A capacitated facility location problem with constrained backlogging probabilities

One of the assumptions of the capacitated facility location problem (CFLP) is that demand is known and fixed. Most often, this is not the case when managers take some strategic decisions such as locating facilities and assigning demand points to those facilities. In this paper we consider demand as stochastic and we model each of the facilities as an independent queue. Stochastic models of manufacturing systems and deterministic location models are put together in order to obtain a formula for the backlogging probability at a potential facility location. Several solution techniques have been proposed to solve the CFLP. One of the most recently proposed heuristics, a reactive greedy adaptive search procedure, is implemented in order to solve the model formulated. We present some computational experiments in order to evaluate the heuristics’ performance and to illustrate the use of this new formulation for the CFLP. The paper finishes with a simple simulation exercise.     

Scenario-based heuristic to two-stage stochastic program for the parallel machine ScheLoc problem

Scheduling-Location (ScheLoc) problem is a new and interesting topic in manufacturing, considering location and scheduling decisions simultaneously. Most existing works focus on the deterministic problems. In practice, however, job-processing times are usually uncertain due to some factors. This paper investigates the stochastic parallel machine ScheLoc problem to minimise the weighted sum of the location cost and the expectation of the total completion time. A two-stage stochastic programming formulation is proposed, then the sample average approximation (SAA) method is adapted to solve the small-size problems. To efficiently address the large-scale problems, a genetic algorithm (GA) and a scenario-based heuristic are designed. Numerical experiments on 450 instances are conducted. Computational results show that the scenario-based heuristic outperforms SAA method and GA in terms of solution quality and computational time.     

Path loss models based on stochastic rays

Two-dimensional percolation lattices are applied to describe wireless propagation environment, and stochastic rays are employed to model the trajectories of radio waves. First, the authors derive the probability that a stochastic ray undergoes certain number of collisions at a specific spatial location. Three classes of stochastic rays with different constraint conditions are considered: stochastic rays of random walks and generic stochastic rays with two different anomalous levels. Subsequently, the authors obtain the closed-form formulation of mean received power of radio waves under non-line-of-sight conditions for each class of stochastic ray. Specifically, the determination of model parameters and the effects of lattice structures on the path loss are investigated. The theoretical results are validated by comparison with the experimental data     

A Dual-based Heuristic for the Simple Facility Location Problem With Stochastic Demand

This paper deals with a stochastic version of the simple facility location problem where the demands of customers are random variables. Under the assumption of step function type distribution of demands, the problem is shown to be approximated by a mixed 0-1 linear programming problem. A heuristic procedure is developed to solve the problem, which successfully extends the well known dual-based approach by Bilde & Krarup, and Erlenkotter. Computational results with 20 test problems are presented to demonstrate the effectiveness of the proposed heuristic.     

基于信噪比的随机设施布局方法

设施布局对于生产需求不确定、产品多样化制造企业十分重要。随机设施布局评价的重要指标就是布局的鲁棒性和稳定性,但这两个特征之间存在一定矛盾,很难同时满足这两个特征。针对布局问题的这两个目标,引入Taguchi稳健设计中信噪比理论,建立了基于信噪比的随机设施布局优化模型,并通过仿真进行验证,实验结果表明新方法在随机设施布局问题中能获得较好的鲁棒性和稳定性。     

Solution methods for the mathematical models of single-loop AGV systems

Guide path simplification can potentially reduce the complexity inherent in conventional, multi-loop automated guided vehicle systems (AGVs). A single-loop configuration is one alternative. A procedure for designing single-loop AGV systems, the OSL method was presented in a previous paper. In this paper, we suggest faster and more efficient methods for solving the two mathematical models in the OSL procedure. The first model called the valid single-loop problem (VSLP) is used to determine an initial single loop for the procedure. The method suggested is a heuristic procedure that starts from a loop around one of the departments and keeps adding departments to the loop until a valid single loop is constructed. The second model called the single-loop station location problem (SLSLP) is used to determine the location of the pick-up and delivery stations along a given loop. The method suggested converts the mixed integer formulation into a linear formulation.     

