生鲜产品的订购、定价与保鲜技术投资策略

研究一个生鲜产品的订购、定价与保鲜技术投资联合决策问题。产品实时质量随时间不断下降且服从两参数Weibull分布,零售商可通过投资保鲜技术减缓产品质量的下降速率。需求同时依赖于产品的实时质量、销售价格和最低质量限制。研究决策最优的订购、定价和保鲜技术投资策略以最大化零售商的平均利润。首先证明了最优订购、定价和保鲜技术投资策略各自的唯一存在性;接着,给出一个迭代算法用以搜索问题的最优解;最后,采用数值方法对主要参数的灵敏度进行了分析,并比较了在投资与不投资保鲜技术两种情况下零售商的最优策略和平均利润。结果显示:零售商是否投资保鲜技术对其订购策略(补货周期和订购量)有较大的影响,而对定价策略的影响较小;投资保鲜技术有利于提高零售商的利润。     

基于安全库存系数的一体化冷链库存价格协调北大核心CSSCI

研究了两级冷链系统中一种易变质食品的一体化库存决策及价格协调问题。产品的补货提前期服从正态分布,变质率函数具有Weibull分布特征,并考虑了安全库存系数,以冷链系统利润最大化为目标建立了数学模型。针对一体化冷链系统中零售商利润受损问题,为实现供应链整体共赢,基于一体化最优安全库存系数进行价格协调,并给出了价格的折扣函数。通过算例分析发现:随着库存成本的增加,供应商需提供更高的价格折扣以保证零售商在供应链系统中的积极性;在基于安全库存系数的价格协调过程中,集中决策的收益明显高于分散决策;同时零售商的订购次数并不会对集中决策产生显著影响。     

基于安全库存系数的一体化冷链库存价格协调

研究了两级冷链系统中一种易变质食品的一体化库存决策及价格协调问题。产品的补货提前期服从正态分布,变质率函数具有Weibull分布特征,并考虑了安全库存系数,以冷链系统利润最大化为目标建立了数学模型。针对一体化冷链系统中零售商利润受损问题,为实现供应链整体共赢,基于一体化最优安全库存系数进行价格协调,并给出了价格的折扣函数。通过算例分析发现:随着库存成本的增加,供应商需提供更高的价格折扣以保证零售商在供应链系统中的积极性;在基于安全库存系数的价格协调过程中,集中决策的收益明显高于分散决策;同时零售商的订购次数并不会对集中决策产生显著影响。     

考虑消费者预期后悔的零售商策略选择

建立随机需求下的两阶段销售模型,研究消费者高价后悔和缺货后悔对零售商定价与库存决策的影响,分析两种运营策略：价格承诺和快速响应。结果表明,高价(缺货)后悔加重(减轻)消费者策略性等待行为,零售商应降低(提高)定价并减少(增加)库存;价格承诺和快速响应均能缓解消费者策略性等待行为,但两者的价值受消费者预期后悔的影响相反;价格承诺仅在补货成本高于某个阈值且消费者预期后悔敏感度低于某个阈值时优于快速响应。     

梯形需求缺货部分拖后的变质物品EOQ模型

研究了变质物品在一般梯形需求率下和缺货部分拖后时的库存模型.假定变质物品的需求为一般形式的梯形需求率函数,允许缺货且缺货部分拖后,缺货拖后率是到达下一周期补货等待时间的凹函数,物品的变质率为一般形式的Weibull时变函数,根据一般梯形需求函数不同的参数取值,建立了不同情形下变质物品的库存决策模型,给出了每种情形下模型的最优订货策略.研究结果表明,库存系统最优库存减少为零的时刻不依赖于具体的需求参数,但库存系统的最优订货策略却依赖于具体的需求参数.     

