Heuristic scheduling of resource-constrained projects with cash flows

Resource-constrained project scheduling with cash flows occurs in many settings, ranging from research and development to commercial and residential construction. Although efforts have been made to develop efficient optimal procedures to maximize the net present value of cash flows for resource-constrained projects, the inherent intractability of the problem has led to the development of a variety of heuristic methods to aid in the development of near-optimal schedules for large projects. This research focuses on the use of insights gained from the solution of a relaxed optimization model in developing heuristic procedures to schedule projects with multiple constrained resources. It is shown that a heuristic procedure with embedded priority rules that uses information from the revised solution of a relaxed optimization model increases project net present value. The heuristic procedure and nine different embedded priority rules are tested in a variety of project environments that account for different network structures, levels of resource constrainedness, and cash-flow parameters. Extensive testing with problems ranging in size from 21 to 1000 activities shows that the new heuristic procedures dominate heuristics using information from the critical path method (CPM), and in most cases outperform heuristics from previous research. The best performing heuristic rules classify activities into priority and secondary queues according to whether they lead to immediate progress payments, thus front loading the project schedule. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 365–381, 1997     

Multiple resource leveling in construction systems through variation of activity intensities

The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical-path-analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.     

Heuristics for the location of inspection stations on a network

This article considers the preventive flow interception problem (FIP) on a network. Given a directed network with known origin‐destination path flows, each generating a certain amount of risk, the preventive FIP consists of optimally locating m facilities on the network in order to maximize the total risk reduction. A greedy search heuristic as well as several variants of an ascent search heuristic and of a tabu search heuristic are presented for the FIP. Computational results indicate that the best versions of the latter heuristics consistently produce optimal or near optimal solutions on test problems. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 287–303, 2000     

A heuristic approach to bicriteria scheduling

We consider the problem of sequencing jobs on a single machine while minimizing a nondecreasing function of two criteria. We develop a heuristic procedure that quickly finds a good solution for bicriteria scheduling. The procedure is based on using several arcs in the criterion space that are representative of the possible locations of nondominated solutions. By sampling a small number of points on these arcs, a promising point is identified in the criterion space for each arc. An efficient sequence in the neighborhood of each of the promising points is found and the best of these efficient sequences is selected as the heuristic solution. We implement the procedure for two different bicriteria scheduling problems: (i) minimizing total flowtime and maximum tardiness and (ii) minimizing total flowtime and maximum earliness. The computational experience on a wide variety of problem instances show that the heuristic approach is very robust and yields good solutions. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 777–789, 1999     

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     

An efficient heuristic for large set covering problems

A heuristic solution procedure for set covering is presented that works well for large, relatively dense problems. In addition, a confidence interval is established about the unknown global optimum. Results are presented for 30 large randomly generated problems.     

Discrete equal‐capacity p‐median problem

This paper examines the discrete equal‐capacity p‐median problem that seeks to locate p new facilities (medians) on a network, each having a given uniform capacity, in order to minimize the sum of distribution costs while satisfying the demand on the network. Such problems arise, for example, in local access and transport area telecommunication network design problems where any number of a set of p facility units can be constructed at the specified candidate sites (hence, the net capacity is an integer multiple of a given unit capacity). We develop various valid inequalities, a separation routine for generating cutting planes that are specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for this class of problems. © 2000 John & Sons, Inc. Naval Research Logistics 47: 166–183, 2000.     

Models and algorithms for shuffling problems in steel plants

In this article, we study item shuffling (IS) problems arising in the logistics system of steel production. An IS problem here is to optimize shuffling operations needed in retrieving a sequence of steel items from a warehouse served by a crane. There are two types of such problems, plate shuffling problems (PSP) and coil shuffling problems (CSP), considering the item shapes. The PSP is modeled as a container storage location assignment problem. For CSP, a novel linear integer programming model is formulated considering the practical stacking and shuffling features. Several valid inequalities are constructed to accelerate the solving of the models. Some properties of optimal solutions of PSP and CSP are also derived. Because of the strong NP‐hardness of the problems, we consider some special cases of them and propose polynomial time algorithms to obtain optimal solutions for these cases. A greedy heuristic is proposed to solve the general problems and its worst‐case performances on both PSP and CSP are analyzed. A tabu search (TS) method with a tabu list of variable length is proposed to further improve the heuristic solutions. Without considering the crane traveling distance, we then construct a rolling variable horizon heuristic for the problems. Numerical experiments show that the proposed heuristic algorithms and the TS method are effective. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A heuristic routine for solving large loading problems

The loading problem involves the optimal allocation of n objects, each having a specified weight and value, to m boxes, each of specified capacity. While special cases of these problems can be solved with relative ease, the general problem having variable item weights and box sizes can become very difficult to solve. This paper presents a heuristic procedure for solving large loading problems of the more general type. The procedure uses a surrogate procedure for reducing the original problem to a simpler knapsack problem, the solution of which is then employed in searching for feasible solutions to the original problem. The procedure is easy to apply, and is capable of identifying optimal solutions if they are found.     