不确定车数的随机车辆路径问题模型及算法

研究了一类有时间约束、车辆数量不确定的随机车辆路径问题;建立了该类问题的随机规划数学模型;设计了模型求解的遗传算法、禁忌搜索算法和遗传-禁忌混合算法.禁忌算法采用了对当前解的车辆-顾客分配结构和解的路径顺序分别禁忌的双层禁忌算法,使算法全局性更好,同时也降低了搜索时间.把禁忌算法作为变异算子应用于遗传算法形成了混合算法.最后给出了计算示例,对算法进行了比较分析.     

A Note on the Facilities Phase-in Problem

This note presents an alternative formulation of the facility phase-in problem and computational results with this new formulation. The new solution approach appears to produce better run times as well as integer-feasible solutions to the linear programming relaxation of the model.     

面向随机环境的带软时间窗多式联运路径优化

针对多式联运运输距离长、中转环节多,易受机械故障、交通堵塞、天气状况等随机因素影响的特点,建立了更加符合实际的带软时间窗约束的多式联运路径优化数学规划模型.考虑到模型求解的复杂度,设计了一种遗传算法,并根据模型最优解的特点减少了搜索空间.最后通过算例对方法进行了验证.     

Optimization of the Second-Order Logarithmic Machining Economics Problem by Extended Geometric Programming Part II: Posynomial Constraints

An algorithm is presented for solution of the machining economics problem with a Quadratic Posylognomial (QPL) objective function and single term posynomial constraints, meeting certain sufficient conditions. The algorithm applies to minimum cost or maximum productivity when the tool-life equation is a single term QPL and the removal rate is a single-term posynomial. A peripheral end-milling example, using the same tool-life equation and cost parameters as Part I, with the addition of experimentally derived constraints, is solved to illustrate the computational aspects of the algorithm. The QPL and posynomial (Taylor) formulations of the constrained machining problem are compared using the same experimental tool-life data. The QPL formulation is based on a quadratic logarithmic model whereas the posynomial formulation is based on a linear logarithmic tool-life model. An optimum without active constraints is possible using the QPL formulation in several independent machining variables, such as feed, speed, and depth, whereas the posynomial optimum, by nature, requires active constraints for more than one independent variable. This is tantamount to having additional “degrees of freedom” for optimization, as illustrated by the example problem.     

Stochastic second-order BEM perturbation formulation

This paper presents the stochastic second order moment perturbation approach to the classical deterministic Boundary Element Method (BEM) formulation. Numerous applications of such a formulation in different problems of stochastic mechanics, especially in the field of computational modeling of structural defects in homogeneous and composite materials occurring randomly in solids and engineering structures, were the main reasons to introduce the proposed model. The stochastic boundary element method (SBEM) formulation of the general linear elasticity boundary value has been provided together with an appropriate discretization. The equations describing the expected values and the covariances of stress and strain tensors for points lying on the boundary and inside the region are considered. This set of equations constitutes a formal mathematical statement of the problem and is suitable for computational implementation.     

A Bayesian stochastic programming approach to an employee scheduling problem

Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited historical data. Unlike deterministic optimization, stochastic programs explicitly incorporate distributions for random parameters in the model formulation, and thus have the advantage that the resulting solutions more fully hedge against future contingencies. In this paper, we exploit the strengths of Bayesian prediction and stochastic programming in a rolling-horizon approach that can be applied to solve real-world problems. We illustrate the methodology on an employee production scheduling problem with uncertain up-times of manufacturing equipment and uncertain production rates. Computational results indicate the value of our approach.     

