A market-based multi-agent system model for decentralized multi-project scheduling

We consider a multi-project scheduling problem, where each project is composed of a set of activities, with precedence relations, requiring specific amounts of local and shared (among projects) resources. The aim is to complete all the project activities, satisfying precedence and resource constraints, and minimizing each project schedule length. The decision making process is supposed to be decentralized, with as many local decision makers as the projects. A multi-agent system model, and an iterative combinatorial auction mechanism for the agent coordination are proposed. We provide a dynamic programming formulation for the combinatorial auction problem, and heuristic algorithms for both the combinatorial auction and the bidding process. An experimental analysis on the whole multi-agent system model is discussed.     

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.     

Heuristics for multimode scheduling problems with dedicated resources

We study scheduling problems with multiple modes and dedicated resources arising in production and project management, which constitute a special class of the general multimode resource-constrained project scheduling problem. A task may require simultaneously a set of discrete, renewable resources to be processed and the processing can be performed in different modes, that is with different resource sets, processing times, or costs. Precedence constraints can exist among tasks. The total budget that can be allocated to the project can be limited. The problem consists of identifying a mode for each task and a starting time for its processing respecting precedence, resource, and budget constraints. A graph model and an iterative solution scheme are presented. Specific heuristic algorithms for the cases with and without budget constraints are given and computational results are discussed.     

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.     

Computing redundant resources for the resource constrained project scheduling problem

Several efficient lower bounds and time-bound adjustment methods for the resource constrained project scheduling problem (RCPSP) have recently been proposed. Some of them are based on redundant resources. In this paper we define redundant functions which are very useful for computing redundant resources. We also describe an algorithm for computing all maximal redundant functions. Once all these redundant functions have been determined, we have to identify those that are useful for bounding. Surprisingly, their number is reasonable even for large resource capacities, so a representative subset of them can be tabulated to be used efficiently. Computational results on classical RCPSP instances confirm their usefulness.     

Multi-project scheduling with two-stage decomposition

We consider a non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources. A two-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. In stage one; each project is reduced to a macro-activity with macro-modes. The macro-activities are combined into a single macro-activity network over which the macro-activity scheduling problem (MP) is defined, where the objective is the maximization of the net present value with positive cash flows and the renewable resource requirements are time-dependent. An exact solution procedure and a genetic algorithm (GA) approach are proposed for solving the MP. A GA is also employed to generate an initial solution for the exact solution procedure. The first stage terminates with a post-processing procedure to distribute the remaining resource capacities. Using the start times and the resource profiles obtained in stage one, each project is scheduled in stage two for minimum makespan. Three new test problem sets are generated with 81, 84 and 27 problems each, and three different configurations of solution procedures are tested.     

An exact algorithm for minimizing resource availability costs in project scheduling

A new exact algorithm that solves the Resource Availability Cost Problem (RACP) in project scheduling is shown to yield a significant improvement over the existing algorithm in the literature. The new algorithm consists of a hybrid method where an initial feasible solution is found heuristically. The branching scheme solves a Resource-Constrained Project Scheduling Problem (RCPSP) at each node where the resources of the RACP are fixed. The knowledge of previously solved RCPSPs is used to produce cuts in the search tree. A worst-case-performance theorem is established for this new algorithm. Experiments are performed on instances adapted from the PSPLIB database. The new algorithm can be used to minimize any resource availability cost problem once a procedure for the underlying resource-constrained problem is available.     

带有资源柔性约束的max-NPV分布式多项目调度问题

现有的分布式资源约束多项目调度问题研究中,假定全局资源限量在多项目工期内不可突破且多以工期为优化目标。针对此问题,考虑全局资源可从外部获取,以净现值为目标,构建带有全局资源柔性约束的分布式多项目调度问题的整数规划模型并设计有效的求解算法。首先,界定问题并确定项目现金流的计算方法;然后,针对求解问题的NP-hard属性,设计了遗传-模拟退火混合算法(GA_SA)求解此模型。最后,通过多组数值实验,设计不同算法与GA_SA算法进行比较,并分析了关键参数对多项目净现值的影响。结果表明,GA_SA算法具有较好的求解效果;与传统的全局资源刚性约束条件相比,全局资源柔性使用状态可以显著改善分布式多项目的收益绩效。     

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.     

