Optimal production lot size and reorder point of a two-stage supply chain while random demand is sensitive with sales teams' initiatives

The paper develops a production-inventory model of a two-stage supply chain consisting of one manufacturer and one retailer to study production lot size/order quantity, reorder point sales teams’ initiatives where demand of the end customers is dependent on random variable and sales teams’ initiatives simultaneously. The manufacturer produces the order quantity of the retailer at one lot in which the procurement cost per unit quantity follows a realistic convex function of production lot size. In the chain, the cost of sales team's initiatives/promotion efforts and wholesale price of the manufacturer are negotiated at the points such that their optimum profits reached nearer to their target profits. This study suggests to the management of firms to determine the optimal order quantity/production quantity, reorder point and sales teams’ initiatives/promotional effort in order to achieve their maximum profits. An analytical method is applied to determine the optimal values of the decision variables. Finally, numerical examples with its graphical presentation and sensitivity analysis of the key parameters are presented to illustrate more insights of the model.     

The benefits of a three-level coordinated distribution policy in the value chain

Several studies have addressed the “buyer–supplier” relationship both qualitatively and quantitatively. Accordingly, this study focuses specifically on shipment sizes, and the number of shipments made under a three-echelon model composed of a manufacturer, a distribution center, and a retailer. A joint model is proposed, in which the system relevant cost is significantly reduced. Each party’s total relevant cost loss was calculated and compared with its optimal strategy. While the retailer was the focal company, the other parties’ loss tended to be the largest.     

基于促销投资的供应链应急协调研究

研究了由单制造商和单零售商组成的供应链中,零售阶段需求依赖于零售商的促销投资水平,当制造商的生产成本和零售商的存货投资成本同时出现扰动时的应急协调问题。通过对生产成本和存货投资成本的扰动程度进行情形分析,提出了不同程度扰动时的最优应对策略和协调机制。该机制为集中供应链系统中的决策者和制造商在面临生产成本和存货投资成本同时扰动时提供了理论决策依据。     

A numerical solution for a two-stage production and inventory system with random demand arrivals

This paper is about the study of a production lot sizing problem consisting of customers, one retailer, and one manufacturer. Demand from customers arrives randomly at a retailer one unit at a time. The retailer replenishes inventory from the manufacturer upon receiving a customer's order after its inventory depleted to zero. The manufacturer's production rate is assumed to be a finite constant. A production cycle starts when the manufacturer's inventory falls to or below zero and stops when its on-hand inventory reaches its optimal level. During the uptime in a production cycle, inventory is being built while randomly arriving orders from retailer are being fulfilled. The order arrival times from customers are independently and identically distributed, hence the inventory processes at both the manufacturer and the retailer become a renewal process that is difficult to solve analytically for a general distribution of order arrival time. Therefore, a numerical approach is used in developing a search procedure to obtain the optimal solution to the problem. Employing such a numerical approach, we also investigate how optimal solutions in different cases will change over the spectrum of some key parameters of the problem.     

Stochastic models for the coordinated production and shipment problem in a supply chain

In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a stochastic environment. The supplier controls the production, holds inventory and ships the products to the retailer to satisfy the external demand. We model the system as a Markov decision process, and show that the optimal production and transportation decisions are complex and non-monotonic. Therefore, we analyze two widely-used shipment policies in the industry as well, namely time-based and quantity-based shipment policies in addition to a hybrid time-and-quantity based shipment policy. We numerically compare the performances of these policies with respect to the optimal policy and analyze the effects of the parameters in the system.     

