服务水平约束下基于可调节鲁棒优化的固定比例生产与库存计划模型

在不确定需求环境下,研究由原材料供应商、制造商和客户组成的三级供应链中,具有固定比例生产系统的制造商多周期生产与库存计划问题.采用区间不确定集描述市场需求不确定性,并利用联合机会约束刻画制造商的服务水平要求,在线性决策规则下建立带有联合机会约束的固定比例生产系统生产与库存仿射可调节鲁棒优化模型.进一步,将所建模型等价转换为易于求解的线性规划问题.考虑到不确定扰动系数在模型鲁棒性与解的保守性之间的调节作用,给出能够有效提高具有固定比例生产系统的制造商利润并同时满足预设服务水平的不确定扰动系数优化算法.数值算例表明,基于所提出模型获得的运作方案能够有效应对供需平衡程度的变化,并且能以较高利润满足预设服务水平要求.     

需求分布不确定条件下的多周期库存鲁棒优化模型

在离散需求情景概率不确定的条件下, 建立基于最大最小方法的多周期库存鲁棒优化模型. 考虑需求分布分别隶属于区间和椭球不确定集两种情形, 运用对偶理论将多周期库存鲁棒优化模型转化为易于求解的凸规划问题. 数值结果表明, 与已知需求分布下的系统最优绩效相比, 采用鲁棒订货策略虽然会导致部分绩效损失, 但损失值很小, 表明基于鲁棒优化的多周期库存订货策略具有良好的鲁棒性, 能够有效抑制需求分布不确定性对库存运作绩效的影响.

     

Inventory Minimization and Production Scheduling: the Case of a Large Hong Kong Company

The background of this study is a rather classical but complex inventory control/production planning/line scheduling problem of a major soft-drink company in Hong Kong. The issue that stands out for this many-product high-sales manufacturer is the storage space of its central warehouse, which often finds itself in the state of overflow or near capacity with finished goods and work-in-process inventory. This phenomenon can create immediate interruptions of production, capital tie-ups and subsequent potential of lost sales. Another obviously important concern is the meeting of forecast demands. A mathematical modelling approach that entails techniques of multi-period aggregate optimization is proposed to tackle the overall problem. The dual objectives are to achieve better production planning and line scheduling in order to minimize inventory build-up and maximize demand satisfaction. Numerical results for a sample problem are reported as an illustration to this proposed two-phase approach.     

Non-fragile robust H ∞ control for uncertain spacecraft rendezvous system with pole and input constraints

This article investigates the robust H _∞ control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint, pole constraint and external and controller perturbations. Based on the Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state-feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimisation problem subject to LMI constraints. With the obtained controller, the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method.     

Reliable Robust Preview Tracking Control Against Actuator Faults

In this paper we provide a solution to the reliable robust preview tracking problem against actuator faults for discrete LTI systems with polytopic uncertainties. This solution is in terms of the solvability of linear matrix inequalities (LMIs). The method is based on multi‐objective optimization and LQ tracking performance indices. To avoid the conservativeness problem associated with using a common LMI solution for the normal case and the fault cases, different LMI solutions are used in the proposed method. Two iterative algorithms are proposed and compared. Numerical examples are used to show the effectiveness of the algorithms.     

Modeling and analysis of single item multi-period procurement lot-sizing problem considering rejections and late deliveries

Integer linear programming approach has been used to solve a multi-period procurement lot-sizing problem for a single product that is procured from a single supplier considering rejections and late deliveries under all-unit quantity discount environment. The intent of proposed model is two fold. First, we aim to establish tradeoffs among cost objectives and determine appropriate lot-size and its timing to minimize total cost over the decision horizon considering quantity discount, economies of scale in transactions and inventory management. Second, the optimization model has been used to analyze the effect of variations in problem parameters such as rejection rate, demand, storage capacity and inventory holding cost for a multi-period procurement lot-sizing problem. This analysis helps the decision maker to figure out opportunities to significantly reduce cost. An illustration is included to demonstrate the effectiveness of the proposed model. The proposed approach provides flexibility to decision maker in multi-period procurement lot-sizing decisions through tradeoff curves and sensitivity analysis.     

