Fuzzy minimum weight edge covering problem

Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model, α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.     

基于倒箱移动路径的集装箱堆场提箱作业优化模型

集装箱堆场提箱作业优化的目标是通过对倒箱搬运过程的优化使总作业成本最小。本文分析了正面吊设备的提箱作业过程,对作业规则和约束建立数学模型,在分析倒箱移动路径的基础上,提出了提箱作业优化模型。该模型为两层嵌套的组合优化模型,外层子模型针对提箱订单实现倒箱策略优化;内层子模型针对每一步倒箱作业寻找使倒箱作业成本最小的移动路径。提出了求解该模型的算法流程。最后,通过数值算例验证了优化模型的有效性。与传统人工作业方式的比较结果表明:本优化模型能够明显降低提箱作业成本。     

Inventory models with variable lead time and present value

The figures for inventory make up a huge proportion of a company's working capital. Because of this, we formulated the optimal replenishment policy considering the time value of money to represent opportunity cost. In this article, we provide a mixed inventory model, in which the distribution of lead time demand is normal, to consider the time value. First, the study tries to find the optimal reorder point and order quantity at all lengths of lead time with components crashed to their minimum duration. Secondly, we develop a method to insure the uniqueness of the reorder point to locate the optimal solution. Finally, some numerical examples are given to illustrate our findings.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Production Equilibrium Point in Multi-Unit Manufacturing Systems and The Vertical Linear Complementarity Problem

A model that selects and produces products at an equilibrium point in multi-unit manufacturing systems is presented. It enables each business subsystem in the company to select and produce products so that the whole organization meets both internal and external demands at minimum inventory cost. Unlike previously proposed models, this model does not place any restrictions on the number of products or services that each business subsystem can provide. Proofs are provided to show existence of solutions and solvability, and a numerical example is given to demonstrate the utility of the model.     

Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction

This study deals with the lead time and ordering cost reduction problem in the single-vendor single-buyer integrated inventory model. We consider that buyer lead time can be shortened at an extra crashing cost which depends on the lead time length to be reduced and the ordering lot size. Additionally, buyer ordering cost can be reduced through further investment. Two models are presented in this study. The first model assumes that the ordering cost reduction has no relation to lead time crashing. The second model assumes that the lead time and ordering cost reduction are interacted. An iterative procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.     

基于线性规划的炼钢装炉最小成本控制

基于线性规划方法研究了炼钢装炉最小成本控制问题.建立了炼钢装炉数学模型,给出了单纯形法的算法设计.这种算法可以大大降低成本,适合在工程中使用.最后用数值例子对所得结果加以验证,说明了文中结果的正确性.     

基于区间数的应急物资储备库最小费用选址模型

本文研究了基于区间数的应急物资储备库最小费用选址问题。给出了区间数的概念和运算,构建了参数为区间数的应急物资储备库最小费用选址模型,提出了求模型满意解的算法,最后通过算例分析说明该方法的有效性。     

Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm

In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.     

Optimal egress time calculation and path generation for large evacuation networks

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.     

Optimizing flow rates in a queueing network with side constraints

In this paper, modified versions of the classical deterministic maximum flow and minimum cost network flow problems are presented in a stochastic queueing environment. In the maximum flow network model, the throughput rate in the network is maximized such that for each arc of the network the resulting probability of finding congestion along that arc in excess of a desirable threshold does not exceed an acceptable value. In the minimum cost network flow model, the minimum cost routing of a flow of given magnitude is determined under the same type of constraints on the arcs. After proper transformations, these models are solved by Ford and Fulkerson's labeling algorithm and out-of-kilter algorithm, respectively.     

顾客部分延期付款下两级商业信用易腐品订货策略

针对易腐品的经济订货批量问题展开研究。在供应商给零售商提供延迟还款的同时,零售商也给顾客提供部分延期还款条件。分五种情况分别讨论零售商的成本构成,并由此建立数学模型以求解最优订货周期使得零售商单位时间总成本最小化。通过数学证明得到了目标函数的解析性质,结果显示每种情况下在可行域范围内至多存在一个极小值点。以此为基础给出了相应的命题以有效地确定零售商的最优决策。最后通过数值算例说明了模型的有效性。     

Optimal control of a removable and non-reliable server in an infinite and a finite M/H2/1 queueing system

This paper deals with a single removable and non-reliable server in both an infinite and a finite queueing system with Poisson arrivals and two-type hyper-exponential distribution for the service times. The server may be turned on at arrival epochs or off at service completion epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Conditions for a stable queueing system, that is steady-state, are provided. Cost models for both system capacities are respectively developed to determine the optimal operating policy numerically at minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values given to the system parameters, as well as to the cost elements. Sensitivity analysis is also investigated.     

