Maximizing project cash availability

Consider a project during the life cycle of which there are cash payouts and in‐flows. To better meet his financial commitments, the project owner would like to meet all deadlines without running out of cash. We show that the cash availability objective is similar to the total weighted flowtime used to measure work‐in‐progress performance in the scheduling and inventory control literatures. In this article we provide several specialized solution methods for the problem of minimizing total weighted flowtime in an arbitrary acyclic project network, subject to activity release times and due dates, where the activity weights may be positive or negative and represent cash in‐ and out‐flows. We describe the structure of an optimal solution and provide several efficient algorithms and their complexity based on mincost and maxflow formulations. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Client‐contractor bargaining on net present value in project scheduling with limited resources

The client‐contractor bargaining problem addressed here is in the context of a multi‐mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity‐on‐Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two‐party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

A bidirectional heuristic for maximizing the net present value of large‐scale projects subject to limited resources

We consider the scheduling of large‐scale projects to maximize the project net present value given temporal and resource constraints. The net present value objective emphasizes the financial aspects of project management. Temporal constraints between the start times of activities make it possible to handle practical problem assumptions. Scarce resources are an expression of rising cost. Since optimization techniques are not expedient to solve such problems and most heuristic methods known from literature cannot deal with general temporal constraints, we propose a new bidirectional priority‐rule based method. Scheduling activities with positive cash flows as early and activities with negative cash flows as late as possible results in a method which is completed by unscheduling techniques to cope with scarce resources. In a computational experiment, we compare the well‐known serial generation scheme where all activities are scheduled as early as possible with the proposed bidirectional approach. On the basis of a comprehensive data set known from literature containing instances with up to 1002 activities, the efficiency of the new approach is demonstrated. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Multi‐period maintenance scheduling of tree networks with minimum flow disruption

We introduce a multi‐period tree network maintenance scheduling model and investigate the effect of maintenance capacity restrictions on traffic/information flow interruptions. Network maintenance refers to activities that are performed to keep a network operational. For linear networks with uniform flow between every pair of nodes, we devise a polynomial‐time combinatorial algorithm that minimizes flow disruption. The spiral structure of the optimal maintenance schedule sheds insights into general network maintenance scheduling. The maintenance problem on linear networks with a general flow structure is strongly NP‐hard. We formulate this problem as a linear integer program, derive strong valid inequalities, and conduct a polyhedral study of the formulation. Polyhedral analysis shows that the relaxation of our linear network formulation is tight when capacities and flows are uniform. The linear network formulation is then extended to an integer program for solving the tree network maintenance scheduling problem. Preliminary computations indicate that the strengthened formulations can solve reasonably sized problems on tree networks and that the intuitions gained from the uniform flow case continue to hold in general settings. Finally, we extend the approach to directed networks and to maintenance of network nodes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A genetic algorithm with neighborhood search for the resource‐constrained project scheduling problem

The resource‐constrained project scheduling problem (RCPSP) consists of a set of non‐preemptive activities that follow precedence relationship and consume resources. Under the limited amount of the resources, the objective of RCPSP is to find a schedule of the activities to minimize the project makespan. This article presents a new genetic algorithm (GA) by incorporating a local search strategy in GA operators. The local search strategy improves the efficiency of searching the solution space while keeping the randomness of the GA approach. Extensive numerical experiments show that the proposed GA with neighborhood search works well regarding solution quality and computational time compared with existing algorithms in the RCPSP literature, especially for the instances with a large number of activities. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Scheduling with parallel processors and linear delay costs

This paper deals with the sequencing problem of minimizing linear delay costs with parallel identical processors. The theoretical properties of this m-machine problem are explored, and the problem of determining an optimum scheduling procedure is examined. Properties of the optimum schedule are given as well as the corresponding reductions in the number of schedules that must be evaluated in the search for an optimum. An experimental comparison of scheduling rules is reported; this indicates that although a class of effective heuristics can be identified, their relative behavior is difficult to characterize.     

