Formulations and solution algorithms for dynamic assembly routing problem

We study a dynamic version of the assembly routing problem. The assembly lot sizing section deals with decisions concerning the production phase, whereas the routing section organises the collection of raw materials necessary for the production. Traditionally, these two problems are treated separately, and more specifically, in a hierarchical way. We propose three linear programming models: a non-vehicle index model, a two-commodity flow formulation and a logic-based benders decomposition. We develop aggregated rounded capacity constraints for non-vehicle index model and separated them dynamically during the Branch & Cut procedure. Logic-based benders decomposition algorithm solves the Dynamic Assembly Routing Problem iteratively and obtains a feasible solution at each iteration. The numerical tests show that, the two first models are particularly effective at finding the optimal solutions in a reasonable amount of time on instances with up to 50 components and 3 periods.     

Design of an ambulatory piezoelectric actuator which has T-shape stator

Abstract

T-shaped ambulatory piezoelectric actuator which can be used for various purposes such as lifesaving and environmental monitoring was proposed. The actuator consists of eight piezoelectric benders, t-shaped stator, and four legs, and it is very simple in structure and has the advantages of being easily manufactured and downsizing. It is also driven by four legs and can be moved forward and backward. The piezoelectric bender was composed of a carbon body and a ceramic plate. Vibration motions of the piezoelectric benders in x and z axes were transfer to the legs and the elliptical displacements at the ends of the legs were obtained by combination of the phase difference of 90 degrees. Characteristics of the actuators were simulated by finite element analysis, and the optimized prototype actuator was fabricated and experimented.     

Covariance‐based hardware selection part IV: Solution using the generalized benders decomposition

Recently the covariance based hardware selection problem has been shown to be of the mixed integer convex programming (MICP) class. While such a formulation provides a route to global optimality, use of the branch and bound search procedure has limited application to fairly small systems. The particular bottleneck is that during each iteration of the branch and bound search, a fairly slow semi‐definite programming (SDP) problem must be solved to its global optimum. In this work, we illustrate that a simple reformulation of the MICP and subsequent application of the generalized Benders decomposition algorithm will result in massive reductions in computational effort. While the resulting algorithm must solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by the reduction in the number of SDP problems that must be solved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3628–3638, 2016     

考虑需求侧响应的电气设备调度混合分散式优化

为了缓解用能持续增加对电力系统造成的负担和解决大规模电气设备联合调度时的优化计算问题,提出了考虑需求侧响应的大规模可控用电设备和储能设备的混合分布式优化调度方法。首先建立可控用电设备负荷和储能设备的数学模型,在此基础上,构建了以系统和各设备运行特性为约束,以系统购电费用、用户不满意费用和储能设备损耗费用之和最小为目标函数的混合整数非线性集中式优化数学模型。其次,针对此高维、多目标和多约束且难于求解的非线性集中式优化模型,采用拉格朗日松弛法将其分解为两个子问题,即分别对应可控电气设备负荷的优化调度问题和储能设备的优化调度问题。而且,对于前者又可进一步分解为各可控电气设备负荷的优化调度子问题并通过内点法求解计算;对于后者又可分解为各个储能设备问题的混合整数线性优化调度子问题并通过Benders分解法并行求解计算。然后,为了验证所提混合分布式优化方法的有效性及其优越性,基于算例,对比分析集中式和分散式优化调度时的目标函数值和电气设备优化调度结果,不同规模电气设备对集中式和分散式优化方法计算效率的影响。根据结果可见,所提优化调度方法与集中式优化方法的目标函数值基本一致,但所提方法对应的电气设备优化调度结果可以很好地响应分时电价策略,储能设备削峰填谷效果好;而且所提混合分布式优化方法可以降低优化问题的求解复杂度,计算效率高,几乎不受电气设备规模的影响。     

A realistic multi-manned five-sided mixed-model assembly line balancing and scheduling problem with moving workers and limited workspace

The assembly line balancing problem can completely vary from one production line to the other. This paper deals with a realistic assembly line for the automotive industry inspired by Fiat Chrysler Automotive in North America and Parskhodro in Iran (both large-scale automotive companies). This problem includes some specific requirements that have not been studied in the literature. For example, the assembly line is five-sided, and workers can move along these sides. Due to the limited workspace, all the sides cannot work simultaneously at one station. First, a mixed integer linear programming model is proposed for the problem. Then, the model is improved to have a tighter linear relaxation. Moreover, an effective logic-based Benders’ decomposition algorithm is developed. After careful analysis of problem’s structure, three propositions are introduced. The master problem is well restricted by eight valid inequalities. Two different sub-problem types are defined to extract more information from the master problem’s solution. In this case, the algorithm adds effective cuts that reduce the solution space to the extent possible at each iteration. Thus, the number of iterations is significantly cut down. The performance of the model and algorithm, as well as improvement made on both, is evaluated.     