直销渠道选择对供应链成员决策的影响研究

在考虑直销渠道单位产品运作成本和消费者区域性差异特点的情况下,研究了处于主导地位的制造商开通直销渠道的条件,探讨了直销渠道对渠道需求、制造商和零售商的最优定价和利润的影响。结果表明,开通直销渠道不影响制造商的批发价定价,但可以迫使零售商降低零售价格;开通直销渠道使制造商在分散式供应链中和协调式供应链中都能获得更多利润,使零售商利润减少;只有当运作成本和消费者区域性差异都很大时,开通直销渠道对双方都是有利的,实现“双赢”局面。     

Optimal dual-channel supply chain configuration for product categories with different customer preference of online channel

This study addresses the supply chain configuration problem of manufacturer faced with multiple channel choices. We investigate the optimal combination of traditional and online sales channels for different product categories with differing customer preference of the online channel. We have considered three distinct dual-channel supply chain configurations comprising of a manufacturer, a traditional channel and an online channel viz. retailer–e-tailer; company store–e-tailer; and retailer–e-marketplace. As the manufacturer will face a quantity allocation decision between traditional and online channels, the competition is modeled using Cournot model with the manufacturer as the Stackelberg leader. Values of optimal order quantity and price for the different entities have been established. Influence of variation in customer preference of online channel on the optimal policies is also examined. We find that the manufacturer prefers retailer–e-marketplace configuration for products with high customer preference of online channel and company store–e-tailer configuration for products with low customer preference of online channel. In addition, we find that the retailer–e-tailer configuration is dominated by company store–e-tailer and retailer–e-marketplace configuration irrespective of the product’s customer preference of online channel.     

A multi-stage production-inventory model with learning and forgetting effects,rework and scrap

This paper studies a serial production line where a proportion of defective items is produced at each stage. Defective units enter a rework process, which is imperfect as well. Twice defective items are scrapped. This paper also considers learning and forgetting in production and rework processes and studies how the number of shipments of a lot from a production stage to the next influences the overall performance of the system. A model for a multi-stage production-inventory system is developed and optimized against an aggregate performance measure of four partial measures that are based on production time, process yield, in-process inventory and shipment frequency. Each of these partial performance measures is weighed by the system’s decision maker in accordance to importance. The numerical results show how the values of learning rates, weights assigned to the partial performance measures and the number of production stages influence the overall performance of the system.     

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered supplier’s production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailer’s and holding costs, production cost, transportation cost, setup cost of the supplier’s and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.     

The production size and inventory policy for a manufacturer in a two-echelon inventory model

This paper proposes a two-echelon inventory model for a periodical commodity, in which the market and manufacturing channels are combined. This model can be used to solve the production policy, the order policies of the raw materials for the manufacturer, and order size for the retailer. By assuming that the retailers’ demand obeys normal distribution and that the retailer makes orders according to the Newsboy Rule, we derive the necessary and sufficient conditions for the optimal solution of production size, wholesale price, and replenishment cycle of raw materials for the manufacturer. Also, the necessary condition is explored in order to gain managerial insights and economic implications based on numerical examples and sensitivity analysis.     

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.     

Optimal distribution channel strategy for new and remanufactured products

The market for remanufactured products is large and growing rapidly, accelerated by the widespread popularity of internet sales and online auctions. Whereas extant remanufacturing research focuses primarily on such operations management issues in collecting of end-of-life products, remanufacturing technologies, production planning, and inventory control, we consider an operations-marketing interaction issue by identifying the optimal channel structures for marketing new and remanufactured products. Specifically, based on observations from current practice, we consider three channel strategies a dominant manufacturer can adopt: (1) marketing both new and remanufactured products through an independent retailer; (2) marketing the remanufactured products through the independent retailer, while controlling the new product sales by using its own online channel; (3) marketing the remanufactured products through the manufacturer-owned online channel, while selling new products through the independent retailer. Our results show that the manufacturer prefers to differentiate new and remanufactured products by opening a direct online channel, no matter how the system parameters change. However, which type of products (new or remanufactured) the manufacturer should sell through the online channel depends on the cost saving from remanufacturing, the customer’s acceptance of remanufactured products and the online inconvenience cost. Furthermore, this paper shows that, compared with channel strategy I where the manufacturer sells both new and remanufactured products through an independent retailer, this dual channel strategy benefits the end consumers, but might do harm to the retailer and the total supply chain in some situations.     

