Coordinating supplier׳s reorder point: A coordination mechanism for supply chains with long supplier lead time

In this paper, the issue of the upstream stochastic lead time in supply chain (SC) is investigated. A coordination mechanism is developed for reducing the harmful effect of upstream lead time. The supplier stochastic lead time can substantially harm the whole supply chain service level, especially when it is accumulated with downstream stochastic lead times. In this study, aggregation of both the supplier and the retailer stochastic lead time is analyzed in a two-stage supply chain (SC). To dampen harmful effects of a long aggregate lead time, a ‘per order extra payment’ model is developed for convincing the supplier to increase its reorder point. Numerical experiments show that coordinating the supplier׳s reorder point creates a significant profit for the whole supply chain. In addition, the proposed model is capable of optimizing the supplier׳s reorder point and fairly sharing the extra benefits. Some conditions are also extracted, under which the proposed model shows good performance.     

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.     

Some remarks on an optimal order quantity and reorder point when supply and demand are uncertain

In the reports in the literature on inventory control, the effects of the random capacity on an order quantity and reorder point inventory control model have been integrated with lead time demand following general distribution. An iterative solution procedure has been proposed for obtaining the optimal solution. However, the resulting solution may not exist or it may not guarantee to give a minimum to the objective cost function, the expected cost per unit time. The aim of this study was to introduce a complete solution of the order quantity/reorder point problem, optimality, properties and bounds on the optimal order quantity and reorder point. The two most appealing distributions of lead time demand, normal and uniform distributions, in conjunction with an exponentially distributed capacity, are used to illustrate our findings in determining the optimal order quantity and reorder point.     

Sole versus dual sourcing under order dependent lead times and prices

In this paper, we consider a dual-sourcing model with constant demand and stochastic lead times. Two suppliers may be different in terms of purchasing prices and lead-time parameters. The ordering takes place when the inventory level depletes to a reorder level, and the order is split among two suppliers. Unlike previous works in the order splitting literature, the supply lead time between vendor and buyer as well as unit purchasing prices is considered to be order quantity dependent. The proposed model finds out the optimal reorder point, order quantity and splitting proportion, using a solution procedure. Numerical results show that neglecting the relationship between ordering batch size and lead times is a shortcoming that hides one of order splitting advantages. Moreover, connecting unit prices to order quantity can decrease the percentage saving from dual sourcing compared to sole sourcing. Furthermore, sensitivity analysis shows some managerial insights.     

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.     

Reducing the negative effects of sales promotions in supply chains using genetic algorithms

This paper considers the detrimental effect of promotions on the supply chain (SC), one of the main causes of the bullwhip effect. A genetic algorithm (GA) is proposed to reduce these negative effects. In order to validate the GA, it is used to determine the optimal ordering policy in an online version of the MIT beer distribution game. Subsequently, the GA is applied in a number of experiments involving deterministic and random demand and lead times combined with sales promotions. It is shown how GAs can be used to dampen the impact of the bullwhip effect and can be used to assist supply managers in predicting reorder quantities along the supply chain.     

Coordinating a two-level supply chain with delay in payments and profit sharing

Achieving effective coordination among suppliers and retailers has become a pertinent research issue in supply chain management. Channel coordination is a joint decision policy achieved by a supplier(s) and a retailer(s) characterized by an agreement on the order quantity and the trade credit scenario (e.g., quantity discounts, delay in payments). This paper proposes a centralized model where players in a two-level (supplier–retailer) supply chain coordinate their orders to minimize their local costs and that of the chain. In the proposed supply chain model the permissible delay in payments is considered as a decision variable and it is adopted as a trade credit scenario to coordinate the order quantity between the two-levels. Computational results indicate that with coordination, the retailer orders in larger quantities than its economic order quantity, with savings to either both players, or to one in the supply chain. Moreover, a profit-sharing scenario for the distribution of generated net savings among the players in the supply chain is presented. Analytical and experimental results are presented and discussed to demonstrate the effectiveness of the proposed model.     

Coordination-based inventory management for deteriorating items in a two-echelon supply chain with profit sharing

This study develops a model for inventory management consisting of a two-echelon supply chain (SC) with profit sharing and deteriorating items. The retailer and the supplier act as the leader and follower, in which the supplier faces a huge setup cost and economic order quantity ordering strategy. The market demand is affected by the sale price of the product, and the inventory has a deterioration rate following a Weibull distribution. The retailer executes three profit-sharing mechanisms to motivate the supplier to participate in SC optimisation and to extend the life cycle of the product. A search algorithm is developed to determine the solutions as using the profit-sharing mechanisms. The outcomes from numerical experiments demonstrate the profitability of the proposed model.     