An efficient metaheuristic for integrated scheduling and staffing IT projects based on a generalized minimum cost flow network

Scheduling IT projects and assigning the project work to human resources are an important and common tasks in almost any IT service company. It is particularly complex because human resources usually have multiple skills. Up to now only little work has considered IT‐specific properties of the project structure and human resources. In this article, we present an optimization model that simultaneously schedules the activities of multiple IT projects with serial network structures and assigns the project work to multiskilled internal and external human resources with different efficiencies. The goal is to minimize costs. We introduce a metaheuristic that decomposes the problem into a binary scheduling problem and a continuous staffing problem where the latter is solved efficiently by exploiting its underlying network structure. For comparison, we solve the mixed–binary linear program with a state–of–the–art commercial solver. The impacts of problem parameters on computation time and solution gaps between the metaheuristic and the solver are assessed in an experimental study. Our results show that the metaheuristic provides very favorable results in considerable less time than the solver for midsize problems. For larger problems, it shows a similar performance while the solver fails to return feasible solutions. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 111–127, 2012     

Sensitivity curves for effective project management

A key problem in project management is to decide which activities are the most important to manage and how best to manage them. A considerable amount of literature has been devoted to assigning “importance” measures to activities to help with this important task. When activity times are modeled as random variables, these activity importance measures are more complex and difficult to use. A key problem with all existing measures is that they summarize the importance in a single number. The result is that it is difficult for managers to determine a range of times for an activity that might be acceptable or unacceptable. In this paper, we develop sensitivity curves that display the most useful measures of project performance (in terms of schedule) as a function of an activity's time. The structure of the networks allows us to efficiently estimate these curves for all desired activities, all desired time ranges, and all desired measures in a single set of simulation runs. The resulting curves provide insights that are not available when considering summarized measures alone. Chief among these insights is the ability to identify an acceptable range of times for an activity that will not lead to negative scheduling consequences. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 481–497, 2003     

一种用于SpaceWire网络的混合路由机制设计*

针对星上系统总线多元性导致的星载网络接口和协议不能标准化的发展瓶颈,本文基于SpaceWire总线协议,通过将静态路由(时间触发)与动态路由(事件触发)机制结合,实现了控制数据和载荷数据共用网络。静态路由完全遵循SpaceWire-D协议,在保证确定性传输的同时,通过启发式调度算法首次实现了多时间窗并行调度,并提出利用最大公约数法设计时间窗,以提高网络吞吐量；动态路由通过对随机事件和载荷数据分配优先级,实现传输路径冲突时对紧急任务的优先处理。最后在OPENT中搭建网络系统仿真模型,对所提出的路由机制进行了仿真。实验结果表明,静态路由时段网络吞吐量较现有调度算法有明显提高,动态路由实现了紧急事件优先传输。     

Two‐agent scheduling on a single sequential and compatible batching machine

We study two‐agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that depends on the completion times of its own jobs only. We consider several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. Our goal is to find an optimal schedule that minimizes the objective value of one agent, subject to an upper bound on the objective value of the other agent. For each problem under consideration, we provide either a polynomial‐time or a pseudo‐polynomial‐time algorithm to solve it. We also devise a fully polynomial‐time approximation scheme when both agents’ scheduling criteria are the weighted number of tardy jobs.     

