A three-echelon supply chain coordination with quantity discounts for multiple items

This study derives an integrated model for three-echelon supply chain (i.e. single-supplier, single-vendor and multi-retailer) to minimise the joint costs of all participants associated with holding costs, ordering costs, and purchasing costs. We particularly emphasise that quantity discounts and joint replenishment policies can be utilised as coordination mechanisms among all parties. In addition, a linearisation approach and mixed integer method are developed not only to obtain an executable integer solution for a finite planning horizon problem but also to simplify the conventional multiple-step procedure used in the quantity discount. The result indicates that the coordination and consolidation of orders can lead to the total cost reduction. Finally, a numerical example is given to illustrate the benefits of orders coordination and consolidation.     

Joint replenishment with imperfect items and price discount

A joint replenishment problem is presented to determine the ordering policy for multiple items having a certain percentage of defective units. The purpose of this paper is to study the impact of the percentage of defective units on the ordering policy. Two different scenarios are presented for joint replenishment problem: (1) without price discount and (2) with price discount. For each scenario, the total expected cost per unit time is derived and algorithms are presented to determine the family cycle length and the integer number of intervals that the replenishment quantity of each item will last. Numerical examples are presented and the results are discussed.     

Maximising profits for an EPQ model with unreliable machine and rework of random defective items

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in ‘out-of-control’ state from ‘in-control’ state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in ‘out-of-control’ state are reworked at a cost just after the regular production time. Occurrence of the ‘out-of-control’ state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.     

Optimal order policy in response to announced price increase for deteriorating items with limited special order quantity

When a supplier announces an impending price increase due to take effect at a certain time in the future, it is important for each retailer to decide whether to purchase additional stock to take advantage of the present lower price. This study explores the possible effects of price increases on a retailer's replenishment policy when the special order quantity is limited and the rate of deterioration of the goods is assumed to be constant. The two situations discussed in this study are as follows: (1) when the special order time coincides with the retailer's replenishment time and (2) when the special order time occurs during the retailer's sales period. By analysing the total cost savings between special and regular orders during the depletion time of the special order quantity, the optimal order policy for each situation can be determined. We provide several numerical examples to illustrate the theories in practice. Additionally, we conduct a sensitivity analysis on the optimal solution with respect to the main parameters.     

Solving lot-sizing problem with quantity discount and transportation cost

Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.     

A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain

Supply chain management is concerned with the coordination of different parts of the production system. Companies have realized that they must closely collaborate with the suppliers of their strategic components or products. Recently, developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers. In these models some incentives are required from the vendors to motivate the buyer to change his (her) policies to the policy which is optimal for the entire system. Quantity discount policies are used as common incentives in the literature. However, the literature on this problem does not incorporate quantity discount into the coordination model. This paper develops a multi-objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all-unit quantity discount policy for the vendors. Due to the complexity of the problem two well known meta-heuristic algorithms are proposed to solve the problem. An illustrative example is given to show the behavior of the model. Results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions.     

Supply chain coordination based on return contracts with a threshold ordering quantity

Return contracts are commonly used by companies selling products with short life cycles and highly uncertain demand. Current research on return contracts assumes suppliers are responsible for all surplus products. In practice, retailers tend to order more than necessary and leave suppliers with large after‐season returns. To mitigate the problem, a new type of return contract with a threshold ordering quantity has been developed by some enterprises. Under these contracts, suppliers specify a threshold for retailers’ ordering quantity. They buy back only the portion in excess of the threshold. In this paper, we show that this new type of contract can achieve two objectives: (a) the supply chain is coordinated, and (b) both the supplier and the retailer can gain more profit than they can gain under a wholesale‐price‐only contract. The new contract does not require any manipulation of wholesale prices. This makes it more acceptable in practice by supply chain members. We also illustrate our findings in a numerical example.     

