Goal programming using multiple objective tabu search

Goal programming (GP) is one of the most commonly used mathematical programming tools to model multiple objective optimisation (MOO) problems. There are numerous MOO problems of various complexity modelled using GP in the literature. One of the main difficulties in the GP is to solve their mathematical formulations optimally. Due to difficulties imposed by the classical solution techniques there is a trend in the literature to solve mathematical programming formulations including goal programmes, using the modern heuristics optimisation techniques, namely genetic algorithms (GA), tabu search (TS) and simulated annealing (SA). This paper uses the multiple objective tabu search (MOTS) algorithm, which was proposed previously by the author to solve GP models. In the proposed approach, GP models are first converted to their classical MOO equivalent by using some simple conversion procedures. Then the problem is solved using the MOTS algorithm. The results obtained from the computational experiment show that MOTS can be considered as a promising candidate tool for solving GP models.     

A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

This paper deals with the operational issues of a two-echelon single vendor–multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.     

Optimizing inventory decisions in a two-level supply chain with order quantity constraints

A fundamental assumption in traditional inventory models is that all of the ordered items are of perfect quality. A two-level supply chain is considered consists of one retailer and a collection of suppliers that operate within a finite planning horizon, including multiple periods, and a model is formulated that simultaneously determines both supplier selection and inventory allocation problems in the supply chain. It is supposed that the ordered products dependent on the suppliers include a certain percentage of imperfect quality products and have different prices. In this paper, we study the impact of the retailer’s financial constraint. On the other hand, suppliers have restricted capacities and set minimum order quantity (MOQ) policy for the retailer’s order amount happened in each period. So, the problem is modeled as a mixed integer nonlinear programming. The purpose of this model is to maximize the total profit. The nutrients, fishery and fruitage industries give good examples for the proposed model. A numerical example is presented to indicate the efficiency of the proposed model. Considering the complexity of the model, a genetic algorithm (GA) is presented to solve the model. We demonstrate analytically that the proposed genetic algorithm is suitable in the feasible situations.     

An integrated model for lot sizing with supplier selection and quantity discounts

Good inventory management is essential for a firm to be cost competitive and to acquire decent profit in the market, and how to achieve an outstanding inventory management has been a popular topic in both the academic field and in real practice for decades. As the production environment getting increasingly complex, various kinds of mathematical models have been developed, such as linear programming, nonlinear programming, mixed integer programming, geometric programming, gradient-based nonlinear programming and dynamic programming, to name a few. However, when the problem becomes NP-hard, heuristics tools may be necessary to solve the problem. In this paper, a mixed integer programming (MIP) model is constructed first to solve the lot-sizing problem with multiple suppliers, multiple periods and quantity discounts. An efficient Genetic Algorithm (GA) is proposed next to tackle the problem when it becomes too complicated. The objectives are to minimize total costs, where the costs include ordering cost, holding cost, purchase cost and transportation cost, under the requirement that no inventory shortage is allowed in the system, and to determine an appropriate inventory level for each planning period. The results demonstrate that the proposed GA model is an effective and accurate tool for determining the replenishment for a manufacturer for multi-periods.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.     

Flying-V型仓储布局货位分配优化方法研究

Flying-V是一种典型的非传统布局方式,根据其布局方式的特性,针对仓储货位分配优化问题,以货物出入库效率最高和货物存放的重心最低为优化目标,建立了货位分配多目标优化模型,并采用自适应策略的遗传算法(GA),以及粒子群算法(PSO)进行求解。根据货位分配的优化特点,在GA算法的选择、交叉和变异环节均采用自适应策略, 同时采用惯性权重线性递减的方法设计了PSO算法,有效地解决了两种算法收敛速度慢和易“早熟”的问题,提高了算法的寻优性能。为了更好地表现两种优化求解算法的有效性和优越性,结合具体的货位分配实例利用MATLAB软件编程实现。通过对比分析优化结果表明,PSO算法在收敛速度和优化效果方面相比于自适应GA算法更具有优势,更加合适于解决Flying-V型仓储布局货位分配优化问题。     

Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

Optimal pricing and ordering policy for non-instantaneous deteriorating items under inflation and customer returns

This paper deals with an economic production quantity inventory model for non-instantaneous deteriorating items under inflationary conditions considering customer returns. We adopt a price- and time-dependent demand function. Also, the customer returns are considered as a function of both price and demand. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal replenishment cycles, and the optimal production quantity simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution. Finally, numerical examples are provided to solve the presented inventory model using our proposed algorithm, which is further clarified through a sensitivity analysis. The results of analysing customer returns provide important suggestions to financial managers who use price as a control to match the quantity sold to inventory while maximizing revenues. The paper ends with a conclusion and an outlook to future studies.     