Project scheduling under competition

We introduce and investigate the problem of scheduling activities of a project by a firm that competes with another firm (the competitor) that has to perform the same project. The profit that the firm gets from each activity depends on whether the firm finishes the activity before or after its competitor. The objective is to maximize the guaranteed (worst‐case) profit. We assume that both the firm and the competitor can perform only one activity at a time. We perform a detailed complexity analysis of the problem, and consider problems with and without precedence constraints, with and without delay of the competitor, with general and equal processing times of activities. For polynomially solvable cases (which include, for example, all the considered problems without delay of the competitor), we present easily implementable and intuitive rules that allow us to obtain optimal schedules in linear or almost linear time. For some NP‐hard cases, we present pseudopolynomial algorithms and fast heuristics with worst‐case approximation guarantees. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A self‐adapting genetic algorithm for project scheduling under resource constraints

This papers deals with the classical resource‐constrained project scheduling problem (RCPSP). There, the activities of a project have to be scheduled subject to precedence and resource constraints. The objective is to minimize the makespan of the project. We propose a new heuristic called self‐adapting genetic algorithm to solve the RCPSP. The heuristic employs the well‐known activity list representation and considers two different decoding procedures. An additional gene in the representation determines which of the two decoding procedures is actually used to compute a schedule for an individual. This allows the genetic algorithm to adapt itself to the problem instance actually solved. That is, the genetic algorithm learns which of the alternative decoding procedures is the more successful one for this instance. In other words, not only the solution for the problem, but also the algorithm itself is subject to genetic optimization. Computational experiments show that the mechanism of self‐adaptation is capable to exploit the benefits of both decoding procedures. Moreover, the tests show that the proposed heuristic is among the best ones currently available for the RCPSP. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 433–448, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10029     

Balancing and optimizing a portfolio of R&D projects

A mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), is presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multidimensional knapsack problem. Exact solution of such problems is generally difficult, but can be accomplished in reasonable time using specialized algorithms. The main contribution of this paper is an examination of two important issues related to formulation of project selection models such as the one presented here. If partial funding and implementation of projects is allowed, the resulting formulation is a linear programming (LP) problem which can be solved quite easily. Several plausible assumptions about how partial funding impacts project value are presented. In general, our examples suggest that the problem might best be formulated as a nonlinear programming (NLP) problem, but that there is a need for further research to determine an appropriate expression for the value of a partially funded project. In light of that gap in the current body of knowledge and for practical reasons, the LP relaxation of this model is preferred. The LP relaxation can be implemented in a spreadsheet (even for relatively large problems) and gives reasonable results when applied to a test problem based on GM's R&D project selection process. There has been much discussion in the literature on the topic of assigning a quantitative measure of value to each project. Although many alternatives are suggested, no one way is universally accepted as the preferred way. There does seem to be general agreement that all of the proposed methods are subject to considerable uncertainty. A systematic way to examine the sensitivity of project selection decisions to variations in the measure of value is developed. It is shown that the solution for the illustrative problem is reasonably robust to rather large variations in the measure of value. We cannot, however, conclude that this would be the case in general. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 18–40, 2001     

Scheduling for parallel dedicated machines with a single server

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is N P‐hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst‐case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two‐machine flow shop and the open shop problems with a single server are also shown to be N P‐hard in the strong sense. However, we reduce the two‐machine flow shop no‐wait problem with a single server to the Gilmore—Gomory traveling salesman problem and solve it in polynomial time. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 304–328, 2000     

A metaheuristic scheduling procedure for resource-constrained projects with cash flows

Resource-constrained project scheduling problems with cash flows (RCPSPCF) are complex, combinatorial optimization problems. Many heuristics have been reported in the literature that produce reasonable schedules in limited project environments. However, the lack of a heuristic that dominates under differing project conditions can lead to a suboptimal choice of an appropriate heuristic for scheduling any given project. This may result in poor schedules and monetary losses. This paper reports on the application of the tabu search metaheuristic procedure for the RCPSPCF. Strategies for neighborhood generation and candidate selection that exploit the special features of the problem are combined with a simple multiheuristic start procedure. Extensive experimentation, with multiple data sets and comparison with an upper bound, indicates a significant improvement, both in project Net Present Value (NPV) as well as the number of projects, where the metaheuristic outperforms the best known heuristics in the literature. More specifically, this procedure produces the best schedules in over 85% of the projects tested, in contrast to the best single-pass heuristics which have been shown to dominate in at most 20% of the same cases. This iterative, general purpose heuristic is able to adapt significantly better to the complex interactions of the many critical parameters of the RCPSPCF than single-pass heuristics that use more specific information about each project environment. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 912–927, 1999     

