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.     

Geometric programming with multiplicative slack variables

A posynomial geometric programming problem formulated so that the number of objective function terms is equal to the number of primal variables will have a zero degree of difficulty when augmented by multiplying each constraint term by a slack variable and including a surrogate constraint composed of the product of the slack variables, each raised to an undetermined negative exponent or surrogate multiplier. It is assumed that the original problem is canonical. The exponents in the constraint on the product of the slack variables must be estimated so that the associated solution to the augmented problem, obtained immediately, also solves the original problem. An iterative search procedure for finding the required exponents, thus solving the original problem, is described. The search procedure has proven quite efficient, often requiring only two or three iterations per degree of difficulty of the original problem. At each iteration the well-known procedure for solving a geometric programming problem with a zero degree of difficulty is used and so computations are simple. The solution generated at each iteration is optimal for a problem which differs from the original problem only in the values of some of the constraint coefficients, so intermediate solutions provide useful information.     

Local search techniques for the generalized resource constrained project scheduling problem

In this article we address the problem of scheduling a single project network with both precedence and resource constraints through the use of a local search technique. We choose a solution definition which guarantees precedence feasibility, allowing the procedure to focus on overcoming resource infeasibility. We use the 110-problem data set of Patterson to test our procedure. Our results indicate a significant improvement over the best heuristic results reported to date for these problems (Bell and Han [1]). Two major advantages of the local search algorithm are its ability to handle arbitrary objective functions and constraints and its effectiveness over a wide range of problem sizes. We present a problem example with an objective function and resource constraints which include nonlinear and non-continuous components, which are easily considered by the procedure. The results of our algorithm are significantly better than random solutions to the problem. © 1993 John Wiley & Sons, Inc.     

The pure fixed charge transportation problem

The pure fixed charge transportation problem (PFCTP) is a variation of the fixed charge transportation problem (FCTP) in which there are only fixed costs to be incurred when a route is opened. We present in this paper a direct search procedure using the LIFO decision rule for branching. This procedure is enhanced by the use of 0–1 knapsack problems which determine bounds on partial solutions. Computational results are presented and discussed.     

A node covering algorithm

This paper describes a node covering algorithm, i.e., a procedure for finding a smallest set of nodes covering all edges of an arbitrary graph. The algorithm is based on the concept of a dual node-clique set, which allows us to identify partial covers associated with integer dual feasible solutions to the linear programming equivalent of the node covering problem. An initial partial cover with the above property is first found by a labeling procedure. Another labeling procedure then successively modifies the dual node-clique set, so that more and more edges are covered, i.e., the (primal) infeasibility of the solution is gradually reduced, while integrality and dual feasibility are preserved. When this cannot be continued, the problem is partitioned and the procedure applied to the resulting subproblems. While the steps of the algorithm correspond to sequences of dual simplex pivots, these are carried out implicitly, by labeling. The procedure is illustrated by examples, and some early computational experience is reported. We conclude with a discussion of potential improvements and extensions.     

Routing in packet-switched communication networks with different criticality classes of communicating node pairs

This paper addresses the routing problem with reliability requirements in packet-switched communication networks. In this problem, two classes of communicating node pairs are considered: less critical and highly critical node pairs. We develop a model which identifies a primary route for each less critical node pair and both a primary and a secondary (back up) route for each highly critical node pair. The objective is to minimize the average delay encountered by messages. A solution procedure based on a relaxation of the problem is presented. Computational results over a wide range of problem structures show that the procedure is very effective. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 485–505, 1997     

An iterative algorithm for the multifacility minimax location problem with euclidean distances

An iterative solution method is presented for solving the multifacility location problem with Euclidean distances under the minimax criterion. The iterative procedure is based on the transformation of the multifacility minimax problem into a sequence of squared Euclidean minisum problems which have analytical solutions. Computational experience with the new method is also presented.     

Capacitated lot‐sizing and scheduling with parallel machines,back‐orders,and setup carry‐over

We address the capacitated lot‐sizing and scheduling problem with setup times, setup carry‐over, back‐orders, and parallel machines as it appears in a semiconductor assembly facility. The problem can be formulated as an extension of the capacitated lot‐sizing problem with linked lot‐sizes (CLSPL). We present a mixed integer (MIP) formulation of the problem and a new solution procedure. The solution procedure is based on a novel “aggregate model,” which uses integer instead of binary variables. The model is embedded in a period‐by‐period heuristic and is solved to optimality or near‐optimality in each iteration using standard procedures (CPLEX). A subsequent scheduling routine loads and sequences the products on the parallel machines. Six variants of the heuristic are presented and tested in an extensive computational study. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

Solving the multiperiod assignment problem with start-up costs using dual ascent

In this article we consider a multiperiod assignment problem where the assignment cost of assigning job i to machine j varies from one time period to the next. A start-up cost is incurred whenever the job processed by a machine in the current time period is different from the one processed in the previous time period. This problem is modeled as an integer programming problem for which a dual ascent approximate procedure is developed. Our computational results show that our procedure outperforms the more common Lagrangian-relaxation-based subgradient procedure by a significant margin. It is also found to be faster than MPSX/370 by many orders of magnitude. © 1993 John Wiley & Sons, Inc.     