A hybrid polynomial-time algorithm for the dynamic quantity discount lot size model with resale

We propose an efficient optimal algorithm for determining the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system with single price break point and resale of the excess units is acceptable at the ordering time. The problem is divided into the sub-plans with specific properties by the dynamic programming (DP) method already presented. By modifying the main structure of the DP method, we present a branch-and-bound algorithm to obtain the optimal ordering policy for each sub-plans. Furthermore, we prove some useful fathoming rules to make the branch-and-bound algorithm very efficient. It has also been shown that the worst-case time complexity function of the presented algorithm is O(N⁴) where N is the number of periods in the planning horizon. Finally, we show the efficiency of the presented algorithm and its fathoming rules by solving some test problems which are randomly generated in various environments.     

持续补货模式下的改良品库存模型研究

改良品的订货问题一直没有引起足够的重视。分别建立持续补货模式下不允许缺货与允许缺货的改良品库存模型,并分析改良率与补货周期、各种费用参数的相关关系,研究表明：改良率与补货周期、单位时间存储费用呈负相关关系,与单位时间订货费用、单位时间改良费用、单位时间缺货费用、单位时间总费用呈正相关关系。同时,对不允许缺货与允许缺货的改良品库存模型单位时间总费用进行比较,并分析库存模型各参数对两种库存模型单位时间总费用差值的影响方式,研究表明：单位时间总费用差值与改良率、补充速率、单次订货费用、单位存储费用、单位改良费用呈正相关关系,与单位缺货费用成呈负相关关系,与需求速率的相关关系取决于补充速率与需求速率的大小关系。     

需求随机偏差下带有主从零售商的供应链协调

研究了确定环境下带有主从零售商的供应链协调的基本模型,提出了应急环境下当需求偏差随机发生时集权和分权供应链的最优决策.证明了无论需求随机偏差存在与否都可以运用线性数量折扣合同使得供应链有效达到协调,并相应给出了最优批发单价、最优线性折扣率和转移支付的范围.最后对最优售价、最优总订货量和最优批发单价随需求偏差幅度及其概率的变化进行了仿真分析.     

An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown

In recent years, many researches on economic production quantity (EPQ) models with machine breakdown and preventive maintenance have been developed, but few of them have developed integrated models for deteriorating items. In this study, we develop EPQ models for deteriorating items with preventive maintenance, random machine breakdown and immediate corrective action. Corrective and preventive maintenance times are assumed to be stochastic and the unfulfilled demands are lost sales. Two EPQ models of uniform distribution and exponential distribution of corrective and maintenance times are developed. An example and sensitivity analysis is given to illustrate the models. For the exponential distribution model, it is shown that the corrective time parameter is one of the most sensitive parameters to the optimal total cost.     

Supply chain coordination using time-based temporary price discounts

In this paper, the issue of supply chain coordination (SCC) in a buyer–seller supply chain (SC) with an order size constraint is investigated. The buyer keeps safety stock to cope with lead time demand uncertainties from customers’ side. Unsatisfied demand will be lost. Therefore the whole SC sales volume depends on the service level provided by the buyer. By proposing a time-based temporary price discount in each replenishment cycle, the seller intends to convince the buyer to optimize its safety stock globally. Maximum and minimum discounts, which are acceptable for both parties, are determined and an appropriate discount schedule is derived. A set of numerical experiments are conducted to show performance of the proposed model. The results show that the safety stock coordination is profitable; the proposed model is capable of coordinating supply chain. In addition, the model can share extra benefits between SC members fairly.     

双边信息不对称参与者风险厌恶的应急数量折扣契约

探寻双边信息不对称、一个参与者风险厌恶时,应急数量折扣契约协调供应链应对突发事件的内在规律.借助"利他委托人"理论,科学设置参与者的激励和参与约束条件,在市场价格随机的条件下构建双边信息不对称、一个参与者风险厌恶的应急数量折扣契约.分析信息不对称和风险厌恶对供应链上各决策变量、供应链及链上成员绩效的影响,并通过具体的算...     