Cooperative advertising in a capacitated manufacturer–retailer supply chain: a game‐theoretic approach

To achieve a more realistic understanding of how the supply chain's components interact, it is helpful to consider the operational limitations of the underlying supply chain while analyzing cooperative advertising. This paper studies cooperative advertising in a manufacturer–retailer supply chain under the practical operational assumption that the manufacturer's production capacity is limited. The retailer advertises locally, and the manufacturer advertises in national media and supports part of the retailer's promotional costs. Equilibria are determined under two different scenarios. In the first scenario, both retailer and manufacturer move simultaneously, while in the second scenario, they move sequentially, with the manufacturer being the leader. The sales function is a bivariate version of the diminishing returns response function. When the production capacity is unlimited, several important properties can be proven, which cannot be shown analytically for the existing sales functions. Considering the production‐capacity constraint leads to new managerial insights into cooperative advertising. For example, only if the production capacity is large enough, both manufacturer and retailer are better off under the second scenario than the first scenario. In other words, the sequential move is not necessarily Pareto‐improving when the production capacity is limited. It is also observed that, under the first scenario, there are multiple equilibria whenever the production capacity is not too high. Under the second scenario, the manufacturer supports the retailer only when the retailer's margin is relatively small compared to the manufacturer's margin and production capacity.     

网购环境下提供退款保证时的决策模型研究

研究了不同供应链成员提供退款保证策略及其优化选择问题。考虑了由单个制造商和单个零售商组成的单条供应链,共考虑了三种退款保证策略,即制造商和零售商均不提供退款保证、仅零售商提供退款保证以及仅制造商提供退款保证策略。分别求解得到相应的最优消费者需求量、零售价格、批发价格以及利润的联合决策。研究发现：零售商的商品销售价格、制造商的批发价格、消费者的需求量以及零售商和制造商的利润都与是否提供退款保证服务有关。发现只要当供应链成员提供退款保证服务时商品残值满足一定条件,提供退款保证不仅不会使供应链成员利润降低,反而会提高他们的利润水平;当制造商提供退款保证时商品残值与零售商提供退款保证时商品残值的差值满足一定的条件,供应链中制造商和零售商提供退款保证服务都有可能给供应链带来更高的利润水平。     

风险规避制造商市场入侵策略

针对由风险中性的在位制造商、风险规避的外来制造商和风险中性零售商组成的二级供应链系统,基于Stackelberg博弈理论建立不同市场入侵策略下的决策模型,研究风险规避的外来制造商市场入侵策略选择问题,分析市场入侵和风险规避行为对供应链成员均衡决策的影响.研究发现:当外来制造商通过零售商销售产品时,损害在位制造商的利润,但对零售商有利;当外来制造商通过网络渠道直接向消费者销售产品时,不一定损害在位制造商的利润,存在帕累托改进区域;当外来制造商的风险规避程度较大时,价格战愈发激烈,对自身、在位制造商和零售商都是不利的;外来制造商的市场入侵策略受质量差异程度、风险规避程度、生产成本和直销成本的综合影响;外来制造商选择最优的市场入侵策略时,损害在位制造商的利润,而且供应链系统不能实现帕累托改进.     

Two‐echelon manufacturer–retailer supply chain strategies with price,quality, and promotional effort sensitive demand

This study deals with the two‐layer supply chain model of one manufacturer and one retailer for a single commodity where market demand is assumed to be dependent on selling price, quality of the products, and promotional effort of the retailer. We investigate the behavior of the supply chain under centralized, manufacturer Stackelberg, conditional manufacturer Stackelberg, retailer Stackelberg, conditional retailer Stackelberg, and vertical Nash model structure. The nature of the above models provides great insights to a firm's manager for achieving optimal strategy in a competitive marketing system. Quite often, not all items produced in a firm are of perfect quality; some are perfect (conforming) quality and others are imperfect (nonconforming) quality. The nonconforming products are sold in a secondary shop or by other retailers. The procurement cost of finished products depends on the quality of the products due to more investment in advanced technology, better raw materials, and skilled labor, etc. The warranty policy for the products is also imposed to attract the customers to buy more. Here, both members (manufacturer and retailer) jointly share the cost of the warranty policy. The objective of this paper is to determine the optimal selling price and promotional effort of the retailer, while the optimal wholesale price and quality of the products are determined by the manufacturer so that the above strategies are maximized. Finally, numerical examples with sensitivity analysis of the key parameters are illustrated to investigate the proposed model.     

