A novel hybrid method for supply chain optimization with capacity constraint and shipping option

In a modern market, supply chain network design is considered as a strategic decision that provides the proper platform for cost management and increases the competitive edge of enterprise. In a five-tier supply chain, there are several facilities such as suppliers, manufacturers, warehouses, distribution centers, and retailers or customers. For product transportation from one facility to another, different types of options may be used. These options have variety price and the manager should do the best assignment to reduce the total cost. In this paper, we formulated an integer programming model for a five-tier supply chain with capacitated facility and multiple transportation option with fixed lead time. We also proposed a novel meta-heuristic solution methodology that combines the Taguchi's feature with artificial immune approach in order to solve the proposed model. The performance of the proposed solution methodology has been examined against a set of numeric instances and the obtained results are compared with those provided by hybrid genetic algorithm and Taguchi and artificial immune system. Results indicate that this methodology can make better results than previous solutions effectively.     

Deriving the cost function for a class of three-echelon inventory system with N-retailers and one-for-one ordering policy

A three-echelon inventory system with two warehouses and N-retailers is considered in this paper. Transportation times are constant and retailers face independent Poisson demand. Replenishments are one-for-one. The lead time of a retailer is determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. Axsäter [2] evaluated the value of the expected two-echelon inventory system cost with the same assumptions, but in this paper, we add a warehouse as third echelon and therefore this may lead to having one more delay in shipment which was incurred in the new warehouse. We obtained the cost function for the inventory system and tested it by several examples.     

Designing a stochastic distribution network model under risk

In this paper, we present a stochastic supply chain network model under risk, in which three tiers of decision makers of suppliers, distribution centers (DCs), and customers seek to determine their optimal plans. Unlike other studies in the extant literature, we use financial risk measure to model and for the first time, a new methodology based on finance literature is used to optimize the conditional value-at-risk (CVaR) measure for the problem. In fact the aim of this paper is to show the benefits of considering CVaR to control the risks in the supply chain networks. Also in order to obtain the economics of scale, a piecewise linear transportation cost function is applied between suppliers and DCs. We formulate the problem as a convex mixed integer program. A two-phase (constructive and improvement) heuristic method is developed to solve the problem. In the constructive phase, an initial solution is built randomly, and in improvement phase, this solution is improved iteratively by using a hybrid algorithm combining Tabu search and simulated annealing methods. Numerical experiments demonstrate the practicability of considering CVaR in the model which is promising in the supply chain network area, and also the significant efficiency of the heuristic method in terms of CPU times.     

An integrated analytic network process with mixed-integer non-linear programming to supplier selection and order allocation

As the global business environment changed, much more commercial and technological competitions evolved in this environment. Consequently, more attention is devoted to the business partners including suppliers. In this paper, supplier selection with order allocation problem is addressed for strategic items with respect to the materials’ characteristics as well as what has been mostly considered in the literature, suppliers’ characteristics. The proposed model comprises an analytic network process (ANP) sub-model to qualify suppliers and filter-suitable candidates among the available ones. Additionally, the ANP sub-model is applied to evaluate suppliers regarding their qualitative attributes which cannot be modeled with mathematical tools properly. Moreover, a mixed-integer non-linear sub-model is presented to simultaneously allocate order quantities to the chosen suppliers. The model is customized to the strategic items by introducing supplier switching cost which is a notable cost component for products. Finally, experimental results and sensitivity analyses are presented to validate the proposed model.     

Determination of the economical policy of a three-echelon inventory system with (R, Q) ordering policy and information sharing

In this work, we consider a three-echelon serial inventory system with two warehouses (suppliers) and one retailer with information exchange. The retailer applies continuous review (R, Q) policy. The warehouses have online information on the inventory position and demand activities of the retailer. We present a new ordering policy to share information among inventory echelons. The warehouse I and II start with m ₁ and m ₂ initial batches of the same order size of the retailer, respectively. The warehouse I places an order to an outside source immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₁, and the warehouse II places an order to the warehouse I immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₂. Transportation times are constant and the retailer faces independent Poisson demand. The lead times of the retailer and the warehouse II are determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. In this paper using the idea of the one-for-one policy, we implicitly incorporate the distribution function of the random delay to obtain the exact value of the expected inventory system cost. Resorting some numerical examples in three different scenarios, we show how information sharing reduces the inventory costs.     