A probability maximization model based on rough approximation and its application to the inventory problem

In the present paper, we concentrate on dealing with a class of multi-objective programming problems with random coefficients and present its application to the multi-item inventory problem. The P-model is proposed to obtain the maximum probability of the objective functions and rough approximation is applied to deal with the feasible set with random parameters. The fuzzy programming technique and genetic algorithm are then applied to solve the crisp programming problem. Finally, the application to Auchan’s inventory system is given in order to show the efficiency of the proposed models and algorithms.     

An imperialist competitive algorithm for multi-objective U-type assembly line design

Many assembly lines are now being designed as U-type assembly lines rather than straight lines because of the pressure of the just-in-time (JIT) manufacturing concept. Since any type of an assembly line balancing problem is known to be NP-hard, there has been a growing tendency toward using evolutionary algorithms to solve such a hard problem. This paper proposes a new population-based evolutionary algorithm, namely imperialist competitive algorithm (ICA) inspired by the process of socio-political evolution, to address the multi-objective U-type assembly line balancing problem (UALBP). Two considered objectives are to minimize the line efficiency and minimize the variation of workload. Furthermore, the Taguchi design is applied to tune the effective parameters of the proposed ICA. To demonstrate the efficiency of the proposed algorithm, the associated results are compared against an efficient genetic algorithm (GA) in the literature over a large group of benchmarks taken from the literature. The computational results show that the proposed ICA outperforms GA.     

Application of honey-bee mating optimization algorithm on clustering

Cluster analysis is one of attractive data mining technique that use in many fields. One popular class of data clustering algorithms is the center based clustering algorithm. K-means used as a popular clustering method due to its simplicity and high speed in clustering large datasets. However, K-means has two shortcomings: dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies done in clustering. Over the last decade, modeling the behavior of social insects, such as ants and bees, for the purpose of search and problem solving has been the context of the emerging area of swarm intelligence. Honey-bees are among the most closely studied social insects. Honey-bee mating may also be considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of marriage in real honey-bee. Honey-bee has been used to model agent-based systems. In this paper, we proposed application of honeybee mating optimization in clustering (HBMK-means). We compared HBMK-means with other heuristics algorithm in clustering, such as GA, SA, TS, and ACO, by implementing them on several well-known datasets. Our finding shows that the proposed algorithm works than the best one.     

A hybrid metaheuristic algorithm for dynamic rail car fleet sizing problem

The aim of this paper is to present a model and a solution method for rail freight car fleet sizing problem. The mathematical model is dynamic and multi-periodic and car demands and travel times are assumed deterministic, and the proposed solution method is hybridization of genetic algorithms and simulated annealing algorithms. Experimental analysis is conducted using several test problems. The results of the proposed algorithm and CPLEX software are compared. The results show high efficiency and effectiveness of the proposed algorithm. The solution method is applied to solve fleet sizing problem in the Iran Railways as a case study.     

A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products

The joint management of pricing and inventory for perishable products has become an important problem for retailers. This paper investigates a multi-period ordering and clearance pricing model under consideration of the competition between new and out-of-season products. In each period, the ordering quantity of the new product and the clearance price of the out-of-season product are determined as decision variables before the demand is realized, and the unsold new product becomes the out-of-season one of the next period. We establish a finite-horizon Markov decision process model to formulate this problem and analyze its properties. A traditional dynamic program (DP) approach with two-dimensional search is provided. In addition, a myopic policy is derived in which only the profit of the current period is considered. Finally, we apply genetic algorithm (GA) to this problem and design a GA-based heuristic approach, showing by comparison among different algorithms that the GA-based heuristic approach is more performance sound than the myopic policy and much less time consuming than the DP approach.     

