Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.     

An Economic Lot Size Model for Perishable Products with Age-Dependent Inventory and Backorder Costs

This paper presents an Economic Lot Size (ELS) model for perishable products where the costs of holding inventory stocks (having backorders) in each period depend on the age of inventories (backorders). We propose a polynomial-time dynamic programming algorithm to solve two structured problems, one with non-decreasing demands and the other with non-decreasing marginal backorder cost with respect to the age of the backorder. Our results generalize a recent study on an ELS model for perishable product but without backorders.     

允许缺货的可控提前期供应链库存优化与协调

将单个企业的可控提前期库存模型拓展到供应链环境中,并考虑了允许部分缺货后补的情形,分别建立了分散决策和联合决策情形下允许部分缺货后补的可控提前期供应链库存优化模型,并提出价格折扣机制来协调供应链成员的利益.采用数值实验方法,对所建的库存优化模型和协调机制进行了分析,结果表明:随着缺货后补比例的不断减少,供应链必须不断增大订货批量和压缩提前期以提高顾客服务水平;价格折扣机制可以使得允许缺货的可控提前期供应链达到协调的目的.     

斜坡需求下延迟补货的高科技产品EOQ模型

高科技产品是科技发展的产物,对发展国家经济和提高人民群众的生活水平起着重要的作用。考虑高科技产品斜坡需求和延迟补货受时间和价格影响的特点,将顾客分为价格偏好者和时间偏好者,构造了2种不同的延迟函数,建立了相应的经济订货批量模型,采用数值仿真分析了系统主要参数对高科技产品订货策略和总利润的影响。研究结果表明：需求增长因子、价格敏感因子以及资金贴现率对订货次数和服务水平的影响比其它因素大;需求增长期长度、价格偏好者比例对服务水平的影响比订货次数大;计划期长度对服务水平的影响比订货次数小。     

Coordinating orders in supply chains through price discounts

In this paper, we examine the issue of order coordination between a supplier and multiple retailers in a decentralized multi-echelon inventory/distribution system where the supplier provides a product to multiple retailers who experience static demand and standard inventory costs. Specifically, we propose and analyze a new policy where a manufacturer, who outsources production to an Original Equipment Manufacturer, offers a price discount to retailers when they coordinate the timing of their orders with the manufacturer's order cycle. We show that our proposed policy can lead to more efficient supply chains under certain conditions, and present a straightforward method for finding the manufacturer's optimal price discount in this decentralized supply chain. A numerical experiment illustrates the managerial implications of our model as well as conditions when a manufacturer should consider adopting such a policy.     

Decentralized inventory control in a two-stage capacitated supply chain

This paper investigates a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand. Both the supplier and the retailer employ base stock policies for inventory replenishment. All unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer. We investigate the determination of decentralized inventory decisions when the two parties optimize their individual inventory-related costs in a noncooperative manner. We explicitly characterize the Nash equilibrium inventory strategies and identify the causes of inefficiency in the decentralized operation. We then study a set of simple linear contracts to see whether these inefficiencies can be overcome. Finally, we investigate Stackelberg games where one of the parties is assumed to be dominating.     

基于供需一体化协同控制的供应链库存模型

根据供需一体化协同库存控制策略，构建了一个一体化库存模型。在模型里，假定提前期需求是随机的且服从正态分布，允许在提前期内发生缺货，并产生缺货成本；假定提前期是可控的，能够通过增加成本缩短提前期。该模型通过同时计算最优订货量、再订货点、提前期以及运送批次．使供需一体化库存总成本最小。实例分析证明该模型能够达到节约成本的目的。     

Coordinated replenishment systems with discount opportunities

In many practical situations, coordination of replenishment orders for a family of items can lead to considerable cost savings. A well-known class of strategies for the case where cost savings are due to reduced joint ordering costs is the class of can-order strategies. However, these strategies, which are simple to implement in practice, do not take discount possibilities into account. We propose a method to incorporate discounts in the framework of can-order strategies. A continuous review multi-item inventory system is considered with independent compound Poisson demand processes for each of the individual items. Discounts are offered by the supplier as a percentage of the total dollar value whenever this value exceeds a given threshold. Starting from the can-order strategy as a basic decision rule, we develop a simple heuristic to evaluate these discount opportunities. The performance of the can-order strategy with discount evaluation is compared with that of another class of discount evaluation rules as proposed by Miltenburg and Silver.     