Supply chain coordination model with controllable lead time and service level constraint

We consider the coordination issue in a decentralized supply chain composed of a vendor and a buyer in this paper. The vendor offers a single product to the buyer who is faced with service level constraint. In addition, lead time can be reduced by added crashing cost. We analyze two supply chain inventory models. The first one is developed under decentralized mode based on Stackelberg model, the other one is developed under centralized mode of the integrated supply chain. The solution procedures are also provided to get the optimal solutions of these two models. Finally, a price discount mechanism is proposed to induce both the vendor and the buyer to accept the centralized model. The feasibility and efficiency of the proposed models are manifested by numerical examples and some managerial implications are highlighted.     

折损产品整合生产库存系统优化模型研究

在具有两个不同销售周期的销售市场情形下，当需求率、生产率和折损率为常数时，从供应链整合的角度对折损产品的库存系统进行了优化．通过对供应链中产品生产商和销售商库存系统的各自分析，建立了整合库存系统数学模型，给出了优化方法．     

Supply chain coordination with an option contract under vendor‐managed inventory

In this paper, we propose an option contract for a two‐echelon supply chain operating under vendor‐managed inventory (VMI). We find that the supply chain coordination and Pareto improvement can be achieved synchronously. As a comparison, a subsidy contract is introduced to coordinate the supply chain. The paper further considers the influence of a replenishment tactic on the performance of the supply chain. After introducing a replenishment tactic, the supply chain can replenish the products to satisfy unmet demand during the selling season. We further use an option contract to coordinate the supply chain, and a Pareto improvement can be gained. All our findings are numerically illustrated.     

Inventory control model for a supply chain system with multiple types of items and minimum order size requirements

This paper considers a replenishment problem for a single buyer who orders multiple types of items from two or more heterogeneous suppliers in order to sell to end customers. The buyer periodically orders each type of item from the suppliers according to a select inventory control policy. Processing the order, each supplier enforces the policy that an order from the buyer must meet a predetermined minimum order quantity (MOQ). Therefore, the buyer must decide how much to order from each supplier considering the current inventory level, demand forecast, and MOQ requirement. The buyer's problem is formulated as an integer programming model and an efficient implementation strategy is suggested to apply the model to real problems. Numerical experiments are performed to test the validity of the proposed model as well as the efficiency of the implementation strategy. The experimental results show that this model combined with the implementation method yields a considerable cost reduction compared to the most efficient policy currently available.     

物料管理中投料批量和订货批量的决策

通过分析不同种类物料的加工及采购特性,针对物料投料提出一种平衡的优化投料批量决策技术,降低总的加工成本;针对物料采购提出一种订货批量决策技术,合理的降低库存.实验结果表明,该算法简明,便于操作,具有实用价值.     

考虑碳排放量与数量折扣的闭环供应链网络设计与多目标决策优化研究

由于闭环供应链网络在环境法规、客户压力等方面都受到关注,故供应商选择在供应链管理中更具挑战性,本文所提闭环供应链网络模型可解决上述问题.其中,供应商会提供数量折扣以激励买家购买更多的产品.模型的目标函数是将经济成本与碳排放量降至最低,最大限度提升客户满意度等参数,并确定出最佳的供应商、采购量、运输方式、技术类型、碳排放...     

Managing dual warehouses with an incentive policy for deteriorating items

Distributors in a supply chain usually limit their own warehouse in finite capacity for cost reduction and excess stock is held in a rent warehouse. In this study, we examine inventory control for deteriorating items in a two-warehouse setting. Assuming that there is an incentive offered by a rent warehouse that allows the rental fee to decrease over time, the objective of this study is to maximise the joint profit of the manufacturer and the distributor. An optimisation procedure is developed to derive the optimal joint economic lot size policy. Several criteria are identified to select the most appropriate warehouse configuration and inventory policy on the basis of storage duration of materials in a rent warehouse. Sensitivity analysis is done to examine the results of model robustness. The proposed model enables a manufacturer with a channel distributor to coordinate the use of alternative warehouses, and to maximise the joint profit of the manufacturer and the distributor.