Interval estimation of a global optimum for large combinatorial problems

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case

The dynamics of the environment in which supply chains evolve requires that companies frequently redesign their logistics distribution networks. In this paper we address a multiperiod single‐sourcing problem that can be used as a strategic tool for evaluating the costs of logistics network designs in a dynamic environment. The distribution networks that we consider consist of a set of production and storage facilities, and a set of customers who do not hold inventories. The facilities face production capacities, and each customer's demand needs to be delivered by a single facility in each period. We deal with the assignment of customers to facilities, as well as the location, timing, and size of inventories. In addition, to mitigate start and end‐of‐study effects, we view the planning period as a typical future one, which will repeat itself. This leads to a cyclic model, in which starting and ending inventories are equal. Based on an assignment formulation of the problem, we propose a greedy heuristic, and prove that this greedy heuristic is asymptotically feasible and optimal in a probabilistic sense. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 412–437, 2003     

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

A single server is faced with a collection of jobs of varying duration and urgency. Each job has a random lifetime during which it is available for nonpreemptive service. Should a job's lifetime expire before its service begins then it is lost from the system unserved. The goal is to schedule the jobs for service to maximize the expected number served to completion. Two heuristics have been proposed in the literature. One (labeled π^S) operates a static priority among the job classes and works well in a “no premature job loss” limit, whereas the second (π^M) is a myopic heuristic which works well when lifetimes are short. Both can exhibit poor performance for problems at some distance from the regimes for which they were designed. We develop a robustly good heuristic by an approximative approach to the application of a policy improvement step to the asymptotically optimal heuristic π^S, in which we use a fluid model to obtain an approximation for the value function of π^S. The performance of the proposed heuristic is investigated in an extensive numerical study. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

An efficient heuristic procedure for the capacitated warehouse location problem

This paper introduces an efficient heuristic procedure for solving a special class of mixed integer programming problem called the capacitated warehouse (plant) location problem. This procedure parallels the work reported earlier in [9] on the uncapacitated warehouse location problem. The procedure can be viewed as tracing a judiciously selected path of the branch and bound tree (from the initial node to the terminal node) to arrive at a candidate solution. A simple backtracking scheme is also incorporated in the procedure to investigate possible improvement in the solution. Computational results on problems found in the literature look quite encouraging.     

Using hybrid metaheuristics for the one‐way and two‐way network design problem

A network with traffic between nodes is known. The links of the network can be designed either as two‐way links or as one‐way links in either direction. The problem is to find the best configuration of the network which minimizes total travel time for all users. Branch and bound optimal algorithms are practical only for small networks (up to 15 nodes). Effective simulated annealing and genetic algorithms are proposed for the solution of larger problems. Both the simulated annealing and the genetic algorithms propose innovative approaches. These innovative ideas can be used in the implementation of these heuristic algorithms for other problems as well. Additional tabu search iterations are applied on the best results obtained by these two procedures. The special genetic algorithm was found to be the best for solving a set of test problems. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 449–463, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10026     

A heuristic procedure for allocating tasks in fault-tolerant distributed computer systems

One way of achieving the increased levels of system reliability and availability demanded by critical computer-based control systems is through the use of fault-tolerant distributed computer systems. This article addresses the problem of allocating a set of m tasks among a set of n processors in a manner that will satisfy various task assignment, system capacity, and task scheduling constraints while balancing the workload across processors. We discuss problem background, problem formulation, and a known heuristic procedure for the problem. A new solution-improving heuristic procedure is introduced, and computational experience with the heuristics is presented. With only a modest increase in the amount of computational effort, the new procedure is demonstrated to improve dramatically solution quality as well as obtain near-optimal solutions to the test problems.     

An efficient heuristic procedure for the uncapacitated warehouse location problem

This paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.     

A multifacility capacity expansion model with joint expansion set-up costs

This article describes a multifacility capacity expansion model in which the different facility types represent different quality levels. These facility types are used to satisfy a variety of deterministic demands over a finite number of discrete time periods. Applications for the model can be found in cable sizing problems associated with the planning of communication networks. It is assumed that the cost function associated with expanding the capacity of any facility type is concave, and that a joint set-up cost is incurred in any period in which one or more facilities are expanded. The model is formulated as a network flow problem from which properties associated with optimal solutions are derived. Using these properties, we develop a dynamic programming algorithm that finds optimal solutions for problems with a few facilities, and a heuristic algorithm that finds near-optimal solutions for larger problems. Numerical examples for both algorithms are discussed.     

Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998