A coordination system for seasonal demand problems in the supply chain

This article considers a single product coordination system using a periodic review policy, participants of the system including a supplier and one or more heterogeneous buyers over a discrete time planning horizon in a manufacturing supply chain. In the coordination system, the demand of buyer in each period is deterministic, the supplier replenishes all the buyers, and all participants agree to plan replenishment to minimize total system costs. To achieve the objective of the coordination system, we make use of small lot sizing and frequent delivery policies (JIT philosophy) to transport inventory between supplier and buyers. Moreover, demand variations of buyers are allowed in the coordination system to suit real-world situations, especially for hi-tech industries. Furthermore, according to the mechanisms of minimizing the total relevant costs, the proposed method can obtain the optimal number of deliveries, shipping points and shipping quantities in each order for all participants in the coordination system.     

Four-level closed loop supply chain with remanufacturing

This paper addresses the coordination of order quantities in a four-level closed-loop supply chain (CLSC) with remanufacturing. The levels are multiple buyers and tier-1 and tier-2 suppliers, and a manufacturer. The reverse channel consists of an inspection and disassembly center and a remanufacturing center. Customer demand is met from either newly manufactured items, remanufacturing used items collected from customers for recovery, or from both. Mathematical models are developed to find the production (manufacturing and remanufacturing) and inventory policies that minimize the CLSC total cost. One of the models considers emissions from production and transportation and accounts for energy usage. The results showed that higher collection rates of used items reduce the supply chain costs and improves its environmental performance. A mixed strategy of manufacturing and remanufacturing was found to be best for the chain.     

Supply chain coordination for newsvendor-type products with two ordering opportunities and demand information update

This paper studies a coordination issue with two ordering opportunities in a two-echelon supply chain, where one manufacturer sells a single newsvendor-type product through one buyer. The manufacturer does not hold inventory and activates production or order with an infinite capacity and a fixed setup cost in response to the buyer’s order. The buyer places two orderings during the selling period of the product: one happens at the beginning of the period and the other at some specified time within the selling period. The whole selling period is divided into two stages or sub-periods by the buyer’s second order. The stochastic demands in the two sub-periods are assumed to be auto-correlated. The excess demand before the second order is partially backordered, whereas the excess demand at the end of the selling season is utterly lost. Under both the centralized and decentralized settings, we develop the models of how the buyer determines his two-ordering policies. We analyse the existence and uniqueness of the optimal solutions to the models and present the corresponding analytical solutions. Furthermore, we propose an improved revenue-sharing contract that can realize the perfect coordination of the supply chain and study how the revenue-sharing policies affect the supply chain members’ decisions. Finally, we show the superiority of the presented two-ordering strategy through numerical examples.     

Integrated markdown pricing and aggregate production planning in a two echelon supply chain: A hybrid fuzzy multiple objective approach

Given high variability of demands for short life cycle products, a retailer has to decide about the products’ prices and order quantities from a manufacturer. In the meantime, the manufacturer has to determine an aggregate production plan involving for example, production, inventory and work force levels in a multi period, multi product environment. Due to imprecise and fuzzy nature of products’ parameters such as unit production and replenishment costs, a hybrid fuzzy multi-objective programming model including both quantative and qualitative constraints and objectives is proposed to determine the optimalprice markdown policy and aggregate production planning in a two echelon supply chain. The model aims to maximize the total profit of manufacturer, the total profit of retailer and improving service aspects of retailing simultaneously. After applying appropriate strategies to defuzzify the original model, the equivalent multi-objective crisp model is then solved by a fuzzy goal programming method. An illustrative example is also provided to show the applicability and usefulness of the proposed model and solution method.     

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make-to-stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

考虑需求依赖库存及分摊运费的供应链协调

针对单个销售商和单个生产商组成的两层供应链,假定需求依赖于当前库存水平,考虑运输费用与订货量相关,研究了采用分摊运费策略的供应链协调问题.首先在分散式系统下,建立了供需双方的Stackelberg博弈模型;然后设计了分担运输费用的协调策略,建立了供需双方的利润模型.研究结果表明该协调策略不仅能提高供需双方的利润,而且使得供应链达到了完美协调.     