Robust design of (s,S) inventory policy parameters in supply chains with demand and lead time uncertainties

Demand and lead time uncertainties have significant effects on supply chain behaviour. In this paper, we present a single-product three-level multi-period supply chain with uncertain demands and lead times by using robust techniques to study the managerial insights of the supply chain inventory system under uncertainty. We formulate this problem as a robust mixed-integer linear program with minimised expected cost and total cost variation to determine the optimal (s, S) values of the inventory parameters. Several numerical studies are performed to investigate the supply chain behaviour. Useful guidelines for the design of a robust supply chain are also provided. Results show that the order variance and the expected cost in a supply chain significantly increase when the manufacturer’s review period is an integer ratio of the distributor’s and the retailer’s review periods.     

Optimization-Oriented Global Constraints

In this paper, we propose a way of exploiting Operations Research techniques within global constraints for cost-based domain filtering. In Constraint Programming, constraint propagation is aimed at removing from variable domains combinations of values which are proven infeasible. Pruning derives from feasibility reasoning. When coping with optimization problems, pruning can be performed also on the basis of costs, i.e., optimality reasoning. Cost-based filtering removes combination of values which are proven sub-optimal. For this purpose, we encapsulate in global constraints optimization components representing suitable relaxations of the constraint itself. These components embed efficient Operations Research algorithms computing the optimal solution of the relaxed problem and a gradient function representing the estimated cost of each variable-value assignment. We exploit these pieces of information for pruning and for guiding the search. We have applied these techniques to a couple of ILOG Solver global constraints (a constraint of difference and a path constraint) and tested the approach on a variety of combinatorial optimization problems such as Timetabling, Travelling Salesman Problems and Scheduling Problems with sequence dependent setup times. Comparisons with pure Constraint Programming approaches and related literature clearly show the benefits of the proposed approach.     

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.     

Splitting augmented Lagrangian method for optimization problems with a cardinality constraint and semicontinuous variables

We propose a new splitting augmented Lagrangian method (SALM) for solving a class of optimization problems with both cardinality constraint and semicontinuous variables constraint. The proposed approach, inspired by the penalty decomposition method in [Z.S. Lu and Y. Zhang, Sparse approximation via penalty decomposition methods, SIAM J. Optim. 23(4) (2013), pp. 2448–2478], splits the problem into two subproblems using auxiliary variables. SALM solves two subproblems alternatively. Furthermore, we prove the convergence of SALM, under certain assumptions. Finally, SALM is implemented on the portfolio selection problem and the compressed sensing problem, respectively. Numerical results show that SALM outperforms the well-known tailored approach in CPLEX 12.6 and the penalty decomposition method, respectively.     

Optimal ordering decision for deteriorating items with expiration date and uncertain lead time

The ordering policy for the retailers and the suppliers is a function of deterioration, product expiration date, the supplier’s uncertain lead time, available capital constraint and the retailer’s seasonal pattern demand. We develop a deteriorating inventory replenishment model of the system and present an algorithm to derive the retailer’s optimal replenishment cycle, shortage period, order quantity and the supplier’s managing cost. Numerical example and sensitivity analysis are given to illustrate the model.     

A new approach to solve the multi-product multi-period inventory lot sizing with supplier selection problem

This research work deals with the multi-product multi-period inventory lot sizing with supplier selection problem. Formerly, this kind of problem was formulated and solved using an exhaustive enumeration algorithm and a heuristic algorithm. In this paper, a new algorithm based on a reduce and optimize approach and a new valid inequality is proposed to solve the multi-product multi-period inventory lot sizing with supplier selection problem. Numerical experiments ratify the success of the proposed heuristic algorithm. For the set of 150 benchmark instances, including 75 small-sized instances, 30 medium-sized instances, and 45 large-sized instances, the algorithm always obtained better solutions compared with those previously published. Furthermore, according to the computational results, the developed heuristic algorithm outperforms the CPLEX MIP solver in both solution quality and computational time.     

控制输入受限的拦截卫星轨道鲁棒H2/H∞控制

针对拦截卫星在执行轨道拦截任务的过程中存在不确定参数和不同类型外界干扰的轨道控制问题,研究了基于鲁棒H2/H∞稳定的控制器设计方法.首先,考虑参数不确定性、外界干扰、系统的H2/H∞性能和有限时间性能、控制输入限幅和极点配置,建立了相对运动轨道模型和相应的约束条件,并由此提出了控制器设计目标.然后采用线性不等式技术提出并证明了控制器存在的充分条件,并将控制器的设计转化为一个凸优化问题进行求解.仿真结果表明,设计的控制器能够使系统稳定并满足各项约束,且对系统不确定性具有较好的鲁棒性以及对外界干扰有一定的抑制作用.     

