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.     

SHAPE OPTIMIZATION OF A 2D BODY SUBJECTED TO SEVERAL LOADING CONDITIONS

An algorithm for shape optimization based on simultaneous solution of the equations and inequalities arising from Kuhn-Tucker necessary conditions is presented. Regular triangular FE assembly is proposed. Element vertices are associated with design variables directly or through spline parameters defining the boundary of the optimized body. This way, during the iteration procedure, FE assembly is automatically remeshed together with the motion of the optimized boundary. Multiple loading conditions are represented in the problem as equality conditions in the form of a set of equilibrium equations for each loading condition separately. From the necessary condition equations an additional, important relation between cost function, Lagrange multipliers associated with inequality constraints and their limit values is derived. The algorithm combines standard professional FEM programs with an optimizer proposed in the paper which is illustrated with shape optimization of several 2D bodies. The proposed approach is theoretically rigorous and relatively simple for practical applications, and allows considerations sensitivities, adjoint systems and constraints linearization to be avoided.     

A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

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.     

Modeling of surface and subsurface crack behavior under contact load in the presence of lubricant

A new mathematical model for lubricated elastic solids weakened by cracks is proposed. Surface and subsurface cracks are taken into account, and the interaction of lubricant with elastic solids within cavities of surface cracks is regarded as the most interesting aspect of the problem. The boundary conditions characterizing the behavior of lubricant within crack cavities such as pressure rise in crack cavities fully filled with lubricant as well as other boundary and additional conditions are derived. The problem is reduced to a system of integro-differential equations with nonlinear boundary conditions in the form of alternating equations and inequalities. A new iterative numerical method is developed for solution of the proposed problem. The method guarantees conservation of lubricant volumes trapped within closed crack cavities and allows for all three functions (normal and tangential displacement jumps and normal stress applied to crack faces) characterizing the problem solution to be determined simultaneously. Examples of numerical results for surface and subsurface cracks are presented and numerical and asymptotic results for small subsurface cracks are compared to each other. The numerical analysis indicates that depending on a surface crack orientation its normal stress intensity factor may be two or more orders of magnitude higher than the one for a similar subsurface one.     

Use of float consumption rate in resource leveling of construction projects

The management of resources has been claimed to be as important as scheduling methods. Inefficiency in managing resources may bring about severe delays and cost overruns caused by resource shortages in some cases and/or idle resources in others. Therefore, resources should be utilized efficiently to prevent project failures. Resource leveling is one of the approaches that are used for the management of resources. It aims to minimize fluctuations, peaks, and valleys in resource utilization without changing the completion time of a project and the number of resources required. Although the main principle behind traditional resource leveling is achieving an even flow of resources while the original project duration remains unchanged, the literature supports the need to develop an efficient model that discriminates among the activities that are selected for participation in resource leveling. For this purpose, this study has developed a model that considers the float consumption rates of activities in resource leveling. The float consumption rate is the percentage that is set to determine the maximum amount of float which will be consumed to shift the start time of the activity. The proposed model allows a scheduler to assign float consumption rates to each activity that can be used during the resource leveling procedure. When the required information is inputted, the proposed model automatically changes the required daily resources as it shifts the noncritical activities along their available total float times. The proposed model is expected to minimize the likelihood of severe delays and cost overruns. The model is demonstrated by constructing a network and its resource utilization histograms.     

Coordinating supplier selection and project scheduling in resource-constrained construction supply chains

In this paper, we study the problem of coordinating supplier selection and project scheduling, motivated by a real-life operational challenge encountered in the construction industry. In particular, we consider a project network consisting of multiple concurrent projects, with the objective of minimising the total tardiness of all projects. These projects are independent in operation but are subject to shared suppliers and the final quality inspection by the same committee, which then leads to the need for project review sequencing. The earliest starting time of each activity in a project depends on the availability of required resources (both renewable and non-renewable), as well as the activity precedence constraints. We formulate this problem as a mixed integer linear programming model, and propose a mathematical programming-based heuristic to solve the model. The heuristic decomposes the model into subproblems, and solves the subproblems through an iterative process. Each subproblem has a much smaller size and can be solved quickly and independently. The information obtained in solving subproblems is used to guide the search process. Numerical examples show the computational effectiveness of the proposed heuristic, and the benefits of coordination.     

