Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems

Clustering problems are often difficult to solve due to nonlinear cost functions and complicating constraints. Set partitioning formulations can help overcome these challenges, but at the cost of a very large number of variables. Therefore, techniques such as delayed column generation must be used to solve these large integer programs. The underlying pricing problem can suffer from the same challenges (non‐linear cost, complicating constraints) as the original problem, however, making a mathematical programming approach intractable. Motivated by a real‐world problem in printed circuit board (PCB) manufacturing, we develop a search‐based algorithm (Rank‐Cluster‐and‐Prune) as an alternative, present computational results for the PCB problem to demonstrate the tractability of our approach, and identify a broader class of clustering problems for which this approach can be used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

A branch‐and‐cut algorithm for the nonpreemptive swapping problem

In the Swapping Problem (SP), we are given a complete graph, a set of object types, and a vehicle of unit capacity. An initial state specifies the object type currently located at each vertex (at most one type per vertex). A final state describes where these object types must be repositioned. In general, there exist several identical objects for a given object type, yielding multiple possible destinations for each object. The SP consists of finding a shortest vehicle route starting and ending at an arbitrary vertex, in such a way that each object is repositioned in its final state. This article exhibits some structural properties of optimal solutions and proposes a branch‐and‐cut algorithm based on a 0‐1 formulation of the problem. Computational results on random instances containing up to 200 vertices and eight object types are reported. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

On the exponentially weighted moving variance

MacGregor and Harris (J Quality Technol 25 (1993) 106–118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta‐Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

On the polyhedral structure of two‐level lot‐sizing problems with supplier selection

In this article, we study a two‐level lot‐sizing problem with supplier selection (LSS), which is an NP‐hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet‐defining. We show numerically that incorporating these valid inequalities within a branch‐and‐cut framework leads to significant improvements in computation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 647–666, 2017     

Column generation for stochastic green telecommunication network planning with switchable base stations

We present the green telecommunication network planning problem with switchable base stations, where the location and configuration of the base stations are optimized, while taking into account uncertainty and variability of demand. The problem is formulated as a two‐stage stochastic program under demand uncertainty with integers in both stages. Since solving the presented problem is computationally challenging, we develop the corresponding Dantzig‐Wolfe reformulation and propose a solution approach based on column generation. Comprehensive computational results are provided for instances of varying characteristics. The results show that the joint location and dynamic switching of base stations leads to significant savings in terms of energy cost. Up to 30% reduction in power consumption cost is achieved while still serving all users. In certain cases, allowing dynamic configurations leads to more installed base stations and higher user coverage, while having lower total energy consumption. The Dantzig‐Wolfe reformulation provides solutions with a tight LP‐gap eliminating the need for a full branch‐and‐price scheme. Furthermore, the proposed column generation solution approach is computationally efficient and outperforms CPLEX on the majority of the tested instances. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 351–366, 2016     

Capacity investment decisions under risk aversion

This article studies the optimal capacity investment problem for a risk‐averse decision maker. The capacity can be either purchased or salvaged, whereas both involve a fixed cost and a proportional cost/revenue. We incorporate risk preference and use a consumption model to capture the decision maker's risk sensitivity in a multiperiod capacity investment model. We show that, in each period, capacity and consumption decisions can be separately determined. In addition, we characterize the structure of the optimal capacity strategy. When the parameters are stationary, we present certain conditions under which the optimal capacity strategy could be easily characterized by a static two‐sided (s, S) policy, whereby, the capacity is determined only at the beginning of period one, and held constant during the entire planning horizon. It is purchased up to B when the initial capacity is below b, salvaged down to Σ when it is above σ, and remains constant otherwise. Numerical tests are presented to investigate the impact of demand volatility on the optimal capacity strategy. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 218–235, 2016     

Scheduling parallel machines with inclusive processing set restrictions and job rejection

In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a ‐approximation algorithm with a time complexity of . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a ‐approximation algorithm with a time complexity of . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5‐approximation algorithm with a time complexity of . © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 667–681, 2017     

Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

In this article, we propose a branch‐and‐price‐and‐cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time to carry out a job, that is, the routes of the scheduling subjects are dependent. The incorporation of the synchronization constraints increases the difficulty of the MRPSC significantly and makes the existing VRP exact algorithm inapplicable. Although there are many types of valid inequalities for the VRP or its variants, so far we can only adapt the infeasible path elimination inequality and the weak clique inequality to handle the synchronization constraints in our BPC algorithm. The experimental results at the root node of the branch‐and‐bound tree show that the employed inequalities can effectively improve the lower bound of the problem. Compared with ILOG CPLEX, our BPC algorithm managed to find optimal solutions for more test instances within 1 hour. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 138–171, 2016     

基于规则控制的快速高度跟踪算法

提出一种全新的基于模糊推理与规则控制的高度跟踪算法。这种算法无论是在跟踪效果与运算速度上都大大优于以往的最速下降法、动态规划法、最优控制法等,而且可以对最大俯仰角、最大可用过载、希望跟踪程度等跟踪参数进行随意设定。大量的仿真计算证明,该算法具有很好的实时性、收敛性及可扩展性。可以极大地减轻对地攻击低空轨迹规划的工作,对巡航导弹、无人机更具应用价值     

A heuristic for maximizing the number of on‐time jobs on two uniform parallel machines

We consider the problem of maximizing the number of on‐time jobs on two uniform parallel machines. We show that a straightforward extension of an algorithm developed for the simpler two identical parallel machines problem yields a heuristic with a worst‐case ratio bound of at least . We then show that the infusion of a “look ahead” feature into the aforementioned algorithm results in a heuristic with the tight worst‐case ratio bound of , which, to our knowledge, is the tightest worst‐case ratio bound available for the problem. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006