Minimizing mean tardiness and earliness in single-machine scheduling problems with unequal due dates

We consider a single-machine scheduling problem with the objective of minimizing the mean (or equivalently, total) tardiness and earliness when due dates may differ among jobs. Some properties of the optimal solution are discussed, and these properties are used to develop both optimal and heuristic algorithms. Results of computational tests indicate that optimal solutions can be found for problems with up to 20 jobs, and that two of the heuristic procedures provide optimal or very near optimal solutions in many instances. © 1994 John Wiley & Sons, Inc.     

A vertex-closing approach to the p-center problem

This article uses a vertex-closing approach to investigate the p-center problem. The optimal set of vertices to close are found in imbedded subgraphs of the original graph. Properties of these subgraphs are presented and then used to characterize the optimal solution, to establish a priori upper and lower bounds, to establish refined lower bounds, and to verify the optimality of solutions. These subgraphs form the foundation of two polynomial algorithms of complexity O(|E| log |E|) and O(|E|²). The algorithms are proven to converge to an optimum for special cases, and computational evidence is provided which suggests that they produce very good solutions more generally. Both algorithms perform very well on problems where p is large relative to the number of vertices n, specifically, when p/n ≥ 0.30. One of the algorithms is especially efficient for solving a sequence of problems on the same graph.     

An n-step, 2-variable search algorithm for the component placement problem

The component placement problem is a specialization of the quadratic assignment problem that has been extensively studied for a decade and which is of considerable practical value. Recently, interest in component placement algorithms has risen primarily as a result of increased activity in the field of computer-aided design automation. This paper deals with the methodology of component placement and is based on the results of considerable operational experience. A tutorial presentation of tree search placement algorithms is provided, and an improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem. These solutions are completely reproducible and are obtained at an acceptable expenditure of computational resources. An additional objective is an assessment of performance of the class of near optimal algorithms. In particular, the question- how close to optimal are the near optimal solutions- is examined.     

Minimizing weighted mean absolute deviation of flow times in single machine systems

We discuss the problem of scheduling several jobs on a single machine with the objective of minimizing the weighted mean absolute deviation of flow times around the weighted mean flow time. We first show that the optimal schedule is W-shaped. For the unweighted case, we show that all optimal schedules are V-shaped. This characterization enables us to show that the problem is NP-hard. We then provide a pseudopolynomial algorithm for the unweighted problem. Finally, we consider three heuristic algorithms for the unweighted problem and report computational experience with these algorithms. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 297–311, 1998     

Efficient sequential decision‐making algorithms for container inspection operations

Following work of Stroud and Saeger (Proceedings of ISI, Springer Verlag, New York, 2006) and Anand et al. (Proceedings of Computer, Communication and Control Technologies, 2003), we formulate a port of entry inspection sequencing task as a problem of finding an optimal binary decision tree for an appropriate Boolean decision function. We report on new algorithms for finding such optimal trees that are more efficient computationally than those presented by Stroud and Saeger and Anand et al. We achieve these efficiencies through a combination of specific numerical methods for finding optimal thresholds for sensor functions and two novel binary decision tree search algorithms that operate on a space of potentially acceptable binary decision trees. The improvements enable us to analyze substantially larger applications than was previously possible. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.     

Multiperiod resource allocation with a smoothing objective

We consider a multiperiod resource allocation problem, where a single resource is allocated over a finite planning horizon of T periods. Resource allocated to one period can be used to satisfy demand of that period or of future periods, but backordering of demand is not allowed. The objective is to allocate the resource as smoothly as possible throughout the planning horizon. We present two models: the first assumes that the allocation decision variables are continuous, whereas the second considers only integer allocations. Applications for such models are found, for example, in subassembly production planning for complex products in a multistage production environment. Efficient algorithms are presented to find optimal allocations for these models at an effort of O(T²). Among all optimal policies for each model, these algorithms find the one that carries the least excess resources throughout the planning horizon. © 1995 John Wiley & Sons, Inc.     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

Tree-search algorithms for quadratic assignment problems

Problems having the mathematical structure of a quadratic assignment problem are found in a diversity of contexts: by the economist in assigning a number of plants or indivisible operations to a number of different geographical locations; by the architect or indusatrial engineer in laying out activities, offices, or departments in a building; by the human engineer in arranging the indicators and controls in an operators control room; by the electronics engineer in laying out components on a backboard; by the computer systems engineer in arranging information in drum and disc storage; by the production scheduler in sequencing work through a production facility; and so on. In this paper we discuss several types of algorithms for solving such problems, presenting a unifying framework for some of the existing algorithms, and dcscribing some new algorithms. All of the algorithms discussed proceed first to a feasible solution and then to better and better feasible solutions, until ultimately one is discovered which is shown to be optimal.     

Probabilistic ideas in heuristic algorithms for solving some scheduling problems

Heuristic algorithms for positioning a maximal number of independent units and constructing a schedule with minimal fleet size are proposed. These algorithms consist of two stages: defining the “leading” job and finding an optimal position for it. Decisions on both stages use some special criteria which have a probabilistic interpretation. Some experimental data are given.     

