all existing algorithms for large instances. The results also indicate that the optimality gap even within the larger class of elementary policies is very small.

G-RAND: A phase-type approximation for the nonstationary G(t)/G(t)/s(t)+G(t) queue

Abstract We present a Markov model to analyze the queueing behavior of the nonstationary G ( t ) / G ( t ) / s ( t ) + G ( t ) queue. We assume an exhaustive service discipline (where servers complete their current service before leaving) and use acyclic phase-type distributions to approximate the general interarrival, service, and abandonment time distributions. The time-varying performance measures of interest are: (1) the expected number of customers in queue, (2) the variance of the number of customers in queue, (3) the expected number of abandonments, and (4) the virtual waiting time distribution of a customer arriving at an arbitrary moment in time. We refer to our model as G-RAND since it analyzes a general queue using the randomization method. A computational experiment shows that our model allows the accurate analysis of small- to medium-sized problem instances.

Project scheduling for maximum NPV with variable activity durations and uncertain activity outcomes

The literature on project scheduling with uncertain activity durations is still in its burn-in phase. We examine project scheduling with net-present-value objective and exponential activity durations by means of a backward stochastic dynamic programming recursion. We examine the particular setting in which the individual activities carry a risk of failure, and where an activity¿s failure results in the project¿s overall failure. In the project planning and scheduling literature, this technological uncertainty has typically been ignored and project plans are developed only for scenarios in which the project succeeds.

Collaborative shipping under different cost-sharing agreements

We study collaborative shipping where two shippers bundle their shipments to share the same transportation vehicle (also known as co-loading). The goal of such a collaboration is to reduce the total number of transports, thereby reducing transportation costs and CO2 emissions. To synchronize the replenishment of both companies, we adopt a can-order joint replenishment policy for both companies, and we analyze how the costs of each individual company are impacted by the collaboration. We consider different agreements to redistribute the costs (or the gains) of the collaboration, ranging from no cost redistribution at all, sharing the transportation costs (or its gains) only, to sharing the total logistics costs (or its gains) that are impacted by the collaboration, i.e., transportation + inventory costs. We show that the stability (and thus the long-term viability) of the partnership strongly depends on the cost-sharing agreement, in combination with the allocation mechanism used to share the costs (or gains) of the coordination. Although most companies focus on the redistribution of transportation costs, we show that this might not lead to a stable situation where each individual company eventually benefits from collaboration.

Project scheduling with alternative technologies: Incorporating varying activity duration variability

We look into project scheduling with expected-NPV objective and stochastic activity durations. Individual activities carry a risk of failure, and an activitys failure can cause the overall project to fail. More than one alternative may exist for reaching intermediate project deliverables, and these alternatives can be implemented either in parallel or sequentially. In this paper, optimal solutions to the scheduling problem are found by means of stochastic dynamic programming. We examine the impact of the variability of activity durations on the projects value. We also illustrate that higher operational variability does not always lead to lower project values, meaning that (sometimes costly) variance-reduction strategies are not always advisable.

R&D project planning with multiple trials in uncertain environments

We study project scheduling when individual activities carry a risk of failure, and where an activitys failure may lead to the projects overall failure. In the project planning and scheduling literature, this technological uncertainty has typically been ignored and project plans are developed only for scenarios in which the project succeeds. To mitigate the risk that an activitys failure jeopardizes the entire project, more than one alternative may exist for obtaining certain results, and these alternatives can be implemented either in parallel or sequentially, allowing to model the pursuit of alternative technologies.

A column generation approach for solving the examination-timetabling problem

In this paper, we approach the Examination-Timetabling Problem (ETP) from a student-centric point of view. We allow for multiple versions of an exam to be scheduled to increase the spreading of exams for students. We propose two Column Generation (CG) algorithms. In the first approach, a column is defined as an exam schedule for every unique student group, and a Pricing Problem (PPs) is developed to generate these columns. The Master Program (MP) then selects an exam schedule for every unique student group. Instead of using branch-and-price, we heuristically select columns. In the second approach, a column consists of a mask schedule for every unique student group, and a PP is developed to generate the masks. The MP then selects the masks and schedules exams in the mask slots. We compare both models and perform a computational experiment. We solve the ETP at KU Leuven campus Brussels (Belgium) for the business engineering degree program and apply the models to two existing datasets from the literature.