An application of Genetic Algorithm in solving an inventory model with advance payment and interval valued inventory costs

The purpose of this research is to solve the mixed integer constrained optimization problem with interval coefficient by a real-coded genetic algorithm (RCGA) with ranking selection, whole arithmetical crossover and non-uniform mutation for non-integer decision variables. In the ranking selection, as well as in finding the best solution in each generation of RCGA, recently developed modified definitions of order relations between interval numbers with respect to decision-making are used. Also, for integer decision variables, new types of crossover and mutation are introduced. This methodology is applied to solve a finite time horizon inventory model with constant lead-time, uniform demand rate and a discount by paying an amount of money in advance. Moreover, different inventory costs are considered to be interval valued. According to the consumption of items during lead-time and reorder level, two cases may arise. For each case, the mathematical model becomes a constrained nonlinear mixed integer problem with interval objective. Our objective is to determine the optimal number of cycles in the finite time horizon, lot-size in each cycle and optimal profit. The model is illustrated with some numerical examples and sensitivity analysis has been done graphically with the variation of different inventory parameters.     

基于PSO-MAs算法的产品组合问题研究

针对多约束的产品组合问题,提出一种基于PSO的Memetic算法。该算法首先运用约束理论识别并剔除非瓶颈约束,然后基于伪效用比率设计了一个局部搜索算法,并将其加入到PSO算法的种群进化中,以增强PSO算法的局部学习能力。通过对算法在小规模和大规模算例中测试,表明该算法在小规模问题中优于许多已有算法,同时能在相对较短地时间内更有效地求解较大规模产品组合问题。因此本文提出的基于PSO的Memetic算法可以用来有效地求解实际中的产品组合问题。     

The inventory replenishment planning and staggering problem: a bi-objective approach

To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions.     

考虑多仓库的共享单车重新配置问题研究

共享单车是我国大力提倡的低碳交通出行模式,加快共享单车发展是解决最后一公里、城市拥堵和环境污染等问题的重要途径。由于人们停放共享单车的无规律性,使得共享单车系统中各车桩的单车库存量存在不平衡。如何合理的对车桩中的单车进行重新调配,来满足用户的需求,是相关企业亟待解决的问题。共享单车的调配路线优化是优化车桩库存量的重要手段之一。本文研究多仓库条件下的货车调配路线优化问题,建立了一个混合整数非线性规划模型。不同于传统的路径优化问题的研究大多是以成本或时间为目标,本文采用基于车桩库存量的非线性惩罚函数来表示用户需求,从而使得所研究的问题是一个凸函数优化问题。为了简化本文的问题,将目标函数分段线性化。基于车桩网络的特点,设计了变邻域搜索算法,以及构建初始解的贪婪算法。最后,以某共享单车公司为例,进行算例分析,来说明模型和算法的合理性和有效性。     

Two-warehouse production model for deteriorating inventory items with stock-dependent demand under inflation over a random planning horizon

This paper develops a production-inventory model for a deteriorating item with stock-dependent demand under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. The effects of learning in set-up, production, selling and reduced selling is incorporated. Different inflation rates for various inventory costs and time value of money are also considered. A hybrid genetic algorithm is designed to solve the optimization problem which is hard to solve with existing algorithms due to the complexity of the decision variable. To illustrate the model and to show the effectiveness of the proposed approach a numerical example is provided. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.     

价格数量折扣下多阶段报童问题的在线策略

价格数量折扣可以提高订购量, 是库存决策中的一个重要因素. 特别地, 当订购量达到一定水平时, 价格折扣才会发生. 应用理论计算机科学兴起的弱集成算法, 研究具有这种价格数量折扣的多阶段报童问题的在线策略. 弱集成算法是一种在线序列决策算法, 其主要特点是不对未来输入做任何统计假设, 克服了报童问题研究中需要对需求做概率假设的困难. 主要将弱集成算法应用到固定订购量的专家策略, 给出了价格数量折扣下多阶段报童问题的具体在线策略;得到了该在线策略相对于最优专家策略的理论保证. 进一步将回收价值和缺货损失费引入, 给出了推广的在线策略及其理论结果. 最后应用数值算例说明了给出的在线策略具有较好的竞争性能.