Commitment decisions with demand information updating and a capital‐constrained supplier

In this paper, we study a single two‐echelon supply chain with a capital‐constrained supplier (manufacturer) and a retailer. The supply chain faces a stochastic demand. As the production lead time is long, the market demand is updated during the supplier's production lead time. The supplier needs to determine the production quantity based on the original demand forecast, and the retailer needs to determine the time and quantity to order. The retailer can place an order before the supplier's production (preorder) or after the supplier's production (regular order). We prove the existence of optimal equilibrium solutions under both preorder and regular order strategies. We analytically investigate the order strategies for the supply chain agents under perfect and worthless market information updating. Moreover, we numerically analyze the impact of the information updating quality on the order strategy selection, and the effect of exogenous shocks on the supply chain agents.     

考虑双重低碳宣传补贴的供应链碳减排优化

考虑由一个制造商主导的一个零售商构成的供应链,研究供应链的合作减排及低碳宣传问题,运用斯坦伯格博弈理论分别构建了制造商给予零售商的单一低碳宣传补贴（SS）以及政府给予制造商、制造商给予零售商的双重低碳宣传补贴（DS）的分散决策博弈模型,得到最优的减排水平、低碳宣传努力程度以及低碳宣传成本分摊比例。通过比较分析发现：当政府补贴系数超过一定值时,DS模式下供应链利润、制造商利润、零售商利润、减排水平、低碳宣传努力程度及低碳宣传成本分摊比例均优于SS模式;政府补贴系数的增加、减排难度的降低及零售商的宣传努力成本系数降低会增加制造商、零售商以及供应链利润。最后运用算例验证了模型的有效性。     

Supply chain coordination for a deteriorating item with stock and price‐dependent demand under revenue sharing contract

This paper deals with an integrated single‐manufacturer single‐retailer supply chain model for a single item. The market demand is assumed to be dependent on both the on‐hand stock and price, and the manufacturer and the retailer are in an agreement of lot‐for‐lot policy. The proposed model is developed under the contract that the retailer offers the manufacturer a percentage of revenue (s)he generates by selling a lot. We determine optimal policies for both the centralized and decentralized coordination systems. A comparison of these policies is made with a numerical example. Sensitivity analysis is performed to examine the stability of the solution.     

Optimal carbon reduction level and ordering quantity under financial constraints

Carbon tax policy is widely adopted by many countries to curb carbon emissions. In the context of carbon tax policy, firms have more incentive to improve carbon reduction levels by reducing their carbon tax costs. However, firms need to bear carbon reduction costs that may cause shortage of capital. Thus, firms may face problems of financial constraints, which may demotivate firms to produce greener products. To address the decision‐making challenges of firms in the contexts of carbon tax policy and financial constraints, we consider a supply chain with a manufacturer who produces green products and a retailer who sells these products. Our study develops five models to investigate the two firms’ optimal wholesale price, carbon reduction level and ordering quantity, according to the manufacturer and retailer with or without financial constraints. Our goal in this study is to explore how carbon tax policy and banks’ interest rates affect the profits of the two firms, supply chain and consumer surplus. Certain managerial insights are obtained as follows. We demonstrate that carbon tax policy and banks’ interest rates demotivate the manufacturer to produce greener products and demotivate the retailer to order more products. If the interest rate to the manufacturer (retailer) is relatively low, then the manufacturer with financial constraint benefits (harms) the consumers compared with the retailer with financial constraint. Importantly, our analysis suggests that carbon tax policy harms the firms but benefits consumers, and the government in some conditions should reduce unit carbon tax.