Roel Leus

The trade-off between stability and makespan in resource-constrained project scheduling

During the last decade, considerable research efforts in the project scheduling literature have concentrated on resource-constrained project scheduling under uncertainty. Most of this research focuses on protecting the project due date against disruptions during execution. Few efforts have been made to protect the starting times of intermediate activities. In this paper, we develop a heuristic algorithm for minimizing a stability cost function (weighted sum of deviations between planned and realized activity starting times). The algorithm basically proposes a clever way to scatter time buffers throughout the baseline schedule. We provide an extensive simulation experiment to investigate the trade-off between quality robustness (measured in terms of project duration) and solution robustness (stability). We address the issue whether to concentrate safety time in so-called project and feeding buffers in order to protect the planned project completion time or to scatter safety time throughout the baseline schedule in order to enhance stability.

Dynamic Order Acceptance and Capacity Planning within a Multi-Project Environment

We present a tactical decision model for order acceptance and capacity planning that maximizes the expected profits from accepted orders, allowing for regular as well as nonregular capacity. We apply stochastic dynamic programming to determine a profit threshold for the accept/reject decision as well as an optimal capacity allocation for accepted projects, both with an eye on maximizing the expected revenues within the problem horizon. We derive a number of managerial insights based on an analysis of the influence of project and environmental characteristics on optimal project selectionand capacity usage.

Models for the Optimization of Promotion Campaigns: Exact and Heuristic Algorithms

This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. The complexity of the problem makes it very difficult to produce optimal solutions using standard optimization methods. We propose an alternative set covering formulation and develop a branch-and-price algorithm to solve it. We also describe five heuristics to approximate an optimal solution. Two of these heuristics are algorithms based on restricted versions of the basic formulation, the third is a successive exact k-item knapsack procedure. A heuristic inspired by the Next-Product-to-Buy model and a depth-first branch-and-price heuristic are also presented. Finally, we perform extensive computational experiments for the two formulations as well as for the five heuristics.

Extending the Production Dice Game

Purpose: The production dice game is a powerful learning exercise focusing on the impact of variability and dependency on throughput and work-in-process inventory of flow lines. This paper seeks to extend the basic dice game along the following lines. First, it will allow operations to take place concurrently as opposed to sequentially, which works better in a classroom setting. Second, it will allow both starvation and blocking of the line. Third, it will consider balanced lines with workstations characterized by different degrees of variability. Finally, it aims to use different sets of dice in order to represent a wide range of variation coefficients of the production line. The obtained insights can be extended to a supply chain context as well. The developed game can be played on-line and the software is freely downloadable.

Project Scheduling with Modular Project Completion on a Bottleneck Resource

In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project in order to maximize the expected profit when the activities have a probability of failure and when an activity’s failure can cause its module and thereby the overall project to fail. A module succeeds when at least one of its constituent activities is successfully executed. All activities are scheduled on a scarce resource that is modeled as a single machine. We describe various policy classes, establish the relationship between the classes, develop exact algorithms to optimize over two different classes (one dynamic program and one branch-and-bound algorithm), and examine the computational performance of the algorithms on two randomly generated instance sets.

Order Acceptance and Scheduling in a Single-Machine Environment: Exact and Heuristic Algorithms

In this paper, we develop exact and heuristic algorithms for the order acceptance and scheduling problem in a single-machine environment. We consider the case where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and orders are characterized by known processing times, delivery dates, revenues and the weight representing a penalty per unit-time delay beyond the delivery date promised to the customer. We prove the non-approximability of the problem and give two linear formulations that we solve with CPLEX. We devise two exact branch-and-bound procedures able to solve problem instances of practical dimensions. For the solution of large instances, we propose six heuristics. We provide a comparison and comments on the efficiency and quality of the results obtained using both the exact and heuristic algorithms, including the solution of the linear formulations using CPLEX.

Project Portfolio Management: Capacity Allocation, Downsizing Decisions and Sequencing Rules

This paper aims to gain insight into capacity allocation, downsizing decisions and sequencing rules when managing a portfolio of projects. By downsizing, we mean reducing the scale or size of a project and thereby changing the projects content. In previous work, we have determined the amount of critical capacity that is optimally allocated to concurrently executed projects with deterministic or stochastic workloads when the impact of downsizing is known. In this paper, we extend this view with the possibility of sequential processing, which implies that a complete order is imposed on the projects. When projects are sequenced instead of executed in parallel, two effects come into play: firstly, unused capacity can be shifted to later projects in the same period; and secondly, reinvestment revenues gain importance because of the differences in realization time of the sequenced projects. When project workloads are known, only the second effect counts; when project workloads are stochastic, however, the projects capacity usage is uncertain so that unused capacity can be shifted to later projects in the same period. In this case, both effects need to be taken into account. In this paper, we determine optimal sequencing rules when the selection and capacity-allocation decisions for a set of projects have already been made. We also consider a combination of parallel and sequential planning and we perform simulation experiments that confirm the appropriateness of our capacity-allocation methods.

An Investigation of Resource-Allocation Decisions by Means of Project Networks

This paper investigates the relationship between resource allocation and ES-policies, which are a type of scheduling policies introduced for stochastic scheduling and which can be represented by a directed acyclic graph. We present a formal treatment of resource flows as are presentation of resource-allocation decisions, extending the existing literature. A number of complexity results are established, showing that a number of recently proposed objective functions for evaluating the quality of ES-policies lead to difficult problems. Finally, some reflections are provided on possible effciency enhancements to enumeration algorithms for ES-policies.

Efficient and Effective Solution Procedures for Order Acceptance and Capacity Planning

This paper investigates dynamic order acceptance and capacity planning under limited regular and non-regular resources. Our goal is to maximize the profits of the accepted projects within a finite planning horizon. The way in which the projects are planned affects their payout time and, as a consequence, there investment revenues as well as the available capacity for future arriving projects. In general, project proposals arise dynamically to the organization, and their actual characteristics are only revealed upon arrival. Dynamic solution approaches are therefore most likely to obtain good results. Although the problem can theoretically be solved to optimality as a stochastic dynamic program, real-life problem instances are too difficult to be solved exactly within areas on able amount of time. Efficient and effective heuristics are thus required that supply a response without delay. For this reason, this paper considers both single-pass algorithms as well as approximate dynamic-programming algorithms and investigates their suitability to solve the problem. Simulation experiments compare the performance of our procedures to a first-come, first-served policy that is commonly used in practice.

Complexity Analysis of the Discrete Sequential Search Problem with Group Activities

This paper studies the computational complexity of the discrete sequential search problem with group activities, in which a set of boxes is given and a single object is hidden in one of these boxes. Each box is characterized by a probability that it contains that object and the cost of searching that box. Furthermore, each box may be related to one or more `group activities. For `conjunctive group activities, a box can be searched only when all the associated group activities have been performed whereas for `disjunctive group activities, a box can be searched as soon as at least one of the associated group activities has been executed. A cost is also incurred when performing a group activity. The goal is to find a sequence in which the boxes are to be searched and the group activities will be executed to minimize the expected total cost while satisfying the precedence constraints imposed by the group activities. In this paper, we prove that this problem is strongly NP-hard both for conjunctive group activities and for disjunctive group activities, and we discuss some special cases that can be solved in polynomial time.