Artificial intelligence-based inventory management: a Monte Carlo tree search approach

The coordination of order policies constitutes a great challenge in supply chain inventory management as various stochastic factors increase its complexity. Therefore, analytical approaches to determine a policy that minimises overall inventory costs are only suitable to a limited extent. In contrast, we adopt a heuristic approach, from the domain of artificial intelligence (AI), namely, Monte Carlo tree search (MCTS). To the best of our knowledge, MCTS has neither been applied to supply chain inventory management before nor is it yet widely disseminated in other branches of operations research. We develop an offline model as well as an online model which bases decisions on real-time data. For demonstration purposes, we consider a supply chain structure similar to the classical beer game with four actors and both stochastic demand and lead times. We demonstrate that both the offline and the online MCTS models perform better than other previously adopted AI-based approaches. Furthermore, we provide evidence that a dynamic order policy determined by MCTS eliminates the bullwhip effect.

     

Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

基于时变需求的集成多级供应链生产订货策略研究

考虑一个时变需求环境下集成多级供应链问题,在有限的规划时间内销售商以固定周期订货,而生产商以不同的周期生产,目的是寻找销售商最优的订货周期和生产商最佳的生产策略,从而使供应链系统的总运营成本最少.建立了该问题的混合整数非线性规划模型,求解该模型分为两步：先求对应一个订货周期的最佳生产策略,再求最优的订货周期,第一步用到了图论里求最短路方法.给出了两个步骤的算法和程序,实验证明它们是有效的.通过算例对模型进行了分析,研究了各参数对最优解及最小费用的影响.     

Price discount based on early order commitment in a single manufacturer–multiple retailer supply chain

Early order commitment (EOC) is a strategy for supply chain coordination, wherein the retailer commits to purchasing from a manufacturer a fixed order quantity a few periods in advance of the regular delivery lead time. In this paper, we formulate and analyze the EOC strategy for a decentralized, two-level supply chain consisting of a single manufacturer and multiple retailers, who face external demands that follow an autocorrelated AR(1) process over time. We characterize the special structure of the optimal solutions for the retailers’ EOC periods to minimize the total supply chain cost and discuss the impact of demand parameters and cost parameters. We then develop and compare three solution approaches to solving the optimal solution. Using this optimal cost as the benchmark, we investigate the effectiveness of using the wholesale price-discount scheme for the manufacturer to coordinate this decentralized system. We give numerical examples to show the benefits of EOC to the whole supply chain, examine the efficiency of the discount scheme in general situation, and provide the special conditions when the full coordination is achieved.     

Coordinating a three-echelon supply chain under price and quality dependent demand with sub-supply chain and RFM strategies

The paper considers a three-echelon supply chain which consists of one supplier, one manufacturer and one retailer for trading a single product. The market demand at the retailer is influenced by the retail price and the quality of the product. The quality of the finished product at the manufacturer depends on the supplier’s raw material quality. We analyze the model for both deterministic and stochastic demand patterns. We first study the centralized and decentralized systems, and then the decentralized system with a sub-supply chain coordination strategy (where the manufacturer chooses to merge with either the supplier or the retailer and then acts as a single entity) and the two-level retail fixed mark-up (RFM) strategy. In the case of the two-level RFM strategy, the manufacturer and the retailer use fixed mark ups over the supplier’s wholesale price. The proposed models are demonstrated through numerical examples. It is observed from the numerical study that the two-level RFM strategy is superior to the sub-supply chain coordination strategy. Further, the two-level RFM strategy in the stochastic demand scenario is not as effective as in the deterministic demand scenario.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

突发事件下需求信息不对称时的供应链协调应对

协调供应链系统使其具有抗突发事件性的研究是供应链管理的核心议题之一。为了分析突发事件下需求信息不对称时的供应链协调问题,考虑由一个制造商和一个零售商组成的供应链,在随机市场需求下,首先分析了数量折扣契约对供应链的协调作用;然后探讨了突发事件导致市场需求发生变化且变化后的需求信息是不对称信息时数量折扣契约对供应链的协调作用,研究表明:基准的数量折扣契约对突发事件下的供应链不再发挥协调作用,为此,给出了供应链应对突发事件的最优应对策略,并调整了原来的数量折扣契约使其具有抗突发事件性。最后,应用一个算例对比加以说明。     