备件物流系统选址库存路径问题模型及算法

考虑到备件需求的随机性和时间紧迫性,以供应链二级分销网络的备件物流系统为研究对象,以系统总成本最低为目标,建立了带软时间窗的选址-库存-路径问题模型。由于该模型属于NP-Hard问题,因此提出了基于禁忌搜索算法和改进的C-W算法的两阶段混合启发式算法。通过实例演算,结果表明了该算法的实用性与有效性。     

Capacitated dynamic production and remanufacturing planning under demand and return uncertainty

This paper considers a stochastic dynamic multi-product capacitated lot sizing problem with remanufacturing. Finished goods come from two sources: a standard production resource using virgin material and a remanufacturing resource that processes recoverable returns. Both the period demands and the inflow of returns are random. For this integrated stochastic production and remanufacturing problem, we propose a nonlinear model formulation that is approximated by sample averages and a piecewise linear approximation model. In the first approach, the expected values of random variables are replaced by sample averages. The idea of the piecewise linear approximation model is to replace the nonlinear functions with piecewise linear functions. The resulting mixed-integer linear programs are solved to create robust (re)manufacturing plans.     

随机LQ控制在投资组合模型及套期保值问题中的应用

本文提出一类随机线性二次最优控制问题,给出了一个新的Ricatti方程,若此方程有解,可得到系统的最优反馈控制;作为其应用,文中首先讨论了连续时间的投资组合模型,得到最优证券组合;最后将其运用于金融中未定权益的套期保值问题,并得到最优套期保值策略。     

Staffing a call center with uncertain non-stationary arrival rate and flexibility

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.     

供应链中随机需求车辆选径问题的研究

结合供应链的需要给出了允许两次服务失败的数学模型,提出了一种混沌神经网络求解算法,对该问题进行了求解,并与SA算法进行了比较.结果表明该算法具有很强的避免陷入局部极小点的能力,较大地提高了优化的性能和搜索效率,适用于求解车辆选径问题.     

进口物资运输的中转站选址-分配问题

结合进口物资的江海联合中转运输,提出了一类带三重能力约束的中转站选址-分配问题(LAP)模型,即在物流网络节点有最大单批通行能力、中转站吞吐能力、运输工具总运输能力三重能力约束下,如何进行中转站选址,并相关资源分配,使总的费用最小.针对该问题构建了混合整数规划模型,提出了一种先进行选址然后进行资源分配的优化算法.还给出了该模型在武汉钢铁(集团)公司进口铁矿石江海联合运输的中转站选址-分配问题的研究实例.     

A new bi-fidelity model reduction method for Bayesian inverse problems

This work presents a new bi-fidelity model reduction approach to the inverse problem under the framework of Bayesian inference. A low-rank approximation is introduced to the solution of the corresponding forward problem and admits a variable-separation form in terms of stochastic basis functions and physical basis functions. The calculation of stochastic basis functions is computationally predominant for the low-rank expression. To significantly improve the efficiency of constructing the low-rank approximation, we propose a bi-fidelity model reduction based on a novel variable-separation method, where a low-fidelity model is used to compute the stochastic basis functions and a high-fidelity model is used to compute the physical basis functions. The low-fidelity model has lower accuracy but efficient to evaluate compared with the high-fidelity model; it accelerates the derivative of recursive formulation for the stochastic basis functions. The high-fidelity model is computed in parallel for a few samples scattered in the stochastic space when we construct the high-fidelity physical basis functions. The required number of forward model simulations in constructing the basis functions is very limited. The bi-fidelity model can be constructed efficiently while retaining good accuracy simultaneously. In the proposed approach, both the stochastic basis functions and physical basis functions are calculated using the model information. This implies that a few basis functions may accurately represent the model solution in high-dimensional stochastic spaces. The bi-fidelity model reduction is applied to Bayesian inverse problems to accelerate posterior exploration. A few numerical examples in time-fractional derivative diffusion models are carried out to identify the smooth field and channel-structured field in porous media in the framework of Bayesian inverse problems.