Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers

This paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures.The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.     

Uncertainty Modelling in Software Development Projects (With Case Study)

A project scheduling model tailored specifically for software development projects is proposed in this study. The model incorporates uncertainties related to activity durations and network topology. The first type of uncertainty exists due to error-prone coding which might result in elongated task durations caused by validation and debugging sessions. Furthermore, in practice, macro-activities represent groups of sub-tasks in order to simplify the planning and monitoring of the project. Due to the aggregation, it is more difficult to be precise on the duration of a macro-activity.The uncertainty related to the network topology is due to common database design issues or program modules shared among parallel tasks in the project network. These tasks become associated with each other through uncertain Start-to-Start (SS) precedence relationships. On the other hand, SS lags may also be the outcome of technological precedence relationships among pairs of activities. However, the imprecision underlying the work content of a predecessor activity leads to uncertain SS lags.Software development projects are human-intensive projects and hence, the duration of a task depends on the skill of the person assigned to the job as well as his/her learning rate. Thus, a task may be realized by alternative staff members which results in different expected task durations. Hence, a realistic model proposed for software development projects should incorporate staff assignment features under the uncertainties discussed above. In this study, we develop a mathematical model for software development projects and propose heuristic solution methods to be used by the project co-ordinator in preparing the project plan. The heuristic algorithms developed here are tested on real data provided by a consulting firm undertaking software development projects from manufacturing companies in Turkey.     

Multi-objective decision analysis for competence-oriented project portfolio selection

This paper develops a multi-objective optimization model for project portfolio selection taking employee competencies and their evolution into account. The objectives can include economic gains as well as gains expressed in terms of aggregated competence increments according to pre-defined profiles. In order to determine Pareto-optimal solutions, the overall problem is decomposed into a master problem addressing the portfolio selection itself, and a slave problem dealing with a suitable assignment of personnel to the work packages of the selected projects over time. We provide an asymptotic approximation of the problem by a linearized formulation, which allows an efficient and exact solution of the slave problem. For the solution of the master problem, we compare the multi-objective metaheuristics NSGA-II and P-ACO. Experimental results both for synthetically generated test instances and for real-world test instances, based on an application case from the E-Commerce Competence Center Austria, are presented.     

Integrated projects planning in IS departments: A multi-period multi-project selection and assignment approach with a computerized implementation

This paper highlights the subject of integrated projects planning (IPP) in contemporary IS departments, and presents a multi-period, multi-project selection and assignment approach (MPPA) to assist the departments in handling continuous project-based IS requests. The MPPA features a model to optimize the selection and assignment of IS projects. In the scope of multi-project, multi-period planning, the model innovatively considers the losses due to (1) the accumulated postponement of a previously unselected IS request and (2) the expected delay of ongoing projects when inserting a new project request. The MPPA also features an event-based decisional process for cumulative selection and assignment on a multi-period basis. Due to the complex and contextual nature of data in this paper, a computerized system is implemented for aiding the execution of the model and the process. The paper reports on an industrial case for a demonstration of the proposed work. Finally the paper compares the MPPA with related work to summarize the value and role it may play in the IPP context.     

Adaptive policies for multi-mode project scheduling under uncertainty

In this paper we propose an adaptive model for multi-mode project scheduling under uncertainty. We assume that there is a due date for concluding the project and a tardiness penalty for failing to meet this due date, and that several distinct modes may be used to undertake each activity. We define scheduling policies based on a set of thresholds. The starting time of the activity is compared with those thresholds in order to define the execution mode.We propose a procedure, based on the electromagnetism heuristic, for choosing a scheduling policy. In computational tests, we conclude that the adaptive scheduling policy found by using the model and the heuristic solution procedure is consistently better than the optimal non-adaptive policy. When the different modes have very different characteristics and there is a reasonable difference between the average duration of the project and the due date, the cost advantage of the adaptive policy becomes very significant.     

Finding the shortest path with honey-bee mating optimization algorithm in project management problems with constrained/unconstrained resources

Effective project management requires the development of a realistic plan and a clear communication of the plan from the beginning to the end of the project. The critical path method (CPM) of scheduling is the fundamental tool used to develop and interconnect project plans. Ensuring the integrity and transparency of those schedules is paramount for project success. The complex and discrete nature of the solution domain for such problems causes failing of traditional and gradient-based methods in finding the optimal or even feasible solution in some cases. The difficulties encountered in scheduling construction projects with resource constraints are highlighted by means of a simplified bridge construction problem and a basic masonry construction problem. The honey-bee mating optimization (HBMO) algorithm has been previously adopted to solve mathematical and engineering problems and has proven to be efficient for searching optimal solutions in large-problem domains. This paper presents the HBMO algorithm for scheduling projects with both constrained and unconstrained resources. Results show that the HBMO algorithm is applicable to projects with or without resource constraints. Furthermore, results obtained are promising and compare well with those of well-known heuristic approaches and gradient-based methods.     