Channel coordination with price discount mechanism under price‐sensitive market demand

This paper considers a two‐echelon supply chain with single vendor single buyer for trading a single product. The buyer's demand has been assumed to be price‐sensitive. We have assumed three‐level inspection at the vendor's end in order to maintain good quality of the items delivered to the buyer. We have developed models for both decentralized and centralized scenarios and have determined the optimal solution using the basic concepts of analytic geometry and algebra. In addition, we have proposed a price discount mechanism, where the vendor has provided discounts on the purchase cost to the buyer against the buyer's (increased) order quantity. Finally, in order to illustrate and validate the proposed model, a numerical example and sensitivity analysis is carried out, which has provided some important managerial implications. It has been observed from the numerical study that the proposed price discount policy coordinates the supply chain and has improved the profitability of the supply chain and its members.     

Analyzing an inventory system with multiple reorder points and periodic replenishment

This paper investigates multiple reorder point, periodic replenishment systems similar to those utilized on board some U.S. naval vessels for Selected Item Management (SIM). This inventory system is of interest since it involves both regular and priority replenishment, three reorder points, and cyclical restocking of regular orders. A simulation model is developed to study the impact of demand distribution, cycle time, priority order leadtime, and the quantity of units ordered on the performance of the system. It is found that the frequency of service and days without shortages performance measures can be maximized by setting the reorder points at equal intervals between the zero level and the high level. Also, a power approximation model is presented that estimates the high level that will lead to a desired percent days without shortage percentage.     

带有风险规避型销售商的供需链协调

以一个两阶段的供需链系统为背景，针对供需链上决策激励不一致和风险规避效应导致供需链低效的问题，研究了在实践中广泛应用的利益共享合同和批量折扣合同对供需链协调性的影响．证明了两种合同均可克服双重边际效应和风险规避效应，使得供需链协调．并给出了合同参数的设计方案，同时指出在实施上，利益共享合同需强制执行，批量折扣合同自动执行．     

贸易信用下考虑零售商违约风险的供应链协调问题研究

本文研究延迟支付和提前支付同时存在下的供应链协调问题。考虑由一个供应商和一个零售商构成的二级供应链,市场需求随机,延迟支付下零售商会增加订购数量,但由于其违约风险的存在,供应商会降低其交付量,最终导致供应商交付量小于零售商订购量,降低供应链收益。要求零售商提前支付部分货款则可以有效避免零售商的违约问题,通过建立延迟支付和提前支付同时存在下的零售商收益模型和供应商的收益模型,给出了零售商的最优订购量决策和供应商的最优交付量决策,通过调整延迟支付期限和提前支付比例,使得二者相等,并等于供应链整体收益最大化下的生产数量,实现供应链协调。最后通过数值算例分析了相关参数的敏感性等问题。     

Optimal order limit policy under cost effectiveness criterion

The reorder point/reorder quantity policies referred as (r, Q) policies are widely used in industry and extensively studied in the literature. It should be noted, however, that the shortage often occurs in practical situations even if the optimal reorder point and reorder quantity maximizing or minimizing any optimality criteria are rationally determined. In this paper, we present a mathematical model to adjust the shortage period by the emergency order. The problem is to choice the timing for the expedited order. Applying the concept on repair limit policy in the context of reliability theory, the optimal order limit policy maximizing an optimality criterion called cost effectiveness is analytically derived in the framework of (r, Q) inventory system. Finally, some examples for stochastic lead times are given to explain the numerical procedure to obtain the optimal policy.     

Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment

This paper presents a two-stage stochastic programming model used to design and manage biodiesel supply chains. This is a mixed-integer linear program and an extension of the classical two-stage stochastic location-transportation model. The proposed model optimizes not only costs but also emissions in the supply chain. The model captures the impact of biomass supply and technology uncertainty on supply chain-related decisions; the tradeoffs that exist between location and transportation decisions; and the tradeoffs between costs and emissions in the supply chain. The objective function and model constraints reflect the impact of different carbon regulatory policies, such as carbon cap, carbon tax, carbon cap-and-trade, and carbon offset mechanisms on supply chain decisions. We solve this problem using algorithms that combine Lagrangian relaxation and L-shaped solution methods, and we develop a case study using data from the state of Mississippi. The results from the computational analysis point to important observations about the impacts of carbon regulatory mechanisms as well as the uncertainties on the performance of biocrude supply chains.     

