The integration of resource allocation and time buffering for bi-objective robust project scheduling

In the recent decades, the recognition that uncertainty lies at the heart of modern project management has induced considerable research efforts on robust project scheduling for dealing with uncertainty in a scheduling environment. The literature generally provides two main strategies for the development of a robust predictive project schedule, namely robust resource allocation and time buffering. Yet, the previous studies seem to have neglected the potential benefits of an integration between the two. Besides, few efforts have been made to protect simultaneously the project due date and the activity start times against disruptions during execution, which is desperately demanded in practice. In this paper, we aim at constructing a proactive schedule that is not only short in time but also less vulnerable to disruptions. Firstly, a bi-objective optimisation model with a proper normalisation of the two components is proposed in the presence of activity duration variability. Then a two-stage heuristic algorithm is developed which deals with a robust resource allocation problem in the first stage and optimally determines the position and the size of time buffers using a simulated annealing algorithm in the second stage. Finally, an extensive computational experiment on the PSPLIB network instances demonstrates the superiority of the combination between resource allocation and time buffering as well as the effectiveness of the proposed two-stage algorithm for generating proactive project schedules with composite robustness.     

Buffer sizing approach with dependence assumption between activities in critical chain scheduling

The critical chain/buffer management (CC/BM) methodology, proposed by E.M. Goldratt [1997. Critical chain. New York: The North River Press], introduced the concept of buffers to protect the critical chain against the disruptions. The buffer sizes reflect the uncertainty in the estimation of project duration and affect the project scheduling performance. However, the most current buffer sizing approaches make the assumption that project activity durations are independent. In this paper, the effects of the dependence between activities on project duration performances are analysed, a method for determining buffer sizes with dependence assumption between activities is introduced. Specifically, two definitions reflecting dependence, which are the dependence degree and the dependence factor, are integrated into the formulation of buffer sizing approach. The suggested method is tested and compared with the methods with independence assumption, the root square error method, the adaptive procedure with resource tightness and the adaptive procedure with density. The results indicate that the methods with independence assumption may underestimate the buffer size when at least one of the two definitions is at a high level, while the suggested method can provide better protection in such circumstances.     

Resource and time criticality based block spatial scheduling in a shipyard under uncertainty

The block erection area is an important bottleneck resource that determines the throughput and productivity of a shipyard. This study addresses Block Spatial Scheduling (BSS) problem of a shipbuilding project comprising 72 blocks with uncertain erection duration. We adopted priority rules-based simulation approach to overcome the computational complexity of non-deterministic polynomial hard BSS problem. This is one of the earliest studies to introduce resource (space) based criticality index in BSS problem. Four time-based, one resource-based and six combinations of time criticality index (TCI) and resource criticality index (RCI) based priority rules are considered for achieving three objectives: minimisation of expected project duration, minimisation of expected average tardiness of blocks and maximisation of average area utilisation percentage. Seven important implications are derived from results, which can be applied by shipbuilding managers to BSS to increase the productivity of shipyard. Results reveal that priority rule based on TCI×RCI and shortest processing time yield the most and the least efficient trade-off, respectively, between time and resource-oriented objectives. Further, a sensitivity analysis, performed by varying degree of uncertainty, reveals negative effect of uncertainty by increasing variation in objectives. Overall, the derived implications underpin the importance of incorporating RCI in BSS context.     

A new scheduling technique for the resource–constrained project scheduling problem with discounted cash flows

In this paper, we discuss the resource–constrained project scheduling problem with discounted cash flows. We introduce a new schedule construction technique which moves sets of activities to improve the project net present value and consists of two steps. In particular, the inclusion of individual activities into sets, which are then moved together, is crucial in both steps. The first step groups the activities based on the predecessors and successors in the project network, and adds these activities to a set based on their finish time and cash flow. The second step on the contrary does so based on the neighbouring activities in the schedule, which may but need not include precedence related activities. The proposed scheduling method is implemented in a genetic algorithm metaheuristic and we employ a penalty function to improve the algorithm’s feasibility with respect to a tight deadline. All steps of the proposed solution methodology are tested in detail and an extensive computational experiment shows that our results are competitive with existing work.     

基于混合智能算法的多资源约束项目优化调度

 基于关键链项目管理(critical chain project management,CCPM),利用一种混合智能优化算法求解多资源约束项目调度问题,解决传统调度优化算法的不足,提高这类问题的求解质量.首先利用一类启发式算法识别项目关键链,并设置缓冲区尺寸,以项目总工期和在制品库存为优化目标建立数学模型,设计一种混合智能优化算法求解,并对项目问题库中的j30hrs.sm问题和某生产型项目进行实验分析,得到优化的结果.实验表明,采用混合智能算法求解这类问题能得到明显优于一般调度优化算法的结果.     