A Constraint-Based Method for Project Scheduling with Time Windows

This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

Project selection,scheduling and resource allocation with time dependent returns

In this paper we formulate and analyze the joint problem of project selection and task scheduling. We study the situation where a manager has many alternative projects to pursue such as developing new product platforms or technologies, incremental product upgrades, or continuing education of human resources. Project return is assumed to be a known function of project completion time. Resources are limited and renewable. The objective is to maximize present worth of profit. A general mathematical formulation that can address several versions of the problem is presented. An implicit enumeration procedure is then developed and tested to provide good solutions based on project ordering and a prioritization rule for resource allocation. The algorithm uses an imbedded module for solving the resource-constrained project scheduling problem at each stage. The importance of integrating the impact of resource constraints into the selection of projects is demonstrated.     

A Minimum-Cost Analysts Assignment Model for Asset Evaluation of Insolvent Saving and Loan Institutions

Audit staff planning has been a challenging problem for accounting, auditing and real estate firms. This paper presents a mathematical model and a solution methodology for determining the minimum-cost analysts assignment, when analysts should travel from geographically dispersed locations to evaluate assets of an insolvent Saving and Loan institution. Computational experiments with the solution algorithm on 27 randomly generated projects show (a) that the solution methodology efficiently generates an optimal solution, and (b) provides the decision maker with alternative next best plans through ex post sensitivity analysis. Although specific, variations of the model and algorithm presented here can be applied to a variety of audit staff assignment problems in accounting and real estate firms.     

Priority rule-based heuristic for multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting

This paper presents a priority rule-based heuristic for the multi-mode resource-constrained project scheduling problem with the splitting of activities around unavailable resources allowed. All resources considered are renewable and each resource unit may not be available at all times due to resource vacations, which are known in advance. A new concept called moving resource strength is developed to help identify project situations where activity splitting is likely to be beneficial during scheduling. The moving resource strength concept is implemented in priority rule-based heuristics to control activity splitting when scheduling. Multiple comparisons of the performance of combination of activity–mode priority rules used in the heuristics are provided. Computational experiments demonstrate the effectiveness of the heuristic in reducing project makespan, and minimizing activity splitting.     

Scheduling tests in automotive R&D projects

In automotive R&D projects a major part of development cost is caused by tests which utilize expensive experimental vehicles. In this paper, we introduce an approach for scheduling the individual tests such that the number of required experimental vehicles is minimized. The proposed approach is based on a new type of multi-mode resource-constrained project scheduling model with minimum and maximum time lags as well as renewable and cumulative resources. We propose a MILP formulation, which is solvable for small problem instances, as well as several variants of a priority-rule based method that serve to solve large problem instances. The developed solution methods are examined in a comprehensive computational study. For a real-world problem instance it is shown that the introduced approach may enhance the current methods applied in practice.     

Selection among ranked projects under segmentation,policy and logical constraints

The paper proposes a method for project selection under a specific decision situation, where a final selection is guided by two aspects: (1) satisfaction of certain segmentation, policy and/or logical constraints, and (2) assurance that the individual evaluation of the projects is respected to the maximum degree. This approach is somewhat different than the usual portfolio optimization, where combinations of projects are compared without special concern on respecting the project’s ranking. The entire process is implemented in two phases: the projects are first ranked, usually through a multicriteria approach. The obtained complete preorder of the projects is then used in an integer programming module in order to effectively drive the final selection that satisfies the segmentation and/or logical constraints. The innovative part of the proposed approach is the way it overcomes the well-known bias towards low cost projects which is caused by the knapsack formulation commonly used in the integer programming phase. Actually this is the main source of divergence between the final selection and the initial complete preorder of the projects. The proposed method improves an agreement between the final selection of projects obtained from the integer programming model and the ranking obtained from the multicriteria approach.     

Scheduling projects with heterogeneous resources to meet time and quality objectives

In service organizations, heterogeneity in workforce skills can lead to variation in end-product/service quality. The multi-mode, resource-constrained, project scheduling problem (MRCPSP), which assumes similar skills among resources in a given resource pool, accounts for differences in quality levels of individuals by assigning different activity durations depending on the skill level used. This approach is often inadequate to model the problem type investigated here. Using typical projects from the customer training division of a large telecommunications company (which motivated this research), a labor assignment problem using a successive work–time concept is formulated and solved using integer programming optimization procedures. The setting represents a multiple-project environment where projects are separate and independent, but require the same renewable resource mix for their completion. The paper demonstrates how the output of the model can be used to identify bottlenecks (or critical resource skills), and also demonstrates how cross-training the appropriately skilled groups or individuals can increase throughput. The approach guides decision-making concerning which workers to cross-train in order to extract the greatest benefits from worker-flexibility.     