The resource constrained project scheduling problem with multiple crashable modes: An exact solution method

We introduce a formulation and an exact solution method 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) within the mode. This problem is a natural combination of the time/cost tradeoff problem and the resource constrained project scheduling problem. It involves the determination, for each activity, of its resource requirements, the extent of crashing, and its start time so that the total project cost is minimized. We present a branch and bound procedure and report computational results with a set of 160 problems. Computational results demonstrate the effectiveness of our procedure. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 107–127, 2001     

Multiproduct batching and scheduling with buffered rework: The case of a car paint shop

We study a problem of scheduling products on the same facility, which is motivated by a car paint shop. Items of the same product are identical. Operations on the items are performed sequentially in batches, where each batch is a set of operations on the same product. Some of the produced items are of the required good quality and some items can be defective. Defectiveness of an item is determined by a given simulated function of its product, its preceding product, and the position of its operation in the batch. Defective items are kept in a buffer of a limited capacity, and they are then remanufactured at the same facility. A minimum waiting time exists for any defective item before its remanufacturing can commence. Each product has a sequence independent setup time which precedes its first operation or its operation following an operation of another product. A due date is given for each product such that all items of the same product have the same due date and the objective is to find a schedule which minimizes maximum lateness of product completion times with respect to their due dates. The problem is proved NP‐hard in the strong sense, and a heuristic Group Technology (GT) solution approach is suggested and analyzed. The results justify application of the GT approach to scheduling real car paint shops with buffered rework. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 458–471, 2014     

Scheduling recurrent construction

A problem we call recurrent construction involves manufacturing large, complex, expensive products such as airplanes, houses, and ships. Customers order configurations of these products well in advance of due dates for delivery. Early delivery may not be permitted. How should the manufacturer determine when to purchase and release materials before fabrication, assembly, and delivery? Major material expenses, significant penalties for deliveries beyond due dates, and long product makespans in recurrent construction motivate choosing a release timetable that maximizes the net present value of cash flows. Our heuristic first projects an initial schedule that dispatches worker teams to tasks for the backlogged products, and then solves a series of maximal closure problems to find material release times that maximize NPV. This method compares favorably with other well‐known work release heuristics in solution quality for large problems over a wide range of operating conditions, including order strength, cost structure, utilization level, batch policy, and uncertainty level. Computation times exhibit near linear growth in problem size. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

The open shop scheduling problem with a given sequence of jobs on one machine

The paper considers the open shop scheduling problem to minimize the make-span, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not allowed, the problem is NP-hard in the strong sense if the number of machines is variable, and is NP-hard in the ordinary sense in the case of two machines. For the latter case we give a heuristic algorithm that runs in linear time and produces a schedule with the makespan that is at most 5/4 times the optimal value. We also show that the two-machine problem in the nonpreemptive case is solvable in pseudopolynomial time by a dynamic programming algorithm, and that the algorithm can be converted into a fully polynomial approximation scheme. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 705–731, 1998     

Time-cost tradeoffs in uncertain empirical research projects

This paper explores the relationship between research project cost and expected time to completion under various scheduling strategies; it assumes that many potential technical approaches to the research problem can be identified; and that each approach has a low but finite subjective probability of success. It is shown that under a variety of assumptions, expected time to project completion can be reduced, but that as a result expected project cost rises at an increasing rate. Some cases in which this convex time-cost tradeoff relationship might not hold generally are identified. When the time-cost tradeoff function is convex, the desirability of concurrent as opposed to series scheduling of approaches depends crucially upon the depth of the stream of benefits expected to be realized upon successful project completion. The deeper the benefit stream is, the more desirable concurrent scheduling is.