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.     

基于关键链的敏捷软件开发多项目网络模型

敏捷软件开发因其效率和文档量远低于传统方法在一提出就得到广泛应用,但仍无法有效解决软件开发多项目管理中的资源受限调度问题.将关键链思想应用到包含多个项目的敏捷软件开发问题中,在分析敏捷软件开发多项目网络模型的基础上,建立了数学优化模型;提出了一种适宜敏捷软解开发的多项目网络迭代调度假设与规则,并设计了相应的算法,具体包括关键链选择算法和调度算法;最后进行了实例分析,所得结果与遗传算法的相比从52个单位时间的迭代周期减少到42,使得工期节省了近20%.     

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.     

Mixed-integer linear programming for resource leveling problems

We consider project scheduling problems subject to general temporal constraints, where the utilization of a set of renewable resources has to be smoothed over a prescribed planning horizon. In particular, we consider the classical resource leveling problem, where the variation in resource utilization during project execution is to be minimized, and the so-called “overload problem”, where costs are incurred if a given resource-utilization threshold is exceeded. For both problems, we present new mixed-integer linear model formulations and domain-reducing preprocessing techniques. In order to strengthen the models, lower and upper bounds for resource requirements at particular points in time, as well as effective cutting planes, are outlined. We use CPLEX 12.1 to solve medium-scale instances, as well as instances of the well-known test set devised by Kolisch et al. (1999). Instances with up to 50 activities and tight project deadlines are solved to optimality for the first time.     

Single machine scheduling problem with controllable processing times and resource dependent release times

We consider two single machine scheduling problems with resource dependent release times and processing times, in which the release times and processing times are linearly decreasing functions of the amount of resources consumed. The objective is to minimize the total cost of makespan and resource consumption function that is composed of release time reduction and processing time reduction. In the first problem, the cost of reducing a unit release time for each job is common. We show that the problem can be solved in polynomial time. The second problem assumes different reduction costs of job release times. We show that the problem can be reduced polynomially from the partition problem and thus, is NP-complete.     

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.     

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。     

Approximation algorithms for scheduling on multi-core processor with shared speedup resources

We consider a joint resource partition and scheduling problem. We are given $m$ identical cores and discrete resources of total size $k$. We need to partition the resources among these cores. A set of jobs must be processed non-preemptively on these cores after the resource partition. The processing time of a job on a core depends on the size of resources allocated to that corresponding core. The resource allocation scheme is static, i.e., we cannot change the amount of resources that was allocated to a core during the whole scheduling. Hassidim et al. (2013) investigated this problem with a general processing time function, i.e., the processing time of a job is an arbitrary function of the level of resources allocated to that core. They provided an algorithm with approximation ratio of 36. In this paper, we improve the approximation ratio to 8 by presenting a new resource partition scheme. Next, we consider a special model where the core’s speed is proportional to its allocated resource, then we present two algorithms with improved approximation ratios.     

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.     

Branch and bound based solution algorithms for the budget constrained discrete time/cost trade-off problem

The time/cost trade-off models in project management aim to reduce the project completion time by putting extra resources on activity durations. The budget problem in discrete time/cost trade-off scheduling selects a time/cost mode for each activity so as to minimize the project completion time without exceeding the available budget. There may be alternative modes that solve the budget problem optimally and each solution may have a different total cost value. In this study we consider the budget problem and aim to find the minimum cost solution among the minimum project completion time solutions. We analyse the structure of the problem together with its linear programming relaxation and derive some mechanisms for reducing the problem size. We solve the reduced problem by branch and bound based optimization and heuristic algorithms. We find that our branch and bound algorithm finds optimal solutions for medium-sized problem instances in reasonable times and the heuristic algorithms produce high quality solutions very quickly.