Integrating production and transportation scheduling in a two-stage supply chain considering order assignment

This study is concerned with the integration of production and transportation scheduling in a two-stage supply chain environment while considering the assignment of orders to the suppliers. The first stage contains m suppliers distributed in various geographic zones, and the second stage is composed of l vehicles with different speeds and transportation capacities that transport n jobs from the supplier to a manufacturing company. In addition, it is assumed that each job occupies a different vehicle size and could be processed by some permissible suppliers. After modeling the problem as a mixed integer programming problem, a genetic algorithm named dynamic genetic algorithm (DGA) is proposed to solve it. Since this problem has not been mentioned in the literature, DGA performance was evaluated by comparing its outputs with optimum solutions for small-sized problems and to the random search approach for larger problems. Additionally, the performance of the DGA was compared with that of a similar problem from the literature. The results of these comparisons show that the DGA is an excellent approach. In addition, the impact of grouping technology initialization is examined, showing that the quality of the solution was not improved and that there was an increase in the CPU time.     

Modeling and solving a one-supplier multi-vehicle production-inventory-distribution problem with clustered retailers

This paper considers a supply chain management problem which integrates production, inventory, and distribution decisions. The supply chain is composed of one supplier production facility and several retailers located in a given geographic region. The supplier is responsible for the production and the replenishment of the inventory of retailers, in a vendor managed inventory (VMI) context. The distance between retailers is negligible compared to the distance between the supplier and the retailers’ region. Thus, for each vehicle, there is a major fixed cost for traveling to the cluster of retailers and a minor fixed cost for visiting each individual retailer. The problem consists of determining quantities to be produced, quantities to be delivered to retailers, vehicles to be used, and retailers to be serviced by each vehicle. This problem is an extension of the one warehouse multi-retailer problem with the consideration of production planning and storage and vehicle capacity limitations in addition to fixed vehicle utilization costs and retailer servicing costs. The objective is to minimize a total cost composed of production, transportation, and inventory holding costs at the supplier and at the retailers. Two mixed integer linear programming formulations are proposed and six families of valid inequalities are added to strengthen these formulations. Two of these families are new and the others are adapted from the literature. The numerical results show that the valid inequalities considerably improve the quality of the formulations. Moreover, the parameters that influence the most computational times are analyzed.     

Study on multi-agent-based agile supply chain management

In a worldwide network of suppliers, factories, warehouses, distribution centres and retailers, the supply chain plays a very important role in the acquisition, transformation, and delivery of raw materials and products. One of the most important characteristics of agile supply chain is the ability to reconfigure dynamically and quickly according to demand changes in the market. In this paper, concepts and characteristics of an agile supply chain are discussed and the agile supply chain is regarded as one of the pivotal technologies of agile manufacture based on dynamic alliance. Also, the importance of coordination in supply chain is emphasised and a general architecture of agile supply chain management is presented based on a multi-agent theory, in which the supply chain is managed by a set of intelligent agents for one or more activities. The supply chain management system functions are to coordinate its agents. Agent functionalities and responsibilities are defined respectively, and a contract net protocol joint with case-based reasoning for coordination and an algorithm for task allocation is presented.     

基于Lagrange松弛分解的多产品生产--分销系统的联合决策

考虑全球制造环境下多产品生产分销网络系统中的联合物流决策问题,包括供应商指定的生产任务、生产批量、供应商和用户之间的年运输量和订货批量,提出了基于Lagrange松弛的两层分解启发式算法(LRD)来求解联合决策模型(JDM-M),其中第一层是供应商指定的生产任务、生产批量和运输流量的联合决策(APLS-TF),第二层是运输和订货批量的联合决策(TOQ-M)。仿真分析表明LRD对于大规模的集成决策问题是行之有效的方法。     

Synchronization in multi-echelon supply chain applying timing discount

Due to the increasing emphasis on the effective management of the supply chain, synchronization and cooperation issues between suppliers and retailers in decentralized multi-echelon inventory/distribution systems have gained much attention in the recent years. In this paper, we consider coordination issues of a distribution system composed of a manufacturer, a supplier (distributor), and several retailers. The supplier outsourcing a third party offers a timing discount to multiple retailers in order to synchronize the timing of their orders with the order cycle. It is also assumed that retailers are allowed to face stock outs. In this paper, a mathematical model is developed to analyze the problem. Results show that while synchronizing the supplier and the outsourcer enhances the supply chain efficiency, offering any type of timing discount by the supplier decreases the supply chain efficiency. It is also noted that having coordination between the manufacturer and the supplier has no impact on the supplier’s profit but may decrease the retailer’s costs. It is believed that our findings provide potential and significant managerial implications in the area of supply chain coordination when these systems are decentralized.     