Campaign planning in time-indexed model formulations

This paper deals with a production planning problem typical for process industries. There the production amount of one continuous production run – referred to as a campaign – is often constrained by a lower and/or upper bound or such that it has to be in multiples of a predefined batch size. For this kind of problem, a new mixed-integer-programming model formulation is proposed that is based on a standard lot-sizing model with uniform time buckets. Thereby the concept of time continuity is integrated into a standard bucket-oriented lot-sizing model formulation. Furthermore, some algorithmic (valid inequalities) and modelling enhancements to the formulation are presented. Extensive computational tests show that this new model formulation clearly outperforms a benchmark model formulation. Moreover, they show the additional computational effort associated with different types of restrictions imposed on campaigns.     

Looking for the best modes helps solving the MRCPSP/max

The multi-mode resource-constrained project scheduling problem with minimum and maximum time lags MRCPSP/max is a very general project scheduling problem with multiple execution modes per activity, renewable and non-renewable resources and minimum and maximum time lags between activities. In this paper, we describe SA-EVA, an algorithm for the problem. SA-EVA first searches for the best mode for each activity, without considering renewable resources. In this phase a simulated annealing is applied. Once a mode vector has been chosen, the problem reduces to the RCPSP/max, which SA-EVA solves with EVA, an algorithm designed in Ballestín et al. [2009. An evolutionary algorithm for the resource-constrained project scheduling problem with minimum and maximum time-lags. Journal of Scheduling, 14 (4), online]. Computational results show that SA-EVA outperforms the state-of-the-art algorithms in medium and large instances.     

A Compromise Programming to Task Assignment Problem in Software Development Project

The scheduling process that aims to assign tasks to members is a difficult job in project management. It plays a prerequisite role in determining the project’s quality and sometimes winning the bidding process. This study aims to propose an approach based on multi-objective combinatorial optimization to do this automatically. The generated schedule directs the project to be completed with the shortest critical path, at the minimum cost, while maintaining its quality. There are several real-world business constraints related to human resources, the similarity of the tasks added to the optimization model, and the literature’s traditional rules. To support the decision-maker to evaluate different decision strategies, we use compromise programming to transform multi-objective optimization (MOP) into a single-objective problem. We designed a genetic algorithm scheme to solve the transformed problem. The proposed method allows the incorporation of the model as a navigator for search agents in the optimal solution search process by transferring the objective function to the agents’ fitness function. The optimizer can effectively find compromise solutions even if the user may or may not assign a priority to particular objectives. These are achieved through a combination of non-preference and preference approaches. The experimental results show that the proposed method worked well on the tested dataset.     

Queueing network modelling and lead time compression of pharmaceutical drug development

Designing an optimized pharmaceutical drug development process is an important problem in itself and is of significant practical and research interest. Drug development lead time is a critical performance metric for a pharmaceutical company. In this paper, we develop a multiclass queueing network model to capture the project dynamics in drug development organizations that involve multiple, concurrent projects with contention for human/technical resources. We explore how drug development lead times can be reduced using efficient scheduling and critical mass-based resource management. The model captures important facets of any typical drug development organization, such as concurrent execution of multiple projects, contention for resources, feedback and reworking of project tasks, variability of new project initiations and task execution times, and certain scheduling issues. First, we show, using a class of fluctuation smoothing scheduling policies, that development lead times can be compressed impressively, without having to commit additional resources. Next, we show that critical mass-based project teams can compress lead times further. The model presented, though stylized, is sufficiently generic and conceptual, and will be of much value in new drug development project planning and management.     