A model, heuristic procedure and decision support system for solving the movie shoot scheduling problem

Creating a movie shoot schedule is an important part of the movie production process. Even for a small movie project already 50 activities requiring 130 resources such as different actors, director, team, special effects and locations etc. have to be scheduled respecting complex constraints which may be imposed on single resources as well as on every activity. In this paper, we present the movie shoot scheduling problem and formulate a conceptual model. We present a metaheuristic approach for generating operational schedules, outline the modules of the decision support system Schedule This which we have developed and finally we shortly report practical experiences. Our experience from using the DSS in real movie shooting projects shows significant improvements with respect to faster and better scheduling as well as ad hoc re-scheduling.     

Simultaneous planning of the project scheduling and material procurement problem under the presence of multiple suppliers

Simultaneous planning of project scheduling and material procurement can improve the project execution costs. Hence, the issue has been addressed here by a mixed-integer programming model. The proposed model facilitates the procurement decisions by accounting for a number of suppliers offering a distinctive discount formula from which to purchase the required materials. It is aimed at developing schedules with the best net present value regarding the obtained benefit and costs of the project execution. A genetic algorithm is applied to deal with the problem, in addition to a modified version equipped with a variable neighbourhood search. The underlying factors of the solution methods are calibrated by the Taguchi method to obtain robust solutions. The performance of the aforementioned methods is compared for different problem sizes, in which the utilized local search proved efficient. Finally, a sensitivity analysis is carried out to check the effect of inflation on the objective function value.     

不确定资源约束条件下的结构项目排序问题

本文主要建立了具有不确定资源约束条件下的结构项目排序问题的一个数学模型。不确定资源约束主要由固定项目工期、随机项目工期和模糊项目工期组成,其目标函数为项目的整个完工时间(极小)。利用机会约束的置信度(包括某些活动的重要度)和某些有效方法将原不确定问题转化为等价的确定性规划问题。最后我们给出了一个简单的二阶段算法及其数值结果。     

时间—资源权衡协调问题的多目标优化决策模型

时间—资源权衡协调是以追求资源消耗费用极小和项目完工时间最短为目标，在满足项目工期要求下，根据项目活动时间的先后次序与可更新资源约束有效确定项目时间表。提出了一个具有资源约束问题的时间—资源权衡协调问题的多目标优化决策数学模型。在模型中，对相互冲突的项目工期与整个被消耗的资源费用是可权衡调节的。通过权衡协调和调节项目工期与整个资源消耗费用，得到了满足权衡协调关系的满意可行解，并给出了一个数值算例。此外，在对应于资源约束的Lagrangian松弛表示式中，给出了该二人对策问题的有关特性。     

Job shop scheduling heuristics and frequency of scheduling

This paper presents a job scheduling problem. Two important aspects are included in the subsequent analysis. The first is the dynamic nature whereby new jobs arrive to be included intermittently through time. The second is the uncertainty, or error in estimating process times, and the likelihood of machine breakdown. An experiment is presented which shows the performance of a number of heuristics in the form of dispatching disciplines under different scheduling conditions which are determined by the scheduling period and the level of uncertainty in the process times and machine breakdowns. Various different measures of performance which could be of importance to management are considered. These include mean ratio of flow time to process time, mean queueing time, mean lateness, percentage of jobs late and net CPU times required to generate schedules in the simulation process.

Results are presented showing the relationship between the performance of the heuristics relative to the different measures and the rescheduling period. These are discussed in the more general managerial context.     

Robust scheduling in an advanced planning and scheduling environment

A new scheduling problem that appears in an advanced planning and scheduling (APS) environment is discussed. Under the precondition that all materials are available when needed, the problem is formulated as follows: min N i =1 ( D i - E i )/N subject to D i - C i S 0, for all i , where N is the number of customer orders arriving randomly at the shop during a certain period, D i is the estimated due-date for customer order i , E i is the due-date estimation time for customer order i and C i is the completion time for customer order i . Then, D i and C i are endogenous variables and E i is an exogenous variable. The ability to construct a flexible scheduling process that avoids the need to fix ongoing schedules is essential to all APS systems. Therefore, the concept of a due-date buffer is introduced which is expected to enable the production schedules for each customer order to be flexible at the beginning and gradually become fixed as the processing of the order progresses. A simulation-based scheduling algorithm using the concept of a due-date buffer is developed here and subsequently examined through a series of numerical experiments. The obtained computation results show that the performance of due-date buffers is outstanding with respect to complicated production processes having higher utilizations.     

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management. Project scheduling problems depend on precedence relationships and resource constraints, in addition to some other limitations for achieving a subset of goals. Project scheduling problems are dependent on many limitations, including limitations of precedence relationships, resource constraints, and some other limitations for achieving a subset of goals. Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required, which are known and stable during the implementation process. The concept of deterministic project scheduling conflicts with real situations, in which in many cases, some data on the activity' s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations. Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us. We use the multi-mode resource allocation and scheduling model that takes into account the dynamicity features of all parameters, that is, the scheduling process must be flexible to dynamic environment features. In this paper, we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations, in which we apply the proposed heuristic rules (PHR) for scheduling multi-mode resource-constrained projects. Five projects are considered test problems for the PHR. The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems. The results in many cases of the proposed priority rules are very promising, where they achieve better scheduling dates in many test case problems and the same results for the others. The proposed model is based on the dynamic features for project topography.     