基于斯坦克尔伯格博弈的入厂物流利益协调问题

为探讨入厂物流的利益协调问题,提出了由一个制造商和两个零部件供应商组成的两阶供应链.以零部件供应商库存成本和制造商运输成本最小化为目标,以博弈论为基础,建立了由制造商为主方,零部件供应商为从方的两阶斯坦科尔伯格主从博弈模型.制造商采取共同订货期为基础订货和循环取货的方式,并通过相应激励来诱使供应商参与合作.该供应链协调策略实现了两阶供应链库存一配送的联合优化.通过求解斯坦克尔伯格博弈模型,得出了最优的共同订货期.订货期倍数和激励奖金的数值解.最后给出了算法和仿真分析.仿真分析讨论了相关参数变化对制造商成本、零部件供应商成本和系统总成本的影响.     

Simultaneous coordination of capacity building and price decisions in a decentralized supply chain

In this paper, we investigate the simultaneous coordination of price and capacity building decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While the coordination of supply chain with stochastic demand and fixed prices has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand, we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications.     

Possibilistic inventory and supplier selection model for an assembly system

In this paper, the problem of inventory lot-sizing and supplier selection for an assembly system is considered, where the supplier available capacities are assumed as ambiguous dynamic parameters. In this scenario, which is a frequent case in large assembly-based factories such as automobile manufacturers, the final product is assembled from multiple components with different conversion factors, which can be sourced from multi-capacitated suppliers through the multi-period horizon of imprecise demand. Due to high shut-down costs of assembly lines, it is assumed that production never stops even though some components may not be available. Therefore, the unfinished products are transferred to a buffer zone and preserved there until the lacking components become available. In this study, a possibilistic mixed integer mathematical model, with fuzzy objective function and soft constraints, is developed to determine which component in what quantities, from which suppliers, and in which periods should be ordered. The model, inspired by the real case of the Iran Khodro Car Company, aims to maximize the profit while keeping a high customer service level by avoiding shortages. This model also considers the ambiguity of dynamic parameters such as demand, suppliers’ available capacities, prices, and holding and shortage costs. To solve the problem, the possibilistic model is first converted into an auxiliary crisp multi-objective model. Through an interactive fuzzy approach, the suggested multi-objective problem is then transformed into an equivalent single-objective model. Finally, a particle swarm optimization is proposed to achieve the overall satisfactory compromise solution. A numerical sample is used to validate the proposed model.     

A new model to mitigating random disruption risks of facility and transportation in supply chain network design

In this article, we study the design problem of a reliable stochastic supply chain network in the presence of random disruptions in the location of distribution centers (DCs) and the transportation modes. It is assumed that a disrupted DC does not necessarily fail the whole of its capacity, and may lose a fraction of that, and rest of demand can be served by other DCs. We introduce a new strategy called soft-hardening strategy where the fraction of the lost capacity depends on the amount of investment for opening and operating. Additionally, the conditional value-at-risk (CVaR) approach is applied to control the risk of model. Finally, to solve the model, first we present an exact solution method by reformulating the problem as a second-order cone programming model, and second a hybrid algorithm combining tabu search and simulated annealing algorithms is developed.     

Determining the optimum production quantity in three-echelon production system with stochastic demand

This paper considers a three-echelon integrated production inventory model consisting of a central warehouse and a manufacturer including two independent departments as processing and assembly stages. To assemble the finished product, materials are carried to the assembly stage through two different flow channels. One group requires preprocessing in the processing stage, and the other one directly arrives from an outside supplier. Storing inventories either in a warehouse (as finished products) or in the stages (as work-in-process) and shipping them between the stages incur inventory costs that must be balanced to achieve minimum joint total cost. The central warehouse faces stochastic demand, which is assumed to be a generally distributed demand. It is controlled by continuous review (R,Q) policy. Additionally, warehouse ordering cost can be reduced through further investment. To analyze, we formulate a nonlinear cost function to aggregate all the costs. After, a simulated annealing algorithm has been suggested to solve the problem. Numerical experiments are presented to evaluate the performance and effectiveness of the proposed algorithm. Also, we use the branch and bound technique and a nonlinear optimization technique—generalized reduced gradient—for solving this problem. The experimental results show a fine performance of the proposed algorithm in comparison with two other methods.     