Lagrangean relaxation and hybrid simulated annealing tabu search procedure for a two-echelon capacitated facility location problem with plant size selection

In this paper, we study a two-echelon capacitated facility location problem with plant size selection (TECFLP-PSS). Given a set of potential sites for plants, each of which is associated with several possible sizes and corresponding unit production costs, a set of potential sites for capacitated depots and a set of customers with demands, the TECFLP-PSS aims to optimise the plant locations and sizes, the depot locations and the product flows from the opened plants to the opened depots and then to the end customers under single-source constraints. The objective is to satisfy all customers’ demands with a minimum total cost of facility opening, production and transportation. We develop a mixed integer programming model and propose a Lagrangean relaxation approach combined with new valid inequalities and core problem to achieve tight lower and upper bounds for this problem. We then improve the upper bound with a hybrid simulated annealing tabu search procedure. Computational experiments on benchmarks and randomly generated instances are conducted to validate the effectiveness and efficiency of the proposed method.     

R&D project scheduling when activities may fail

An R&D project typically consists of several stages. Due to technological risks, the project may have to be terminated before completion, each stage having a specific likelihood of success. In the project planning and scheduling literature, this technological uncertainty has typically been ignored and project plans are developed only for scenarios in which the project succeeds. In this paper we examine how to schedule projects in order to maximize their expected net present value when the project activities have a probability of failure and when an activity's failure leads to overall project termination. We formulate the problem, show that it is NP-hard, develop a branch-and-bound algorithm that allows us to obtain optimal solutions and provide extensive computational results. In the process, we establish a complexity result for an open problem in single-machine scheduling, namely for the discounted weighted-completion-time objective with general precedence constraints.     

A simulation-based optimization approach to size manufacturing systems

The problem of sizing the resources of a production system is widely encountered both in the literature and in practice. Simulation is a very useful method to identify the necessary number of resources. However, if there are numerous resources, it can become impossible to make a sound ‘trial-and-error’ analysis with simulation models, so that strategies using simulation optimization appear as an attractive approach. Unfortunately, it is necessary to specify a cost function, and, in practice, it is often very difficult to formalize such a function which is used to determine the number of resources that will minimize this cost. In this article, we propose a different modelling approach, which aims at sizing the resources so as to meet the design specifications. In this respect, we search for the minimum number of resources of each type, while satisfying the performance requirements specified in the design project. As a result, the problem is formulated as a stochastic multi-objective optimization problem with constraints. The approach used here is based on simulation, used in conjunction with a bootstrap approach which accounts for the stochastic aspect of the model, and with regression metamodelling in order to derive an analytical formulation of the constraints together. Different multi-objective optimization methods can then be used to solve the problem. An illustrative example is given.     

Simultaneous resource scheduling with batching to minimize weighted flow times

This paper examines scheduling problems in which individual tasks require several resources concurrently. We analyze the situation where, in addition to the need to schedule resources concurrently, it is possible to choose the batch sizes of the tasks. Although such situations arise in both manufacturing and service firms, the likely application of these results will be to repetitive batch manufacturing situations. Several formulations for this problem are presented. Both a lagrangian relaxation and a surrogate relaxation are developed. Heuristics based on these relaxations as well as extensive computational experiments are discussed. The simultaneous resource scheduling problem without batching is quite difficult because jobs need to be synchronized so that individual jobs can capture their required simultaneous resources. Nevertheless, if batch size is introduced as an additional variable, we show that the resulting problem is in some sense easier because of the added flexibility provided by the ability to adjust production batch sizes, which allows us to eliminate 'gaps' in the schedule.     

Single-track multi-hoist scheduling problem: a collision-free resolution based on a branch-and-bound approach

An analytical mathematical model and a branch-and-bound algorithm for single-track cyclic multi-hoist scheduling problems are proposed. The objective is to minimize the cycle time for a given number of hoists. The collision-free single-track constraints are first formulated as disjunctive inequalities. It is then shown that this formulation is a very strict and necessary condition. To be a sufficient and necessary one, two additional properties, like collision-checking rules, must hold in optimal solutions. It is proved that a solution violating these two properties due to their relaxation is always dominated by a collision-free one. Therefore, these two properties are relaxed in the branch-and-bound algorithm. The computation of lower bounds in the branch-and-bound algorithm requires the solution of a specific linear programming problem, which can be solved by using a graph-based polynomial algorithm. Computational results with both benchmark and randomly generated test instances are presented.     