Medium term scheduling of a hydro-thermal system using stochastic model predictive control

A multistage stochastic programming formulation is presented for monthly production planning of a hydro-thermal system. Stochasticity from variations in water reservoir inflows and fluctuations in demand of electric energy are considered explicitly. The problem can be solved efficiently via Nested Benders Decomposition. The solution is implemented in a model predictive control setup and performance of this control technique is demonstrated in simulations. Tuning parameters, such as prediction horizon and shape of the stochastic programming tree are identified and their effects are analyzed.     

基于benders算法的两电压等级网络可用传输容量计算

电力市场的发展进入现货市场阶段,对区域间输电容量在线评估提出新的要求。利用Benders算法求解N-1可用传输容量问题,大幅度降低计算维度,但是也容易产生过矫正、振荡等问题。仅考虑电网的N-1可靠性,忽略下级电网联络线的负荷转供能力,计算结果过于保守,影响电力市场中断面处的交易量。文中提出一种基于Benders算法的ATC计算新方法。分析220 kV片区电网输电容量时考虑到110 kV高压配电网重构对潜在供电能力的挖掘作用。对N-1安全故障进行网络重构,在不增加问题复杂度的前提下,提高区域输电容量,用Benders分解法降低问题求解维度,节约计算时间,适用于在线分析。以IEEE 30节点算例进行仿真,结果表明计及高压配电网重构的多片区整体ATC可相比于无重构能力的片区ATC提高24%。     

基于可信性理论的输电网短期线路检修计划

传统方法将短期线路检修计划作为单重不确定性优化问题进行建模和求解。但是，架空线路的可靠性指标难以表达现场运行中线路发生故障的可能性，所以需要在短期线路检修计划中对双重不确定性(随机性和模糊性)同时进行建模和求解。可信性理论是基础数学领域最近完成的数学分支， 它提供了随机性与模糊性综合评估的严格数学基础。基于可信性理论可建立短期线路检修计划的混合整数随机模糊双重不确定性优化模型(原始模型)，其目标函数是检修费用与停电损失费用之和的随机模糊期望值最小。文中利用Benders分解法将原始模型分解为主问题和子问题进行求解：主问题是一个多目标整数规划问题，利用改进Balas算法求解；子问题是一个随机模糊双重不确定性模型，利用可信性理论和直流潮流求解。IEEE-RBTS系统和IEEE-RTS系统的算例表明，文中提出的算法可以综合协调全网的风险和经济目标。同时由于支持原始数据的随机模糊性，使得该算法具有较强的实用性。     

基于可信性理论的输电网短期线路检修计划

传统方法将短期线路检修计划作为单重不确定性优化问题进行建模和求解。但是，架空线路的可靠性指标难以表达现场运行中线路发生故障的可能性，所以需要在短期线路检修计划中对双重不确定性(随机性和模糊性)同时进行建模和求解。可信性理论是基础数学领域最近完成的数学分支， 它提供了随机性与模糊性综合评估的严格数学基础。基于可信性理论可建立短期线路检修计划的混合整数随机模糊双重不确定性优化模型(原始模型)，其目标函数是检修费用与停电损失费用之和的随机模糊期望值最小。文中利用Benders分解法将原始模型分解为主问题和子问题进行求解：主问题是一个多目标整数规划问题，利用改进Balas算法求解；子问题是一个随机模糊双重不确定性模型，利用可信性理论和直流潮流求解。IEEE-RBTS系统和IEEE-RTS系统的算例表明，文中提出的算法可以综合协调全网的风险和经济目标。同时由于支持原始数据的随机模糊性，使得该算法具有较强的实用性。     

Scheduling routine and call-in clinical appointments with revisits

This paper studies the problem of clinical appointment scheduling when taking revisits into account. We consider two classes of patients: (1) routine patients who have made an appointment weeks in advance and (2) same-day patients who call in at the very beginning of the day, before the first clinical consultation begins. After the first appointment and consultation, patients might need an additional examination and a second consultation to confirm their health status. This paper aims to create an advanced scheduling method for both routine patients and same-day patients to optimise the expected weighted sum of three performance measures: patients’ waiting time, physician’s idle time and overtime. A stochastic programme model is constructed and solved by sample average approximation and benders’ decomposition. Numerical tests show that revisits significantly affect the three performance measures; to improve the hospital system’s operation management, both scheduling of appointment times and daily workload plans are taken into account.