A worst‐case formulation for constrained ranking and selection with input uncertainty

In this research, we consider robust simulation optimization with stochastic constraints. In particular, we focus on the ranking and selection problem in which the computing time is sufficient to evaluate all the designs (solutions) under consideration. Given a fixed simulation budget, we aim at maximizing the probability of correct selection (PCS) for the best feasible design, where the objective and constraint measures are assessed by their worst‐case performances. To simplify the complexity of PCS, we develop an approximated probability measure and derive the asymptotic optimality condition (optimality condition as the simulation budget goes to infinity) of the resulting problem. A sequential selection procedure is then designed within the optimal computing budget allocation framework. The high efficiency of the proposed procedure is tested via a number of numerical examples. In addition, we provide some useful insights into the efficiency of a budget allocation procedure.     

A novel formulation of material nonlinear analysis in structural mechanics

This article demonstrates a novel approach for material nonlinear analysis. This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior. Use of elastic moduli is eliminated. Instead, stress and strain functions are used as the material input in the analysis procedure. These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting. This way, the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior. It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results, easy to adopt and simple in calculations. The method eliminates all types of linearity assumptions in basic derivations of equations and hence, eliminates all types of possibility of errors in the analysis procedure as well. As it is required to know stress distribution in the structural body by proper modelling and structural idealization, the proposed analysis approach can be regarded as stress-based analysis procedure. Basic problems such as uniaxial problem, beam bending, and torsion problems are solved. It is found that approach is very suitable for solving the problems of fracture mechanics. Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated. The approach solves the fracture problem with relative ease in strength of material style calculations. For all problems, results are compared with the classical displacement-based liner theory.     

Determining adjacent vertices on assignment polytopes

To rank the solutions to the assignment problem using an extreme point method, it is necessary to be able to find all extreme points which are adjacent to a given extreme solution. Recent work has shown a procedure for determining adjacent vertices on transportation polytopes using a modification of the Chernikova Algorithm. We present here a procedure for assignment polytopes which is a simplification of the more general procedure for transportation polytopes and which also allows for implicit enumeration of adjacent vertices.     

A primal-dual algorithm for the dynamic lotsizing problem with joint set-up costs

In this article the multi-item dynamic lotsizing problem with joint set-up costs (LPJS) is considered. A tight formulation of the problem and the dual of the linear relaxation of this formulation is presented. A procedure to solve this dual problem is developed where the solution provides a strong lower bound for the LPJS. This lower bound is used in a branch and bound procedure to find an optimal solution to the problem. The extensive computational experiments with this procedure revealed that it outperforms the other available branch and bound algorithm in the literature. With the proposed algorithm the average time requirement was about 113 seconds on a 486DX33 processor for solving a difficult class of LPJS problems that have 50 items and 24 periods. © 1995 John Wiley & Sons, Inc.     

基于NSGA-Ⅱ多目标优化的C2组织设计

把NSGA-Ⅱ算法用于求解C2组织设计问题.分析了C2组织设计常见处理算法在优化目标处理和算法流程两方面存在的问题,给出用NSGA-Ⅱ算法求解C2组织设计问题的算法设置.把NSGA-Ⅱ这样一种多目标优化算法引入C2组织设计问题,改变了以往研究此类问题时只能定义单个指标的情况,使领域专家能定义和研究新的优化目标.针对C2组织设计问题的特性做了调整后,实验结果数据表明NSGA-Ⅱ可以迅速地同时得到高质量和富有启发性的一群优化结果.     

TTT transforms and age replacements with discounted costs

The ordinary age replacement problem consists of finding an optimal age at which a unit, needed in a continuous production process, should be replaced in order to minimize the average long-run cost per unit time. Bergman introduced a graphical procedure based on the total-time-on-test (TTT) concept for the analysis of the age replacement problem. In this article, that idea is generalized to the situation of discounted costs. We also study a more general age replacement problem in which we have a form of imperfect repair.     

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     

Cyclic scheduling in flow lines: Modeling observations,effective heuristics and a cycle time minimization procedure

In this paper we address the cyclic scheduling problem in flow lines. We develop a modeling framework and an integer programming formulation of the problem. We subsequently present exact and approximate solution procedures. The exact solution procedure is a branch-and-bound algorithm which uses Lagrangian and station-based relaxations of the integer programming formulation of the problem as the lower bounding method. Our heuristic procedures show a performance superior to the available ones in the literature. Finally, we address the stability issue in cyclic scheduling, demonstrate its relationship to the work-in-progress inventory control of a flow line, and present a very simple procedure to generate stable schedules in flow lines. © 1996 John Wiley & Sons, Inc.     

Application of the GLM technique to a production planning problem

Generalized Lagrange Multipliers (GLM) are used to develop an algorithm for a type of multiproduct single period production planning problem which involves discontinuities of the fixed charge variety. Several properties of the GLM technique are developed for this class of problems and from these properties an algorithm is obtained. The problem of resolving the gaps which are exposed by the GLM procedure is considered, and an example involving a quadratic cost function is explored in detail.     

An easy solution for a special class of fixed charge problems

The fixed charge problem is a mixed integer mathematical programming problem which has proved difficult to solve in the past. In this paper we look at a special case of that problem and show that this case can be solved by formulating it as a set-covering problem. We then use a branch-and-bound integer programming code to solve test fixed charge problems using the setcovering formulation. Even without a special purpose set-covering algorithm, the results from this solution procedure are dramatically better than those obtained using other solution procedures.