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.     

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.     

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 multiobjective evolutionary approach for linearly constrained project selection under uncertainty

In the project selection problem a decision maker is required to allocate limited resources among an available set of competing projects. These projects could arise, although not exclusively, in an R&D, information technology or capital budgeting context. We propose an evolutionary method for project selection problems with partially funded projects, multiple (stochastic) objectives, project interdependencies (in the objectives), and a linear structure for resource constraints. The method is based on posterior articulation of preferences and is able to approximate the efficient frontier composed of stochastically nondominated solutions. We compared the method with the stochastic parameter space investigation method (PSI) and illustrate it by means of an R&D portfolio problem under uncertainty based on Monte Carlo simulation.     

Competence-driven project portfolio selection,scheduling and staff assignment

This paper presents a new model for project portfolio selection, paying specific attention to competence development. The model seeks to maximize a weighted average of economic gains from projects and strategic gains from the increment of desirable competencies. As a sub-problem, scheduling and staff assignment for a candidate set of selected projects must also be optimized. We provide a nonlinear mixed-integer program formulation for the overall problem, and then propose heuristic solution techniques composed of (1) a greedy heuristic for the scheduling and staff assignment part, and (2) two (alternative) metaheuristics for the project selection part. The paper outlines experimental results on a real-world application provided by the E-Commerce Competence Center Austria and, for a slightly simplified instance, presents comparisons with the exact solution computed by CPLEX.     

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.     

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.     

Optimizing project selection: a perspective from resource constraints

In reality, projects usually consume complex resources. Making good use of the various resources is vital for optimal project selection and maximum profit earning. This paper proposes a new project selection model from the perspective of complex resource constraints. In the model, the resources are divided into non-renewable and renewable categories, and some resources of the two categories can both be shared by different projects. In addition, the paper considers the situation where the company has resources in stock and can purchase them in the marketplace if they are out of stock. The paper proves that the proposed model which considers renewable resource and resource sharing produces higher profit than the ones that do not consider renewable resource and resource sharing. To solve the complex model problem, an improved genetic algorithm is presented. For the sake of illustration, a case study is provided.     

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.     

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.     

A priority-rule method for project scheduling with work-content constraints

The activities of a project are in general characterized by a work content in terms of resource–time units, e.g. person-days. Even though most project scheduling models assume a time-invariant resource usage, normally it is possible to vary the resource usage during the execution of an activity. Typically, a lower and an upper bound on this resource usage and a minimum time lag between consecutive changes of this resource usage are prescribed. The project scheduling problem studied in this paper consists in determining a feasible resource-usage profile for each activity such that the project duration is minimized subject to precedence and resource-capacity constraints. While the known solution methods interpret the prescribed work content as a lower bound, we assume that each activity’s work content must be processed exactly.     

项目鲁棒调度的资源分配启发式算法研究

合理的资源配置是提高项目调度鲁棒性一种有效的方法。本文针对项目鲁棒调度问题,提出了Max-PRUA资源分配启发式算法,以期通过生成鲁棒性高的资源分配方案来提高调度计划的鲁棒性。本算法设计了最大化利用优先关系和不可避免弧传递资源的资源分配两项策略来传递最大资源量,以减少由额外约束传递的资源量,降低对项目调度鲁棒性的影响。为寻优最优资源分配方案,配合局部搜索算法,本算法构建了动态活动组GRA,通过对组内活动顺序重排以生成多种资源分配方案,以利于从解空间中寻优出最佳的鲁棒性方案。最后通过大量的仿真实验验证和与其它算法进行比较,结果表明本算法对于不同规模和不同因素影响的项目均有较好的适应性,生成的资源分配方案对调度计划鲁棒性影响较小,是一种有效的算法。     

A hybrid scatter search for the discrete time/resource trade-off problem in project scheduling

We develop a heuristic procedure for solving the discrete time/resource trade-off problem in the field of project scheduling. In this problem, a project contains activities interrelated by finish-start-type precedence constraints with a time lag of zero, which require one or more constrained renewable resources. Each activity has a specified work content and can be performed in different modes, i.e. with different durations and resource requirements, as long as the required work content is met. The objective is to schedule each activity in one of its modes in order to minimize the project makespan. We use a scatter search algorithm to tackle this problem, using path relinking methodology as a solution combination method. Computational results on randomly generated problem sets are compared with the best available results indicating the efficiency of the proposed algorithm.     

The project scheduling problem with production and consumption of resources: A list-scheduling based algorithm

The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources.     

