Network optimization has always been a core problem domain in operations research, as well as in computer science, applied mathematics, and many fields of engineering and management. Network optimization problems arise in a variety of situations, and often in situations that apparently are quite unrelated to networks. These applications are scattered throughout the literature and until recently no single paper, book, or any other reference, summarized these applications. Consequently, the research and practitioner community has not fully appreciated the richness of these applications. This paper attempts to partially satisfy this important need by presenting a collection of applications of the following fundamental network optimization problems: the shortest path problem, the maximum flow problem, the minimum cost flow problem, assignment and matching problems, and the minimum spanning tree problem. We describe 25 applications of these problems and provide references for more than 100 additional applications. This paper is intended to provide an appreciation for the pervasiveness of network optimization problems. We hope that this paper will stimulate researchers and practitioners to model more decisions problems within the framework of network optimization.

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This report summarizes past work in resource-constrained project scheduling problems (RCPSP) and also presents a new RCPSP with a specialized minimum cost objective function. This new RCPSP model focuses on single-resource problems with resource consumption and late delivery costs. This model applies, for example, to a general contractor or sub-contractor in the construction industry facing project deadlines with limited resources and penalties for late completion. We develop a new bin-packing based algorithm to provide good solutions for this problem and describe some computational experience with this algorithm. This paper is separated into two distinct parts. Part 1 (Sections 1 through 5) summarizes the vast literature on RCPSPs and categorizes this literature. Part 2 (Section 6) presents our new RCPSP variant and our heuristic algorithm. 1. Introduction and Classification of RCPSP Problems Resource constrained project scheduling problems (RCPSPs) involve assigning jobs or tasks to a resource or set of resources with limited capacity in order to meet some predefined objective. As we will see, many different objectives are possible and these depend on the goals of the decision maker, but

Abstract. In knowledge generating production processes such as intelligence gathering and news reporting, the quality of the result produced by a given activity depends on its duration, and, due to resource limitations and process deadlines, tradeoffs must invariably be made regarding how much time to devote to various activities to achieve maximum overall effect. In essense, some activities must be executed in faster time cycles than would be desirable under non-constraining circumstances, with consequent degradation of process quality. In this paper, we consider this type of scheduling problem, which we refer to generally as quality maximization. Starting with normal resource-constrained project scheduling problem (RCPSP) assumptions, we define a new type of scheduling problem by additionally associating a quality profile with each activity in the project. Quality profiles have an “anytime ” property, implying that activities can be terminated at any point, with the quality of the output being proportional to duration. Instead of finishing all activities as fast as possible, the goal of scheduling in this context is to maximize the overall quality given a hard project due date. We formulate this quality maximization problem as a constraint-based optimization problem, and present a new constraint posting algorithm for solving this problem that incorporates a linear optimization program. Different constraint posting heuristics are defined and evaluated on a set of quality maximization RCPSP problems constructed from standard reference RCPSP problems. The experimental results show the overall effectiveness of our approach for generating schedules to maximize quality. And ratio-based heuristics provide a promising starting point for stochastic sampling or other schedule refining techniques by solving 100 % problems without backtracking. 1

We study the problem of the manager of a project consisting of two sub-projects or tasks which are outsourced to different subcontractors. The project manager earns more revenue from the project if it is completed faster, but he cannot observe how hard subcontractors work, only the stochastic duration of their tasks. We derive the optimal linear incentive contracts to offer to the subcontractors when the tasks are conducted in series or in parallel. We compare them to the fixed-price contracts often encountered in practice, and discuss when incentive contracts lead to bigger performance improvement. We characterize how the incentive contracts vary with the subcontractors ’ risk aversion and cost of effort, the marginal effect of subcontractor effort, and the variability of task durations. We find that this dependence is sometimes counter-intuitive in nature. For instance, for parallel tasks, if the first agent’s task is on the critical path and his variability increases, the project manager should induce the first agent to work less hard and the second agent to work harder.

For most #rms, new product development is the engine for growth and pro#tability. A #rm's new product success depends on its ability to manage the product development process in a way that employs scarce resources to achieve the goal of the #rm as well as the speci#c project's objectives. Simple and measurable performance metrics have been proposed and applied in order to monitor and compensate the development teams. In this paper, we develop a modeling framework in order to analyze the implications of setting managerial priorities for three commonly used new product performance metrics: 1) time-to-market, 2) product performance, and 3) total development cost. We model new product development as a product performance production' process that requires scarce development resources. Setting a target for development teams for each of these performance metrics can constrain this performance production process and thereby aect the other performance metrics. We model the constrained process a...

to a degree not previously demanded of the research community. Automated agents must recognize important change, assess its ramifications on its local view of activity, request or propagate information to other agents as necessary to reduce uncertainty and accommodate change, and re-schedule activity or select contingencies to stave off plan failure. Additionally, the agents must manage their own limited resources (computational and informational), make decisions within the allowed rule bounds and learn models of appropriate interaction with their human users. All of these tasks must be accomplished within an intrinsically distributed environment with interaction and knowledge circumscribed by formal organization such as chain of command and need-to-know. The BAA set out five primary technical areas: distributed activity coordination, contextdependent coordination autonomy, machine learning, organizational reasoning and meta-cognition. The BAA also identified four key hard research problems: distributed coordination over large dynamic structures, coordination of multiple role units, learning appropriate decision making autonomy with sparse data, adapting activity in real time in response to change and incorporating military decision policies in coordinated decision making.

Contents 1 Introduction 1 1.1 Preface : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 The Time-Cost Tradeoff Problem : : : : : : : : : : : : : : : : : : : : 2 1.3 Generalizations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 1.4 The Edge Diagram : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.5 General Notations : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2 Optimal Parameter Reduction 15 2.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Case Project Duration : : : : : : : : : : : : : : : : : : : : : : : : : : 16 2.3 Case Sum of Weighted Completion Times : : : : : : : : : : : : : : : 22 2.4 Case Sum of Discrete Functions : : : : : : : : : : : : : : : : : : : : : 29 3 Reduction to a flow problem

We develop a multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time–cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations. Ó 2006 Elsevier B.V. All rights reserved.

In this work, we cast the continuous voltage assignment problem as a minimum convexcost network flow problem to solve it both optimally and efficiently. Experiments show that, on real circuits, our algorithm is two orders of magnitude (100X) faster than previous work [1]. Another research group independently developed and published the continuous voltage assignment algorithm that we describe [2]. The purpose of this technical report is to present an alternative mathematical derivation and experimental evaluation of the same algorithm. We also present a new and elegant dynamicprogramming discrete voltage assignment heuristic.