Cost Comparisons for Out-of-Phase Inventory Models

Inventory costs for a fixed time period have traditionally been determined by allocating total costs per cycle uniformly throughout that cycle as well as any partial cycles. This procedure for cost allocation has led to the solution of numerous inventory problems, most notable of which is the anticipated price-increase model. When comparing two out-of-phase inventory models, if costs are accounted for when they occur over a fixed planning horizon, inventory policies should be changed to reflect the impact of this different cost-allocation procedure. For the anticipated price-increase model, the ‘optimal’ order quantity as well as the implied savings in inventory costs will be different when cost models are developed based on these different cost-allocation methods. If the objective is to maximize over a fixed planning horizon the actual savings in inventory costs as they occur, the cost models presented here should be used.     

易逝品价格连续下降情况下带有随机需求的供应链协调

本文研究了短生命周期产品价格随时间连续下降情况下单供应商和单销售商渠道中的供应链协调。分别建立了分散决策、集中决策和基于收入共享合同的最优订货策略模型,讨论了模型的相关性质,提出了一种基于收入共享合同的供应链协调策略,来实现整个供应链的协调。并指出该策略不仅适用于价格时变情况,能实现整个供应链的期望利润最大化,并且具有很好的适用性。最后,用实例仿真验证了本文所给出的模型和策略的有效性。     

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.     

The scheduling of deliveries in a production-distribution system with multiple buyers

In a real production and distribution business environment with one supplier and multiple heterogeneous buyers, the differences in buyers’ ordering cycles have influence on production arrangements. Consequently, the average inventory level (AIL) at the supplier’s end is affected by both the production policy and the ordering policy, typically by the scheduling of deliveries. Consequently, the average inventory holding cost is most deeply affected. In this paper, it is proposed that the scheduling of deliveries be formulated as a decision problem to determine the time point at which deliveries are made to buyers in order to minimize the supplier’s average inventory. A formulation of the average inventory level (AIL) in a production cycle at the supplier’s end using a lot-for-lot policy is developed. Under the lot-for-lot policy, the scheduling of deliveries (SP) is formulated as a nonlinear programming model used to determine the first delivery point for each buyer with an objective to minimize the sum of the product of the individual demand quantity and the first delivery time for each buyer. Thus, the SP model determines not only the sequence of the first deliveries to individual buyers, but also the time when the deliveries are made. An iterative heuristic procedure (IHP) is developed to solve the SP model assuming a given sequence of buyers. Six sequence rules are considered and evaluated via simulation.     

Equilibrium analysis and corporate social responsibility for supply chain integration

This paper evaluates the profit of coordination between manufacturers on corporate social responsibility (CSR) under network equilibrium. A three-tier supply chain network with multiple manufacturers, distributors, and retailers is considered, and several mathematical models are established to investigate behavior and profits in a decentralized supply chain network, a centralized supply chain network, and a supply chain network with CSR. The system-optimal solution of a supply chain network problem is usually not achievable or stable since each member always tries to maximize its own profit. In order to make such a system-optimal solution in a stable state and ensure the maximization of total profits, a strategy of coordination between manufacturers on CSR is proposed. The amount of payment in CSR of each manufacturer is clearly defined. A hybrid diagonalization method with a super-network representation is proposed and tested with numerical examples. The results show that by taking CSR, the total profits of the whole supply chain network can increase with or without coordination.     

Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy

We investigate a decentralized supply chain that consists of a manufacturer and a retailer where the retailer simultaneously determines the retail price and order quantity while experiencing customer returns and price dependent stochastic demand. We propose an agreement between the manufacturer and the retailer that includes two buyback prices, one for unsold inventory and a second for customer returns, and show that this type of easy-to-implement agreement can achieve perfect supply chain coordination and be a win-win for both manufacturer and retailer when a complementary profit-sharing agreement is included.