Multi-mode resource constrained multi-project scheduling and resource portfolio problem

This paper introduces a multi-project problem environment which involves multiple projects with assigned due dates; activities that have alternative resource usage modes; a resource dedication policy that does not allow sharing of resources among projects throughout the planning horizon; and a total budget. Three issues arise when investigating this multi-project environment. First, the total budget should be distributed among different resource types to determine the general resource capacities, which correspond to the total amount for each renewable resource to be dedicated to the projects. With the general resource capacities at hand, the next issue is to determine the amounts of resources to be dedicated to the individual projects. The dedication of resources reduces the scheduling of the projects’ activities to a multi-mode resource constrained project scheduling problem (MRCPSP) for each individual project. Finally, the last issue is the efficient solution of the resulting MRCPSPs. In this paper, this multi-project environment is modeled in an integrated fashion and designated as the resource portfolio problem. A two-phase and a monolithic genetic algorithm are proposed as two solution approaches, each of which employs a new improvement move designated as the combinatorial auction for resource portfolio and the combinatorial auction for resource dedication. A computational study using test problems demonstrated the effectiveness of the solution approach proposed.     

A heuristic solution framework for the resource constrained (multi-)project scheduling problem with sequence-dependent transfer times

We consider the problem of scheduling multiple projects subject to joint resource constraints. Most approaches proposed in the literature so far are based on the unrealistic assumption that resources can be transferred from one project to the other without any expense in time or cost. In order to contribute to closing this gap to reality, we generalise the multi-project scheduling problem by additionally including sequence- and resource-dependent transfer times, which represent setup activities necessary when a resource is removed from one project and reassigned to another (or from one job to another within the same project). In this paper, we define the modified resource constrained multi-project scheduling problem with transfer times (called RCMPSPTT), which aims at minimising the multi-project duration for the single-project approach or the mean project duration for the multi-project approach. We formulate both perspectives as an integer linear program, propose priority rule based solution procedures and present results of comprehensive computational experiments. Provided that the combination of scheduling scheme and priority rules is chosen appropriately, the procedures obtain good results. In particular, resource oriented priority rules are identified to be successful.     

MIP models for resource-constrained project scheduling with flexible resource profiles

This paper addresses the resource-constrained project scheduling problem with flexible resource profiles (FRCPSP). Such a problem often arises in many real-world applications, in which the resource usage of an activity is not merely constant, but can be adjusted from period to period. The FRCPSP is, therefore, to simultaneously determine the start time, the resource profile, and the duration of each activity in order to minimize the makespan, subject to precedence relationships, limited availability of multiple resources, and restrictions on resource profiles. We propose four discrete-time model formulations and compare their model efficiency in terms of solution quality and computational times. Both preprocessing and priority-based heuristic methods are also applied to compute both upper and lower bounds of the makespan. Our comparative results show significant dominance of one of the models, the so-called “variable-intensity-based” model, in both solution quality and runtimes.     

GRASP and path relinking for project scheduling under partially renewable resources

Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP and Path relinking are then developed and tested on existing test instances, obtaining excellent results.     

A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs

In this paper, we develop a three-step heuristic to address a production scheduling problem at a high volume assemble-to-order electronics manufacturer. The heuristic provides a solution for scheduling multiple product families on parallel, identical production lines so as to minimize setup costs. The heuristic involves assignment, sequencing, and time scheduling steps, with an optimization approach developed for each step. For the most complex step, the sequencing step, we develop a greedy randomized adaptive search procedure (GRASP). We compare the setup costs resulting from the use of our scheduling heuristic against a heuristic previously developed and implemented at the electronics manufacturer that assumes approximately equal, sequence-independent, setup costs. By explicitly considering the sequence-dependent setup costs and applying GRASP, our empirical results show a reduction in setups costs for an entire factory of 14–21% with a range of single production line reductions from 0% to 49%.     

LSSPER: Solving the Resource-Constrained Project Scheduling Problem with Large Neighbourhood Search

This paper presents the Local Search with SubProblem Exact Resolution (LSSPER) method based on large neighbourhood search for solving the resource-constrained project scheduling problem (RCPSP). At each step of the method, a subpart of the current solution is fixed while the other part defines a subproblem solved externally by a heuristic or an exact solution approach (using either constraint programming techniques or mathematical programming techniques). Hence, the method can be seen as a hybrid scheme. The key point of the method deals with the choice of the subproblem to be optimized. In this paper, we investigate the application of the method to the RCPSP. Several strategies for generating the subproblem are proposed. In order to evaluate these strategies, and, also, to compare the whole method with current state-of-the-art heuristics, extensive numerical experiments have been performed. The proposed method appears to be very efficient.