轨道优化实时计算的梯度投影下降算法--防空导弹轨道优化的实时计算方法之二

在防空导弹的发射过程中,需要在给定的响应时间内确定最优轨道,导弹沿此轨道在预定的时间飞达预测遭遇点.为了轨道优化的实时计算,构造了一类梯度投影下降算法,并且给出实际应用的具体步骤.对防空导弹运动的一个数学模型的数字仿真结果表明应用这些算法可以达到很高的控制精度.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

Revenue maximization in two-station tandem queueing systems

We study optimal pricing for tandem queueing systems with finite buffers. The service provider dynamically quotes prices to incoming price sensitive customers to maximize the long-run average revenue. We present a Markov decision process model for the optimization problem. For systems with two stations, general-sized buffers, and two or more prices, we describe the structure of the optimal dynamic pricing policy and develop tailored policy iteration algorithms to find an optimal pricing policy. For systems with two stations but no intermediate buffer, we characterize conditions under which quoting either a high or a low price to all customers is optimal and provide an easy-to-implement algorithm to solve the problem. Numerical experiments are conducted to compare the developed algorithms with the regular policy iteration algorithm. The work also discusses possible extensions of the obtained results to both three-station systems and two-station systems with price and congestion sensitive customers using numerical analysis.     

A hard knapsack problem

In this article we develop a class of general knapsack problems which are hard for branch and bound algorithms. The number of alternate optimal solutions for these problems grows exponentially with problem parameters. In addition the LP bound is shown to be ineffective. Computational tests indicate that these problems are truly difficult for even very small problems. Implications for the testing of algorithms using randomly generated problems is discussed.     

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     

雷达组网系统责任区抗干扰优化部署

针对有源压制干扰对雷达组网系统的威胁,深入分析了雷达组网系统的抗干扰优化部署问题,建立了雷达组网系统责任区抗干扰优化布站决策模型,并给出了具体的算法和求解分析.仿真结果验证了该方法的有效性,可为雷达组网系统的实际优化部署提供参考.     

A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times

We investigate a single‐machine scheduling problem for which both the job processing times and due windows are decision variables to be determined by the decision maker. The job processing times are controllable as a linear or convex function of the amount of a common continuously divisible resource allocated to the jobs, where the resource allocated to the jobs can be used in discrete or continuous quantities. We use the common flow allowances due window assignment method to assign due windows to the jobs. We consider two performance criteria: (i) the total weighted number of early and tardy jobs plus the weighted due window assignment cost, and (ii) the resource consumption cost. For each resource consumption function, the objective is to minimize the first criterion, while keeping the value of the second criterion no greater than a given limit. We analyze the computational complexity, devise pseudo‐polynomial dynamic programming solution algorithms, and provide fully polynomial‐time approximation schemes and an enhanced volume algorithm to find high‐quality solutions quickly for the considered problems. We conduct extensive numerical studies to assess the performance of the algorithms. The computational results show that the proposed algorithms are very efficient in finding optimal or near‐optimal solutions. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 41–63, 2017     

A branch-and-bound algorithm to minimize total flow time with unequal release dates

This article examines the single-machine scheduling problem to minimize total flow time with unequal release dates. This problem has been proven to be NP-hard. We present a necessary and sufficient condition for local optimality which can also be considered as a priority rule. On the basis of this condition, we then define a class of schedules which contains all optimal solutions. We present some efficient heuristic algorithms using the previous condition to build a schedule belonging to this subset. We also prove some new dominance theorems, discuss the results found in the literature for this problem, and propose a branch-and-bound algorithm in which the heuristics are used to provide good upper bounds. We compare this new algorithm with existing algorithms found in the literature. Computational results on problems with up to 100 jobs indicate that the proposed branch-and-bound algorithm is superior to previously published algorithms. © 1992 John Wiley & Sons. Inc.     

混合遗传算法及其在运载火箭最优上升轨道设计中的应用

运载火箭最优上升轨道设计问题是一类终端时刻未定、终端约束苛刻的最优控制问题,经典算法求解这类问题时收敛性差、局部收敛等问题表现得比较突出。针对上述问题,将具有良好全局收敛性的遗传算法应用到运载火箭最优上升段设计问题求解中,为了提高遗传算法的收敛速度和克服早熟问题,结合遗传算法和单纯型算法的优点,设计了两种混合遗传算法。计算结果表明,所设计的混合遗传算法是求解复杂问题的有效全局优化方法,可以成功地解决一类终端时刻可变飞行器最优控制问题。     

Distribution free bounds for service constrained (Q,r) inventory systems

A classical and important problem in stochastic inventory theory is to determine the order quantity (Q) and the reorder level (r) to minimize inventory holding and backorder costs subject to a service constraint that the fill rate, i.e., the fraction of demand satisfied by inventory in stock, is at least equal to a desired value. This problem is often hard to solve because the fill rate constraint is not convex in (Q, r) unless additional assumptions are made about the distribution of demand during the lead‐time. As a consequence, there are no known algorithms, other than exhaustive search, that are available for solving this problem in its full generality. Our paper derives the first known bounds to the fill‐rate constrained (Q, r) inventory problem. We derive upper and lower bounds for the optimal values of the order quantity and the reorder level for this problem that are independent of the distribution of demand during the lead time and its variance. We show that the classical economic order quantity is a lower bound on the optimal ordering quantity. We present an efficient solution procedure that exploits these bounds and has a guaranteed bound on the error. When the Lagrangian of the fill rate constraint is convex or when the fill rate constraint does not exist, our bounds can be used to enhance the efficiency of existing algorithms. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 635–656, 2000