Dealing with uncertainty in multi-project rough-cut capacity planning Gerhard Wullink Dpt. Operation Management and System Theory, University of Twente
[email protected] Erwin W. Hans Dpt. Operation Management and System Theory, University of Twente Aart van Harten Dpt. Operation Management and System Theory, University of Twente
Abstract In this presentation we propose a method for dealing with uncertainty in the resource-constrained multi-project planning (RCCP) problem, by incorporating stochasticity. This tactical planning level is typically characterized by many uncertainties, such as processing time uncertainty, project release date delay, network uncertainty, rush orders, resource availability, project scenarios, etc. So far, there are no techniques available that can simultaneously handle stochasticity issues as well as resource capacity flexibility, and complex technological constraints, such as generic precedence relations, and release and due dates. In this presentation we propose a generic integer linear programming model for RCCP problems, which can deal with many of the aforementioned uncertainty aspects. We focus on creating robust project plans, while at the same time optimizing resource usage and project tardiness minimization. We propose a branch-and-price based exact algorithm, and various heuristic approaches for solving this model. We study the application of the techniques in several Dutch ship repair yards.
1.
Problem formulation
In this presentation we address the resource-constrained multi-project rough-cut capacity planning (RCCP) problem [1]. RCCP is a tactical planning problem, which addresses the determination of (non)regular resource capacity levels required to complete projects on time, as well as the determination of project tardiness due to limited resource capacity. Typically, at this tactical planning level, engineering and process planning still have to be performed. Much planning information, such as resource requirements, precedence relations, resource availability, exclusion relations, etc., is generally not readily available. Nevertheless, at this stage it is often required to quote reliable project due dates, and to determine the required resource usage levels to complete the projects on time. Hence, RCCP methods are required that can deal with these uncertainty aspects [4]. Traditionally, uncertainty in project planning is dealt with by, e.g., PERT-techniques [2], or by selecting an appropriate aggregation level. However, there exist no techniques that can simultaneously deal with resource capacity flexibility, tardiness minimization, and complex technological constraints, such as generic precedence relations, and project release and due dates. The aim of our research project is to develop RCCP methods that deal with stochasticity, and try to
find project plans that are robust in as many scenarios as possible. At the same time, these methods optimize the resource capacity usage, and minimize the project tardiness.
2.
Model development and algorithms
We propose model extensions for a mixed integer linear programming (MILP) formulation for RCCP that was proposed by Hans [3]. This model assumes deterministic input data. We propose model extensions to be able to deal with stochasticity in resource requirements, project release dates, resource availability, project design uncertainty, network uncertainty, etc. The model can already handle many technological constraints, such as generic precedence relations, minimum activity durations, nonregular resource usage, project tardiness, etc. We use a scenario-based approach to model stochasticity. We model scenarios by defining execution modes for each activity. An activity may, for example, have two execution modes: in the first it has a processing time of 30 hours, in the second it has a processing time of 50 hours. Each activity execution mode has a probability. Each set of execution modes (i.e., one for each activity) corresponds to a scenario, of which the probability is the product of the probabilities of the respective activity execution modes. We study several scenario-based approaches for rough-cut capacity planning problems with stochasticity. These approaches aim to find project plans and project schedules that are as robust as possible. To be able to compare computational results of the aforementioned approaches we propose several measures of robustness in rough-cut capacity plans. We optimize the MILP model using branch-and-price based exact algorithms, and various approximation algorithms. In order to test our algorithms in a dynamic environment, we have built a simulation model of a typical manufacture-to-order system. We have embedded an order processing tool, a capacity loading tool (discussed in this presentation), and a scheduling tool, in order to be able to cover all levels of planning. We simulate an order arrival process, in which orders may have various (uncertain) characteristics. The simulation study allows us to evaluate decision making in a rolling horizon, at various planning levels, and with various types of uncertainty.
3.
Uncertainty in RCCP: application in Dutch ship repair yards
The background of our study is the REPRO project, a project that aims to improve the productivity of 5 large Dutch ship repair yards. In these environments, uncertainty typically plays an important role in planning. Before a ship arrives at the shipyard for repair, agreements are usually made between the shipowner and the shipyard, concerning the arrival time, the desired activity list, the costs, and the departure time. Based on what the shipowner demands from the shipyard, the shipyard must make a realistic offer, without even having seen the damage on the ship. The actual project execution is not free from uncertainty, and unexpected events. The arrival of the ship may be delayed, additional work may appear to be necessary once the ship has been inspected, and required resources may be unavailable. Furthermore, usually more than one ship is being repaired at the same time. So, in order to optimize resource usage, multi-project planning is required. We present computational results of experiments with typical cases from the REPRO project, using the model and algorithms discussed in the previous section. We compare several approaches for determining robust project plans. We also present computational results from the simulation study.
References [1] De Boer, R. (1998). Resource-Constrained Multi-Project Management – A Hierarchical Decision Support System, Ph.D. Thesis, University of Twente. [2] Pontrandolfo, P. (2000). Project duration in stochastic networks by the PERT-path technique, Int. J. of Project Management, no. 18, pp. 215-222. [3] Hans, E.W. (2001). Resource Loading by Branch-and-Price Techniques, Ph.D. Thesis, University Of Twente. [4] P. Brucker, A. Drexl, R. Möhring, K. Neumann, E. Pesch, (1999), Resource-constrained project scheduling: Notation, classification, models and methods, European J. of Op. Research, no.112, pp.3-41.