基于横向补货的库存协调近似模型

以给定零售商独自拟定订货策略为前提,提出了一种在横向补货允许的情况下,能够有效地刻画系统库存的近似模型.该模型在"最近邻居"优先补货原则下,详细地阐述了系统中的产品需求走势和相应的需求满足率.并通过和仿真试验的数值结果进行比较,验证了该模型的有效性,还对横向补货允许和补货不允许两种不同情况下的系统库存成本进行了比较,形象地给出了横向补货策略在优化库存成本方面的绩效.关于单个零售商订货策略一般性的拓展以及系统联合订货策略的可能性研究也给予了相关说明.     

电子商务环境下两级供应链库存管理决策研究

本文利用order up to level策略建立需求不确定时两级供应链供应商的库存策略模型并进行参数求解,给出最优库存水平以及管理绩效考核指标的求解方法。并通过实例计算,给出电子商务环境下基于两级供应链的供应商库存最优解决方案,提出随着零售商需求波动程度、库存水准的变动,对于供应商最优库存水平、库存成本、缺货成本的相应策略。     

具有有效期易变质品的最优补货策略研究

易变质物品库存管理策略一直是实务界与学术界高度关注的问题,其中具有有效期易变质物品的最优补货策略是研究中的难点。本文研究了有限销售时域内具有有效期易变质物品的库存补货策略,在物品的需求率依赖于物品的库存水平,且物品有效期已知的假设下,本文建立了一个确定易变质物品最优补货策略的优化模型,并给出了具体的求解算法。文章最后给出了数值算例,并对模型中的相关参数作了敏感性分析。     

短缺量拖后率与价格折扣相关变质品VMI模型

考虑短缺量拖后率与订货商给予顾客的价格折扣正线性相关,提出一种需求指数时变的变质物品供应商管理库存模型,研究了供应链最优库存策略。数值仿真和主要参数灵敏度分析表明,订货商在缺货期间向顾客提供价格折扣有利于降低丢单损失和系统库存总成本;当需求增长因子变化时,VMI系统应保持库存控制策略不变;当变质系数和拖后率上限变大时,VMI系统则应保持订货商补货次数和价格折扣不变,同时适当降低订货商服务水平。     

提前转运还是紧急转运?考虑消费者缺货后悔的补货策略研究

对零售商来说,缺货意味着部分订单得不到满足,进而导致利润损失;另一方面,缺货导致的后悔却能缓解消费者的策略性等待。因此是否采取补货,采取何种补货策略对零售商来说显得尤为重要。本文构建模型,比较当消费者具有缺货后悔倾向时,提前转运和紧急转运下零售商的最优补货决策。研究发现:当期初库存水平较高时,补货策略能带来利润改善;当期初库存水平较低时,补货缓解消费者的后悔预期进而带来利润损失,并且该损失超过更多交易量带来的利润提升,此时不采取补货反而更优。比较两种补货策略可知:当期初库存水平较高时,提前转运下因预期缺货率降低带来的损失少于紧急转运时因额外费用带来的损失,此时提前转运更优;当库存水平较低时,预期缺货率降低带来的损失较大,此时紧急转运更优。另外,相较于紧急转运带来额外费用,提前转运有着预测偏差。两种转运策略的相对优劣还受到策略自身的影响,即较高(低)的偏差成本或者较低(高)的额外费用使得零售商更倾向于选择紧急(提前)转运。     

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.     

Optimal two-level piecewise-constant price discrimination for a storable perishable product

Price differentiation over time is an additional policy that firms might consider when determining prices for perishable products. The common policy of a fixed price regardless of freshness might result in leaving some expired inventory unsold. Price differentiation can impact the demand for perishable products, which declines as the expiration date approaches. We develop an optimisation model with the goal of evaluating the monetary effectiveness of the strategy of simultaneously combining price discrimination across heterogeneous consumers with price differentiation over time for perishable inventory under separable multiplicative demand factors of price and time. Necessary optimality equations are derived, and their solutions are proved to constitute a unique global optimal solution. It is proved that an optimal pricing policy is to implement price discrimination with respect to consumers’ sensitivity to freshness, while dynamically changing the price over time, starting with a lower price at the early stages of the product’s shelf life and increasing it at a later stage. The monetary benefit that the retailer and consumer can derive from the suggested pricing policy is evaluated by comparing the model to other models in which price discrimination or dynamic pricing are not implemented. A numerical example that illustrates the significance is introduced. From the analysis of a numerical illustration of the model, it is concluded that a dynamic price discrimination policy can be approximated by an identical-to-all dynamic pricing policy in order to maximise the retailer’s profit and thus, mitigate the retailer’s risk from failing in the process of implementing price discrimination.     

Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under buyback of defective items

In this article, the economic production and inventory model in a three-layer supply chain including one distributor, one manufacturer and one retailer for a single-product and general demand functions under three scenarios is developed. We assume that during the production process, both healthy and defective items are generated. As the first scenario, we develop the first model, in which the defective items are not reworked and all considered as scrape, while in the second model, we assume that the defective items are reworked and are sold as perfect item. In the second scenario, we assume that defective item can be sold with lower price than the selling price. Moreover, raw materials with imperfect quality are sent back from a distributor to outside supplier under a lower price. Determining the order quantity of the distributor and the selling prices of the distributor and the manufacturer as well as the retailer was the goal of this article such that the total profit of each member is maximised. In order to solve the models, the Stackelberg approach is employed between the members, and the concavity of the profit functions is proved using several theorems. Then, closed form solutions are derived for the decision variables and a solution algorithm is proposed to determine the optimal solutions. Finally, a numerical example is presented to illustrate the applicability of the model.     

The Interaction of Economic Ordering Quantities and Marketing Policies

A general net profit model is developed consisting of the difference between the gross profit and the total inventory costs. This model considers that the demand is a function of the selling price, that the selling price depends on the pricing policy and on the unit cost which in its turn varies according to the order quantity. It is shown that the correct treatment of inventory problems is that which considers its interaction with problems of pricing since the obtainable net profit can be increased over the amounts achieved when inventory problems were regarded as independent subsystems. Further it has been found that there exists a critical demand elasticity such that the preferable pricing policy is different for prevailing elasticities above this value than for elasticities below it.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.     

新鲜度差异下两种可替代生鲜品的多阶段定价策略研究

研究单个零售商销售2种可替代生鲜产品时的价格决策,建立3种定价策略下的决策模型,得到2种产品的最优固定价格、最优折扣价格和最优捆绑价格售价;通过数值仿真分析影响零售商价格决策的因素及其影响大小。研究结果表明,3种策略下产品价格都与产品新鲜度临界值同方向变化;最优固定价格随销售期临近度的增大而变高;对比3种策略下零售商的利润发现,有时捆绑价格是占优策略,有时折扣价格是占优策略,参数的大小是关键因素。     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.     

价格增长下两阶段存货影响销售率EOQ模型

考虑产品采购价随时间指数增长和两阶段存货影响销售,建立了一个价格增长和两阶段存货影响销售率EOQ模型。采用实际调查数据对模型进行了验算,分析了农产品和食品价格大幅度上涨对经销商订货策略的影响。研究结果表明：初始采购价和采购价增长因子对订购策略和各项成本影响较大,存货影响销售率因子和存货影响销售率临界点对订购策略和各项成本有一定影响。     

The value of updated information on future price behaviour

This paper studies the value of information on future price behaviour. We consider a one-period inventory modelling framework with random period length and two order opportunities. The selling price is determined dynamically and the demand is price-sensitive. The second ordering-pricing decision reflects the updated information on future price behaviour on supply chain flexibility. We consider three models with different levels of flexibility: the static model, the quantity flexible model and the combined quantity and timing (fully) flexible model. We compare between the values of three different features in the supply chain: updated information on price behaviour, dynamic pricing and supply flexibility. And we demonstrate the effect of holding cost and demand uncertainty on these three values. We also consider a specific condition with fixed selling prices. We give explicit analysis on the optimal order decisions, and analytically show the impact of information and quantity flexibility on the optimal order decisions.