A vulcanising decision planning as a particular one-dimensional cutting stock problem with limited part-related tooling in make-to-order industrial environments

A specialised case of the classical one-dimensional cutting stock problem (1D-CSP) with six main additional features is adapted in this paper to model and solve planning unit operations with limited resources in the make-to-order industrial environment, generating a new decision-making problem. The objective is to satisfy demand using the minimum number of manufacturing cycles. Although there is a large number of applications, this paper proposes a decision model directed at the vulcanising operation during the manufacturing of rubber curved hoses in the automotive industry. Because each vulcanising cycle (VC) uses a considerable amount of resources, the need to minimise the total number of VCs is of importance due to its direct relationship with lead time and productivity. An integer-programming model based on a network optimisation formulation is proposed to solve the problem to optimality and allows for construction of the mathematical model. In addition, due to the limited capacity of computers to solve large instances, a heuristic is developed to obtain near-optimal solutions. Scheduling issues are found in the optimal solution of the integer-programming model, but the heuristic overcomes such obstacles. Numerical experiments demonstrate the efficiency of the heuristic.     

An Examination of Engineering Personnel Assignment Policies in the Multi-Project,Capacity Constrained Situation

Abstract:

Engineering management is often done in a multiproject setting where projects arrive dynamically, engineering human resources are overloaded, and preemption is allowed. In this simulation research, factors of that setting are varied to identify ideal resource assignment policies associated with personnel capacity loading and the use of personnel preemption. The experimental factors include resource overloading, learning rate, and the frequency and length of preemption. The performance measures are project set flow time, resource utilization, and mean project duration. The best situation is one where preemption is not allowed but where engineering resources are overloaded to 200% of capacity. The results of this research are important for engineering resource utilization and for the timely project completion, and have the additional benefit of recommending a best practice for project initiation and engineering project portfolio management.     

Developing a new model for simultaneous scheduling of two grand projects based on game theory and solving the model with Benders decomposition

Grand infrastructure projects, such as dam, power plant, petroleum, and gas industry projects, have several contractors working on them in several independent sub-projects. The concern of reducing the duration of these projects is one of the important issues among various aspects; thus, our aim is to fulfill the requirements by using the game theory approach. In this study, a mixed-integer programming model consisting of game theory and project scheduling is developed to reduce the duration of projects with a minimum increase in costs. In this model, two contractors in successive periods are entered into a step-by-step competition by the employer during dynamic games, considering an exchange in their limited resources. The optimum solution of the game in each stage are selected as the strategy, and the resources during the game are considered to be renewable and limited. The strategy of each contractor can be described as follows: 1) share their resources with the other contractor and 2) not share the resources with the other contractor. This model can act dynamically in all circumstances during project implementation. If a player chooses a non-optimum strategy, then this strategy can immediately update itself at the succeeding time period. The proposed model is solved using the exact Benders decomposition method, which is coded in GAMS software. The results suggest the implementation of four step-by-step games between the contractors. Then, the results of our model are compared with those of the conventional models. The projects’ duration in our model is reduced by 22.2%. The nominal revenue of both contractors has also reached a significant value of 46078 units compared with the relative value of zero units in the original model. Moreover, we observed in both projects the decreases of 19.5%, 20.9%, and 19.7% in the total stagnation of resources of types 1, 2, and 3, respectively.     

New formulations for the setup assembly line balancing and scheduling problem

We present three new formulations for the setup assembly line balancing and scheduling problem (SUALBSP). Unlike the simple assembly line balancing problem, sequence-dependent setup times are considered between the tasks in the SUALBSP. These setup times may significantly influence the station times. Thus, there is a need for scheduling the list of tasks within each station so as to optimize the overall performance of the assembly line. In this study, we first scrutinize the previous formulation of the problem, which is a station-based model. Then, three new formulations are developed by the use of new sets of decision variables. In one of these formulations, the schedule-based formulation, SUALBSP is completely formulated as a scheduling problem. That is, no decision variable in the model directly denotes a station. All the proposed formulations will be improved by the use of several enhancement techniques such as preprocessing and valid inequalities. These improved formulations can be applied to establishing lower bounds on the problem. To assess the performance of new formulations, results of an extensive computational study on the benchmark data sets are also reported.