Proactive policies for the stochastic resource-constrained project scheduling problem

The resource-constrained project scheduling problem involves the determination of a schedule of the project activities, satisfying the precedence and resource constraints while minimizing the project duration. In practice, activity durations may be subject to variability. We propose a stochastic methodology for the determination of a project execution policy and a vector of predictive activity starting times with the objective of minimizing a cost function that consists of the weighted expected activity starting time deviations and the penalties or bonuses associated with late or early project completion. In a computational experiment, we show that our procedure greatly outperforms existing algorithms described in the literature.     

PROGRESS: Optimally solving the generalized resource-constrained project scheduling problem

This paper deals with the generalized resource-constrained project scheduling problem (GRCPSP) which extends the well-known resource-constrained project scheduling problem (RCPSP) by considering job specific release and due dates, non-negative minimum start-to-start time lags as well as time-varying resource availabilities. The structure of the project is represented by an acyclic network diagram. Though the extensions are of high practical importance, only a few exact solution procedures have been presented in the literature so far. Therefore, a new exact procedure PROGRESS is developed which includes new dominance rules as well as enhancements of existing ones. For evaluating the efficiency experimentally, new GRCPSP instances with 30 and 60 jobs are considered which extend the standard benchmark sets for the RCPSP generated by ProGen. PROGRESS shows superior performance when applied to the GRCPSP and is also very competitive in comparison to approaches proposed for the RCPSP.     

The resource constrained project scheduling problem with multiple crashable modes: A heuristic procedure

We present a heuristic procedure for a nonpreemptive resource constrained project scheduling problem in which the duration/cost of an activity is determined by the mode selection and the duration reduction (crashing) applied within the selected mode. This problem is a natural combination of the time/cost trade-off problem and the resource constrained project scheduling problem. The objective is to determine each activity's start (finish) time, mode and duration so that the total project cost is minimized. Total project cost is the sum of all activity costs and the penalty cost for completing the project beyond its due date. We introduce a multi-pass algorithm. We report computational results with a set of 100 test problems and demonstrate the efficacy of the proposed heuristic procedure.     

On the complexity of project scheduling to minimize exposed time

We consider project scheduling where the project manager’s objective is to minimize the time from when an adversary discovers the project until the completion of the project. We analyze the complexity of the problem identifying both polynomially solvable and NP-hard versions of the problem. The complexity of the problem is seen to be dependent on the nature of renewable resource constraints, precedence constraints, and the ability to crash activities in the project.     

A bi-objective hierarchical program scheduling problem and its solution based on NSGA-III

In enterprise project management systems, a program at the tactical level coordinates and manages multiple projects at the operational level. There are close relationships between multiple projects in a program, which are typically manifested as shared resources and precedence relationships. Most research efforts have concentrated on the resource sharing by projects, while the precedence relationships between projects have yet to be comprehensively investigated. In this paper, a bi-objective hierarchical resource-constrained program scheduling problem proposed, where both resource sharing and precedence relationships between projects are considered in a distributed environment. The problem contains two different sub-problems at the operational level and the tactical level, and they are modeled in the same way as two bi-objective multi-mode scheduling problems. Shared resources are allocated from the tactical level to the operational level, and once they are allocated to a project, they can only be re-allocated to other projects once the current project is finished. Subsequently, a two-phase algorithm based on NSGA-III is developed. The algorithm runs at the operational level and the tactical level in turn. According to the Pareto fronts of projects that are submitted from the operational level, the bi-objective program planning at the tactical level is conducted under the constraints of precedence relationships and shared resources. The results of computational simulations demonstrate the satisfactory performance of the improved algorithm. By coordinating the local optimization of projects and the global optimization of the program in a hierarchical framework, the method proposed in this paper provides an effective integrated scheduling method for decision-makers at various levels of a program.

     

Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases

In many large-scale project scheduling problems, multiple projects are either taking place at the same time or scheduled into a tight sequence in order to efficiently share a common resource. One example of this is the computing resource allocation at an Application Service Provider (ASP) which provides data processing services for multiple paying customers. Typical services provided by ASPs are data mining, payroll processing, internet-based storage backup services and Customer Relation Management (CRM) services. The processing mode of an ASP can be either batch or concurrent, depending on the type service rendered. For example, for CPU intensive or long processing time required services, it would be more economical to processes one customer request at a time in order to minimize the context switching overhead. While the data transaction processes within a service request are subject to certain precedence relationships, the requests from different customers to an ASP are independent of each other, and the total time required to process a service request depends on the computing resource allocated to that request. The related issue of achieving an optimal use of resources at ASPs leads to problem of project scheduling with controllable project duration.In this paper, we present efficient algorithms for solving several special cases of such multi-project scheduling problems with controllable project duration and hard resource constraints. Two types of problems are considered. In type I, the duration of each project includes a constant and a term that is inversely proportional to the amount of resource allocated. In type II, the duration of each individual project is a continuous decreasing function of the amount of resource allocated.