A mixed inventory model with variable lead time and random back-order rate

In this paper, we study the determination of the optimal lead time, reorder point and order quantity considering that the back-order probability of a demand made during a stock-out period depends on the interval from the moment in which the order is placed until the next replenishment. Two models are analysed for the specification of the back-order probability: exponential functions and piecewise constant functions. The distribution of the lead time demand is assumed to be Poisson. An algorithm for the determination of the optimal order quantity, reorder point and lead time is given. A numerical example is presented to illustrate the results.     

Supply chain financing with advance selling under disruption

We study a financing problem in a supply chain (SC) consisting of one supplier and one buyer under supply disruption. The supplier could face a disruption at its end which could effectively reduce its yield in case of disruption, thereby resulting in supply yield uncertainty. The retailer can finance the supplier using advance selling that can help mitigate the impact of disruption. We model this problem as a Stackelberg game, where the supplier as the leader announces the wholesale price and the retailer responds by deciding its optimal order quantity given stochastic demand and an exogenous fixed retail price. The supplier then commences production and a disruption can happen with a known probability. We assume that under disruption the quantity delivered is a fraction of the initial quantity ordered by the retailer. The retailer loses any unmet demand. We analyze three different scenarios of the Stackelberg game, namely no advance selling with disruption, advance selling without disruption, and advance selling with disruption. Our results indicate that advance selling can be used to mitigate the impact of supply disruption and at the same time could lead to an increase in the overall SC profit.     

模糊需求下的闭环供应链协调机制研究

研究一个由制造商和零售商在模糊需求环境下的两级闭环供应链的协调机制问题。将市场需求视为模糊变量,建立模糊截集理论下的集中决策模型和收益-费用共享契约模型,给出模型中的最优策略,并以三角形模糊变量为例,对模型进行优化。通过数值算例对模型中的参数进行求解,并对分析结论进行验证。研究结果表明,在模糊需求环境下的闭环供应链中,零售商的最优订购量在模糊需求中心点的左、右浮动,并随着零售价格的提高而增加,通过改变收益-费用系数可以实现供应链成员之间的完美协调。     

Quality improvement and backorder price discount under controllable lead time in an inventory model

The proposed study investigates a continuous review inventory model with order quantity, reorder point, backorder price discount, process quality, and lead time as decision variables. An investment function is used to improve the process quality. Two models are developed based on the probability distribution of lead time demand. The lead time demand follows a normal distribution in the first model and in the second model it does not follow any specific distribution but mean and standard deviation are known. We prove two lemmas to obtain optimal solutions for the normal distribution model and distribution free model. Finally, some numerical examples are given to illustrate the model.     

Dynamic reorder point replenishment strategies for a capacitated supply chain with seasonal demand

Managing inventory and service levels in a capacitated supply chain environment with seasonal demand requires appropriate selection and readjustment of replenishment decision variables. This study focuses on the dynamic adjustment of decision variables within supply chains using continuous-review reorder point (ROP) replenishment. A framework is proposed to adjust reorder points and lot sizes based on optimal settings within different regions of a seasonal demand cycle. This framework also includes the optimal timing of adjustments defining these regions. A discrete-event simulation model of a simple, capacity-constrained supply chain is developed and simulation–optimization experiments are performed, the objective being to minimize the total supply chain inventory subject to a target delivery service level. The performance of ROP systems with optimal static and optimal dynamic decision variable settings are compared using two different seasonal demand patterns. The results confirm that performance with dynamic decision variable adjustment is better. For a given delivery service level, average work-in-process inventory levels are almost the same for both systems. However average finished goods inventory levels decrease significantly and are more stable under dynamic adjustment. The practical implication is that both finished goods holding costs and maximum storage capacity requirements are reduced.     

考虑损失厌恶和锚定心理的供应链订货与协调

为更合理地实现供应链协调的整体最优绩效,以具有损失厌恶和锚定心理的零售商和风险中性的供应商组成的两级供应链为研究对象,探讨回购契约下的供应链订货及协调情况。建立集中和分散决策下考虑零售商损失厌恶和锚定心理的回购契约协调模型,分析了零售商最优订货量与批发价格、回购价格之间的关系,以及各契约参数对回购价格和各节点利润的影响,并给出了供应链实现协调需要达成的条件。结果表明,当零售商订购的产品为高利润产品时,能够实现供应链整体最优绩效,达到供应链协调,且利润在供应链双方之间的分配随着批发和回购价格的提升而向供应商倾斜,但零售商损失厌恶和锚定心理的加深会使得供应商提升回购价格,使整体供应链的利润下降,成本费用增加。