BASS预测模型与库存控制集成研究

根据短生命周期产品的特征调整BASS扩散模型,并将其应用于短生命周期产品的需求预测,同时考虑产品需求对无形变质和短缺拖后量的影响,进而建立短生命周期产品多周期订货模型。通过算例分析获得短生命周期产品的成熟期开始时间和持续时间,进而求订货次数和订货量,给出多周期最优订货策略。数据实验结果显示基于BASS需求函数的库存控制模型可以提高需求预测精确度,有效降低库存成本,对企业库存控制具有指导意义。     

A capacity constrained production-inventory system with stochastic demand and production times

This paper considers a simple model of a capacity constrained production-inventory system with Poisson demand. The system is controlled by an S policy. The production time for a unit is modelled as a gamma distributed stochastic variable. Using M/G/1 queuing theory it is very easy to evaluate holding and backorder costs and optimise the ordering policy. The suggested model may be useful when evaluating investments in production.     

A joint replenishment policy with individual control and constant size orders

We consider inventory systems with multiple items under stochastic demand and jointly incurred order setup costs. The problem is to determine the replenishment policy that minimises the total expected ordering, inventory holding, and backordering costs–the so-called stochastic joint replenishment problem. In particular, we study the settings in which order setup costs reflect the transportation costs and have a step-wise cost structure, each step corresponding to an additional transportation vehicle. For this setting, we propose a new policy that we call the (s, 𝒬) policy, under which a replenishment order of constant size 𝒬 is triggered whenever the inventory position of one of the items drops to its reorder point s. The replenishment order is allocated to multiple items so that the inventory positions are equalised as much as possible. The policy is designed for settings in which backorder and setup costs are high, as it allows the items to independently trigger replenishment orders and fully exploits the economies of scale by consistently ordering the same quantity. A numerical study is conducted to show that the proposed (s, 𝒬) policy outperforms the well-known (𝒬, S) policy when backorder costs are high and lead times are small.     

Inventory and lead time planning with lead-time-sensitive demand

Supply and order lead times can have substantial effects on operations performance and perceived customer service, particularly under uncertain customer demand. Certain customers place a high premium on shorter order lead times, while others may be willing to trade a longer lead time for a lower price. This paper studies a problem in which a supplier wishes to determine the best positioning of a product with respect to order lead time and price. We consider a continuous review inventory replenishment system, where the difference between the procurement lead time and promised sales order lead time influences both cycle stock and safety stock costs, and procurement costs may increase as a result of investment in procurement lead time reduction. We provide models and methods for determining the best combination of price and sales lead time for systems with high economies of scale when demand depends on both sales lead time and price. Our results indicate that for a broad range of practical settings, such systems employ a pure make-to-stock policy or a policy that sets sales lead time equal to the procurement lead time at optimality.     

A Hybrid Inventory System with a Time Limit on Backorders

Traditionally, in ( Q , r ) inventory systems, when a shortage occurs, incoming demands are either filled by emergency orders or backordered. However, the backorder costs are usually time-dependent, hence it is costly to backorder early in the lead time. On the other hand, it is obviously expensive to fill the shortages with emergency orders alone. In this paper, we propose a hybrid inventory control system to handle shortages. A cutoff time τis incorporated with the traditional ( Q , r ) systems. Poisson demands and a constant lead time are assumed. Shortages are covered by emergency orders before τand backordered after τ. The traditional backorder and emergency order systems are special cases of the hybrid system with τ= 0 and τ= lead time, respectively. The optimal control variables Q *, r *, and τ* are determined by minimizing the expected annual cost. Numerical examples to illustrate the model are presented together with discussions on the conditions under which the hybrid system provides cost savings over the two traditional systems.     

短生命周期产品的延期交货和价格折扣模型

用斜坡型函数来描述短生命周期产品需求变化特征,用持有成本不断增加表示短生命周期产品无形变质所带来的损失,研究在允许缺货情况下,如何设置合理价格折扣来控制订单的流失,确定各周期的最佳延迟供货量、最优价格折扣、最优订货时间和订货量,从而实现企业总成本的最优。给出了一种迭代逼近的方法来寻求在有限时域内的最优订购策略,通过数值分析验证了该模型的有效性和可操作性,对相应的参数做出了灵敏度分析。该模型能够确定出企业最佳的价格折扣以挽留住更多的顾客,使其总利润达到最优。     

竞争环境下两级供应链提前订购模式研究

针对两个零售商和单一供应商组成的某易逝品供应链,在考虑零售商之间的价格竞争前提下,分析了供应商对零售商实施提前订购折扣销售模式的决策过程.应用报童模型和Stackelberg模型,研究了零售商的最佳订购时期以及供应商的最优折扣因子的制定策略,构建了相应的决策模型,并对模型最优性进行了分析.     

Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints

In this paper, we study a duopolistic market of suppliers competing for the business of a retailer. The retailer sets the order cycle and quantities from each supplier to minimize its annual costs. Different from other studies in the literature, our work simultaneously considers the order size restriction and the benefit of order consolidation, and shows non-trivial pricing behaviour of the suppliers under different settings. Under asymmetric information setting, we formulate the pricing problem of the preferred supplier as a non-linear programming problem and use Karush–Kuhn–Tucker conditions to find the optimal solution. In general, unless the preferred supplier has high-order size limit, it prefers sharing the market with its competitor when retailer’s demand, benefit of order consolidation or fixed cost of ordering from the preferred supplier is high. We model the symmetric information setting as a two-agent non-zero sum pricing game and establish the equilibrium conditions. We show that a supplier might set a ‘threshold price’ to capture the entire market if its per unit fixed ordering cost is sufficiently small. Finally, we prove that there exists a joint-order Nash equilibrium only if the suppliers set identical prices low enough to make the retailer place full-size orders from both.     

Coordinated order and production policies in supply chains

This paper is focused on the coordination of order and production policy between buyers and suppliers in supply chains. When a buyer of an item decides independently, he will place orders based on his economic order quantity (EOQ). However, the buyers EOQ may not lead to an optimal policy for the supplier. Should the buyer have the more powerful position to enforce his EOQ on the supplier, then no incentive exists for him to deviate from his EOQ. To provide an incentive to order in quantities suitable to the supplier, the supplier could offer a price discount or side payment. One critical assumption made throughout the literature dealing with incentive schemes to influence buyers ordering policy is that the supplier has complete information regarding buyers cost structure. This paper provides a bargaining model with asymmetric information about the buyers cost structure. A self-selection model for the determination of an optimal set of contracts which are specifically designed for different cost structures of the buyer, assumed by the supplier, will be presented.     

Blockchain adoption or contingent sourcing? Advancing food supply chain resilience in the post-pandemic era

In the post-pandemic era, food supply chains and firms therein are facing unprecedented severe challenges, because once infection is detected, numerous products must be recalled or abandoned, and both suppliers and retailers in the supply chain suffer enormous loss. To survive under the pandemic, retailers have adopted different sourcing strategies, such as contingent sourcing, which, in turn, affect the upstream suppliers and hence the resilience of the whole supply chain. With the rapid development of digital technologies, retailers nowadays can utilize blockchain as a reliable and efficient way to reduce product risk and hence advance the resilience of food supply chains by improving product traceability and inspection accuracy, and making sourcing transparent. In this paper, we develop a game-theoretic model to investigate the interrelation between the retailer’s decisions on blockchain adoption and sourcing strategies. We consider that a retailer originally orders from a risky supplier while conducting an imperfect inspection to detect infected products before selling. The retailer may speculatively keep on ordering from the risky supplier or adopt contingent sourcing by ordering from an alternative safe supplier. The retailer also has an option to implement blockchain to improve the inspection accuracy and product traceability. We derive the optimal retail prices under different sourcing strategies with and without blockchain adoption and then analyze the incentives for sourcing strategy and blockchain adoption. Then, we identify the conditions of an all-win situation for food retailer, supplier, supply chain resilience, and consumers with/without government subsidy. Finally, we extend to consider the situation that some consumers have health-safety concerns and preferences for blockchain adoption.     

随机需求条件下供应链的补货及折扣策略研究

研究一个供应商和多个零售商围绕单品种商品组成的供应链体系中,以供应商为核心的供应链库存管理,目标是通过直接降低供应商的库存成本,从而降低供应链的总成本.假设每个零售商面对服从随机正态分布的提前期客户需求,在不考虑交货时间的情况下,供应商在固定的时间间隔满足零售商的补货需要,并以价格折扣的方式补偿零售商的成本增加.由此得到较优的补货间隔,并给出了求解方法.最后,通过仿真验证了该解法的可行性并评估了该策略对各方的影响.     

Dynamic pricing for multiple class deterministic demand fulfillment

We consider how a firm should allocate inventory to multiple customer classes that differ based on the price they pay and their willingness to incur delay in fulfillment of their demand. The problem is set in a deterministic demand, economic-order-quantity-like environment with holding, backorder, lost demand and setup costs. The firm either fulfills demand or offers a price discount to induce the demand to wait for fulfillment from the next reorder. We determine the optimal policy and discuss how changes in various parameters affect profitability, customer service, and operational measures such as order frequency and base stock levels. We compare the results to a policy that only rations inventory without dynamic discounting and to a policy that only provides discounts. Through the comparison, we observe that dynamic pricing can be seen as a combination of a pricing mechanism which determines demand and an allocation mechanism that differentiates between customer classes, serving each ones needs. We show that if lower-value customers are distinguished by accepting reduced service, it is possible that both high and low-value customer classes see better levels of service under the optimal policy than under a discounting only policy. In addition we demonstrate the applicability of the results to a stochastic version of the problem.