Chance constraint-based multi-objective stochastic model for supplier selection

Nowadays, every business organization has to execute all decisions in a highly competitive and uncertain scenario for improving its performance. One of such decision that every organization has to undergo is to select best suppliers for timely delivery of good quality parts at minimum cost. Therefore, effective and cost-efficient supplier selection in a stochastic or uncertain scenario helps an organization in achieving its goal. Hence, this paper deals with the supplier selection problem under stochastic environment. In the present work, an attempt is made to model Stochastic Multi-objective Supplier Selection Problem (SMoSSP) applying chance constraint approach. The proposed model considers operational risks involving uncertainties-related supplier’s capacity, product demand, transportation and variable costs and lead time probability distributions. The SMoSSP is solved using non-preemptive goal programming and weighted aggregate function technique. To validate the proposed model data is generated randomly and solved in LINGO 10. Illustrative examples are presented to demonstrate the SMoSSP.     

Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain

This study concerns the coordination of pricing and inventory decisions in a multiproduct two-stage supply chain that consists of one manufacturer and multiple retailers within a competitive environment. The retailers order some substitutable products from a common manufacturer. It is assumed that channel members have different market power. The purpose of this paper is to coordinate pricing and inventory decisions such that utility of all involved levels (manufacturer and retailers) is met. Hence, a nonlinear multidivisional bi-level programming model is developed. This model considers both retailers and manufacturer when deciding about the pricing and production volume (for manufacturer) or amount of purchase (for retailers). A hybrid of genetic algorithm (GA) and local search method is proposed to solve the nonlinear bi-level model. This model is reduced to a nonlinear programming by replacing the Karush–Kuhn–Tucker (KKT) conditions of followers to the lower level of the model. Then, the obtained single-level model is relaxed to a linear model to achieve an upper bound (UB). Finally, a numerical example is presented to analyze which parameters have more effect on the price, lot size and, consequently, on the profit. Results show that increasing the market scale parameter of the manufacturer increases the profit of the manufacturer, but the market scale parameter of retailers has no effect on the manufacturer’s profit, although it increases the retailers’ profit.     

基于免疫算法的并行机间歇过程模糊生产调度

研究了一类具有顺序无关模糊产品切换时间和成本以及模糊单位加工时间和成本的并行机间歇过程调度问题,目的是确定每种产品在每个设备上处理的批次数目、批量以及批次顺序,优化目标为最小化总完成时间和最小化总生产成本。根据任意设备上同种产品的所有批次均顺序处理的性质,建立了问题的模糊运输模型。利用加权和方法将多目标函数转化为单目标函数,并使用基于积分值的方法对模糊数进行排序。提出了基于排列边集编码的免疫算法,通过求解不同规模的问题实例证明,免疫算法不仅能获得比遗传算法和免疫遗传算法更好的解,而且比免疫遗传算法更高效,同时具有良好的动态性能。     

季节性商品两级供应链契约设计与协调模型研究综述

在季节性商品销售环境下,讨论了单节点成员两级供应链契约设计与协调模型研究状况。在此基础上,讨论了多供应商对单零售商、单供应商对多零售商、多供应商对多零售商等不同供应链结构下的契约设计与协调模型研究现状。综述了复杂决策环境对契约设计与供应链协调的影响。总结了目前的研究现状,并提出了今后的研究方向。     

信息共享环境下多级复杂供需链系统的库存成本分析

以一个制造商、多个互异的分销商和多个互异的零售商组成的复杂供需链系统为研究对象,建立了供需链系统库存成本模型,对各个企业的信息共享价值进行了分析计算.结果表明,制造商和分销商均能够从共享零售商的需求信息中获利,而零售商则从信息共享中得不到任何利益,因此需要制订一定的利益分配机制,以促进供需链信息共享的实现.