A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty

We propose a two-stage robust optimization model for the mobile facility fleet sizing and routing problem with demand uncertainty. A two-level cutting plane based method is developed, which includes an algorithm to generate problem-specific lower bound inequalities in the outer level, and a hybrid algorithm in the inner level that combines heuristic and exact methods to solve the recourse problem. Numerical tests show that the design and operation from the proposed method outperforms other solution approaches. The efficiency of the proposed solution algorithm in identifying the optimal solution is quantified and the robustness of the proposed model is demonstrated for varying degrees of uncertainty in demand.     

Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?₂‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?_∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?_∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?_∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

A genetic algorithm approach for multi-product multi-period continuous review inventory models

This paper formulates an approach for multi-product multi-period (Q, r) inventory models that calculates the optimal order quantity and optimal reorder point under the constraints of shelf life, budget, storage capacity, and “extra number of products” promotions according to the ordered quantity. Detailed literature reviews conducted in both fields have uncovered no other study proposing such a multi-product (Q, r) policy that also has a multi-period aspect and which takes all the aforementioned constraints into consideration. A real case study of a pharmaceutical distributor in Turkey dealing with large quantities of perishable products, for whom the demand structure varies from product to product and shows deterministic and variable characteristics, is presented and an easily-applicable (Q, r) model for distributors operating in this manner proposed. First, the problem is modeled as an integer linear programming (ILP) model. Next, a genetic algorithm (GA) solution approach with an embedded local search is proposed to solve larger scale problems. The results indicate that the proposed approach yields high-quality solutions within reasonable computation times.     

Control of robust design in multiobjective optimization under uncertainties

In design and optimization problems, a solution is called robust if it is stable enough with respect to perturbation of model input parameters. In engineering design optimization, the designer may prefer a use of robust solution to a more optimal one to set a stable system design. Although in literature there is a handful of methods for obtaining such solutions, they do not provide a designer with a direct and systematic control over a required robustness. In this paper, a new approach to robust design in multiobjective optimization is introduced, which is able to generate robust design with model uncertainties. In addition, it introduces an opportunity to control the extent of robustness by designer preferences. The presented method is different from its other counterparts. For keeping robust design feasible, it does not change any constraint. Conversely, only a special tunable objective function is constructed to incorporate the preferences of the designer related to the robustness. The effectiveness of the method is tested on well known engineering design problems.     

线性自抗扰控制系统的鲁棒稳定性

针对线性自抗扰控制系统,研究了模型参数不确定情况下的鲁棒稳定性问题.首先给出对象为非自治模型时该系统的H∞判据.然后针对线性误差模型的状态矩阵只在某一行存在不确定参数的情况,基于奇异值理论,得到H∞判据的一种新的等价描述,把H∞范数约束转化为对奈奎斯特图的约束.之后为了降低新判据在实际应用中的保守性,对不确定性矩阵的分解方式进行优化.在此基础之上提出了一种新的方法,用于计算时变参数不确定性的最大边界,为线性自抗扰控制器设计提供理论依据.数值实例表明该方法不仅保守性小,而且计算简单.     

Particle Swarm Optimization and Pure Adaptive Search in Finish Goods’ Inventory Management

Abstract

Inventory management deals with a tradeoff between the benefits of keeping stocks of goods that allows fulfillment of the customer’s demand, and the cost of carrying inventory. Inventory control techniques are very important components and the most organizations can substantially reduce their costs associated with the flow of materials. This paper presents new inventory management model based on particle swarm optimization and pure adaptive search global optimization algorithm in production-inventory system. The proposed model is focusing on planned level of demand for finished goods, production and raw materials cost, production capacity as the norm, change of the production cost and inventory capital cost, all of which are typical factors in automobile manufacture industry. The model determines different factors such as the minimizing inventory quantity, minimizing inventory value, and minimizing production cost based on demand for production items. The model is tested with original real-world dataset obtained from the automotive company Lear from US and its factory in Novi Sad, Serbia.     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.