Job-shop scheduling with limited capacity buffers

In this paper we investigate job-shop problems where limited capacity buffers to store jobs in non-processing periods are present. In such a problem setting, after finishing processing on a machine, a job either directly has to be processed on the following machine or it has to be stored in a prespecified buffer. If the buffer is completely occupied the job may wait on its current machine but blocks this machine for other jobs. Besides a general buffer model, also specific configurations are considered. The aim of this paper is to find a compact representation of solutions for the jobshop problem with buffers. In contrast to the classical job-shop problem, where a solution may be given by the sequences of the jobs on the machines, now also the buffers have to be incorporated in the solution representation. In a first part, two such representations are proposed, one which is achieved by adapting the alternative graph model and a second which is based on the disjunctive graph model. In a second part, it is investigated whether the given solution representation can be simplified for specific buffer configurations. For the general buffer configuration it is shown that an incorporation of the buffers in the solution representation is necessary, whereas for specific buffer configurations possible simplifications are presented.     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

A multi-objective model for multi-project scheduling and multi-skilled staff assignment for IT product development considering competency evolution

We address a multi-skill project scheduling problem for IT product development in this article. The goal is for product development managers to be able to generate an initial schedule at an early stage of development activities. Due to the complexity of the product structure and functionality, an IT product development effort is divided into multiple projects. Each project includes several tasks, and each task must be completed by an employee who has mastered a certain skill to complete it. A pool of multi-skilled employees is available, and the employees’ skill efficiencies are influenced by both learning and forgetting phenomena. Based on the real-world demands of product development managers, three objectives are simultaneously considered: skill efficiency gain, product development cycle time and costs. To solve this problem, we propose a multi-objective non-linear mixed integer programming model. The Non-dominated Sorting Genetic Algorithm II (NSGA-II)is designed to generate an approximation to the optimal Pareto front of this NP-hard multi-objective optimisation problem. The algorithm produces feasible schedules for all the development projects using the serial schedule generation scheme. We adopt penalty values and individual employee adjustments to address resource conflicts and constraint violations. A weighted ideal point method is used to select the final solution from the approximate Pareto solution set. An application case of a new electrical energy saving product implementation in a leading electrical device company in China is used to illustrate the proposed model and algorithm.     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.     

Optimal feeding buffers for projects or batch supply chains by an exact generalization of the newsvendor result

In project scheduling or batch supply chain operations, a positive (negative) feeding buffer is created by starting an activity before (after) its expected latest start time. Positive feeding buffers provide protection against project tardiness. Assuming linear costs for starting activities earlier and a linear project tardiness penalty, early optimization models for project buffers addressed particular project network structures. By these models it can be shown that when the gating activities precede the only stochastic elements in a project, then there exists an exact generalization of the newsvendor optimal result that characterizes the optimal feeding buffers: the marginal cost of a buffer should match its criticality. This insight is associated with an effective and efficient solution approach by simulation. We show that this result also holds when stochastic elements exist anywhere else within the project and when activities are statistically correlated. Furthermore, the same simulation approach applies. This yields practically optimal feeding buffers even when it is impossible to compute the completion time distribution.     

施工项目中的资源投入比问题

本文的研究,是基于公认的6种基于优先权的启发式方法在本行业的有代表性的项目中的应用,综合项目工期、项目成本和资源利用率等因素,以寻求典型资源的合理的投入比,为项目经理在进行资源分配和进度安排时选择启发式方法和资源投入比时提供一定的参考。     

An iterated-local-search heuristic for the resource-constrained weighted earliness-tardiness project scheduling problem

This paper deals with the weighted earliness-tardiness resource-constrained project scheduling problem with minimum and maximum time lags (WET-RCPSP/max). The problem consists of scheduling the activities of a project subject to prescribed resource and temporal constraints such that the total weighted deviation of the activities' completion times from prescribed due dates is minimized. Key applications are planning of just-in-time production and reactive scheduling. For the (approximative) solution of the WET-RCPSP/max, we present a population-based iterated-local-search heuristic. We also report the results of an experimental performance analysis where this heuristic outperformed state-of-the-art methods.     

Project scheduling with time-varying resource constraints

With industrial projects increasing in complexity and size, determining realizable schedules that efficiently utilize limited resources represents one of the most challenging project management tasks. In this context, the well-known resourceconstrained project scheduling problem has been extensively studied. However, due to its restrictive assumptions, it allows only partial modelling of real-world scheduling problems. Therefore, this paper deals with a generalized version that considers more evolved types of precedence relationships as well as time-varying resource availabilities, e.g. due to maintenance or vacations. For this problem, appropriate heuristic solution methods, based on priority rules and tabu search, are proposed and evaluated concerning their effectiveness.