An optimal replenishment policy for deteriorating items with effective investment in preservation technology

In this paper, considering the amount invested in preservation technology and the replenishment schedule as decision variables, we formulate an inventory model with a time-varying rate of deterioration and partial backlogging. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, under given replenishment schedule, we show that the total profit per unit time is a concave function of preservation technology cost. We then provide a simple algorithm to figure out the optimal preservation technology cost and replenishment schedule for the proposed model. We use numerical examples to illustrate the model.     

Cost,Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the $\alpha$-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.     

New modelling approach concerning integrated disease control and cost-effectivity

Two new models for controlling diseases, incorporating the best features of different control measures, are proposed and analyzed. These models would draw from poultry, livestock and government expertise to quickly, cooperatively and cost-effectively stop disease outbreaks. The combination strategy of pulse vaccination and treatment (or isolation) is implemented in both models if the number of infectives reaches the risk level (RL). Firstly, for one time impulsive effect we compare three different control strategies for both models in terms of cost. The theoretical and numerical results show that there is an optimal vaccination and treatment proportion such that integrated pulse vaccination and treatment (or isolation) reaches its minimum in terms of cost. Moreover, this minimum cost of integrated strategy is less than any cost of single pulse vaccination or single treatment. Secondly, a more realistic case for the second model is investigated based on periodic impulsive control strategies. The existence and stability of periodic solution with the maximum value of the infectives no larger than RL is obtained. Further, the period T of the periodic solution is calculated, which can be used to estimate how long the infectious population will take to return back to its pre-control level (RL) once integrated control tactics cease. This implies that we can control the disease if we implement the integrated disease control tactics every period T. For periodic control strategy, if we aim to control the disease such that the maximum number of infectives is relatively small, our results show that the periodic pulse vaccination is optimal in terms of cost.     

Transportation policies for single and multi-objective transportation problem using fuzzy logic

In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.     

时变需求等量进货情形下集成供应链生产订货策略研究

构建了一个包含原料采购、生产和销售过程的集成供应链模型,研究了由原料、生产商和销售商产品构成的三层库存系统的生产订货问题。在有限的规划期内,销售商每次进货量相同,生产商按照EOQ模型采购原材料。以最小化供应链系统的总运营成本为目标,构建一个混合整数非线性规划模型,寻找销售商最优订货方案和生产商最佳生产策略。首先利用网络优化方法求解生产商的最优生产计划,其次利用定界穷举法寻求销售商最优的订货周期,给出了具体的计算方法和Matlab程序。通过算例分析验证了算法的有效性,并研究了各参数对最小费用及最优解的影响。     

Linear,non-approximated models for optimal routing in hazardous environments

A linear optimisation model is presented for the routing of vehicles through hazardous environments or for routing vehicles carrying hazardous materials. The model seeks to find the route with the minimum cost and the minimum probability of accident. As opposed to previously published models, the formulation is linear and no approximations are needed, even in the case of high risk. Several forms of considering risk are presented, as well as a simple method of solution in polynomial time. An example is shown and solved.     

An optimization approach for supply chain management models with quantity discount policy

Owing to the difficulty of treating nonlinear functions, many supply chain management (SCM) models assume that the average prices of materials, production, transportation, and inventory are constant. This assumption, however, is not practical. Vendors usually offer quantity discounts to encourage the buyers to order more, and the producer intends to discount the unit production cost if the amount of production is large. This study solves a nonlinear SCM model capable of treating various quantity discount functions simultaneously, including linear, single breakpoint, step, and multiple breakpoint functions. By utilizing the presented linearization techniques, such a nonlinear model is approximated to a linear mixed 0–1 program solvable to obtain a global optimum.