Optimal pricing,production, and inventory for deteriorating items under demand uncertainty: The finite horizon case

This paper aims to investigate the joint dynamic pricing and production decisions of deteriorating items with uncertain demand over a finite selling season, where the demand is price sensitive and the potential demand is characterized by a stochastic process. The stocks deteriorate physically at a constant fraction of the on-hand inventory. A joint dynamic pricing and production problem to maximize the total expected profit is modeled as a stochastic optimal control problem. We derive the closed-form solutions, which are in time-dependent linear feedback form of the inventory level when it is either positive or negative. It is shown that the manufacturer always benefits from a reduction in the volatility of potential market demand. In addition, to highlight the effectiveness of the joint dynamic strategy, we also consider the case of optimal production with a static price. A numerical example is presented to illustrate the validity of the optimal control policy, and sensitivity analysis on major parameters is performed to provide more managerial insights into deteriorating items.     

Pricing and two-tier advertising with one manufacturer and one retailer

This paper considers the pricing decisions and two-tier advertising levels between one manufacturer and one retailer where customer demand depends on the retail price and advertisement by a manufacturer and a retailer. We solve a Stackelberg game with the manufacturer as the leader and the retailer as the follower. With price sensitive customer demand and a linear wholesale contract, we obtain the optimal decisions by the manufacturer and the optimal responses by the retailer. Our results show that cost sharing of local advertising does not work well, it is better for the manufacturer to advertise nationally and offer the retailer a lower wholesale price.     

A portfolio approach to managing procurement risk using multi-stage stochastic programming

Procurement is a critical supply chain management function that is susceptible to risk, due mainly to uncertain customer demand and purchase price volatility. A procurement approach in the form of a portfolio that incorporates the common procurement means is proposed. Such means include long-term contracts, spot procurements and option-based supply contracts. The objective is to explore possible synergies among the various procurement means, and so be able to produce optimal or near optimal results in profit while mitigating risk. The implementation of the portfolio approach is based on a multi-stage stochastic programming model in which replenishment decisions are made at various stages along a time horizon, with replenishment quantities being determined by simultaneously considering the stochastic demand and the price volatility of the spot market. The model attempts to minimise the risk exposure of procurement decisions measured as conditional value-at-risk. Numerical experiments to test the effectiveness of the proposed model are performed using demand data from a large air conditioner manufacturer in China and price volatility data from the Shanghai steel market. The results indicate that the proposed model can fairly reliably outperform other approaches, especially when either the demand and/or prices exhibit significant variability.     

Supply chain coordination through integration of innovation effort and advertising support

This study integrates firms’ innovation and advertising decisions in a two-echelon supply chain, where a monopoly manufacturer sells products to ultimate consumers through an autonomous retailer. Considering that both innovation and advertising contribute to the product demand, we first investigate the optimal equilibriums of channel members under two different game structures: the non-cooperative and cooperative. In the non-cooperative structure, the manufacturer controls the innovation effort and wholesale price while the retailer controls the advertising rate and retail pricing. In the cooperative structure, the manufacturer agrees to share part of retailer’s advertising expenditure. We find that both the optimal operation and marketing decisions are sensitive to effects of innovation and advertising on demand as well as the manufacturer’s cost reduction coefficient due to innovation. Further, we find that the manufacturer always prefers cooperation. Meanwhile, only when the firms’ investments significantly contribute to the market mechanism, does the retailer have incentive to implement a cooperative program. In addition, we further propose a new two-way subsidy policy to coordinate channel members’ business functions.     

Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount

We studied the coordination of cooperative advertisement in a manufacturer–retailer supply chain when the manufacturer offers price deductions to customers. With a price sensitive market, the expected demand with cooperative advertising and price deduction is demonstrated. When the manufacturer is a leader, we obtained the optimal national brand name investment, local advertisement and associated manufacturer’s allowance with any given price deduction. When the manufacturer offers more price deduction to customers, the retailer will increase local advertisement if the manufacturer provides the same portion of the local advertising allowance. We obtained the necessary and sufficient condition for the price deduction to ensure an increase of manufacturer’s profit, and a search procedure for determining such an optimal price deduction is provided as well. When the manufacturer and retailer are partners, we obtained the optimal national brand name investment and local advertisement. For any given price deduction, the total profit for the supply chain with cooperative scheme is always higher than that with the non-cooperative scheme. When price elasticity of demand is larger than one, the resulting closed form optimal price deduction with partnership is also obtained. To increase profits for both parties in a supply chain, we recommend that coordination in local and national cooperative advertising with a partnership relationship between manufacturer and retailer is the best solution. The bargaining results show how to share the profit gain between the manufacturer and the retailer, and determine the associated pricing and advertising policies for both parties.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

An integrated inventory model for a deteriorating item with allowable shortages and credit linked wholesale price

This study proposes a single manufacturer, single retailer integrated inventory model that includes deterioration and shortages in the retailer’s inventory. The manufacturer’s production process is assumed to be imperfect as it produces a certain percentage of defective items. The retailer performs a 100  % screening process immediately on receiving a lot from the manufacturer and returns the detected defective items to the manufacturer in the next delivery. The manufacturer disposes the defective items and incurs a disposal cost. To increase sales, (s)he offers a trade credit to the retailer. The retailer’s wholesale price varies linearly with the credit period. The objective is to determine the optimal replenishment cycle time, the time of running out of stock, the length of the credit period and the number of lots from the manufacturer to the retailer so as to maximize the total profit of the integrated system. A solution algorithm is designed and illustrated through numerical examples. Furthermore, a sensitivity analysis is carried out to study the influence of the model-parameters on the optimal solution.     

A study on the effect of yield uncertainty in price-setting newsvendor models with additive-multiplicative demand

Random yield and uncertain demand usually both exist in many industries, such as the semiconductor industry. In this paper, the price-setting newsvendor model is studied which involves a single manufacturer and a single retailer with random yield and uncertain demand respectively. Under the condition of additive-multiplicative demand, we investigate the varying effects of random yield on the optimal price, order quantity, and expected profit in two situations with different cost structures. The first case is an in-house production case where the firm pays for the raw material quantity it has ordered, and the second one is a procurement case where the firm pays for the real product quantity it receives only. By using the theory of stochastic comparisons, we find that a less variable and a stochastically larger yield rate both lead to a lower optimal price and a higher expected profit for the in-house production case. Moreover, a less variable yield rate also results in a lower optimal price and a higher profit for the procurement case, but this is not true for a stochastically larger yield rate. Numerical examples illustrate that the effect of yield randomness on the optimal order quantity is not general.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Some properties of buyback and other related schemes in a newsvendor-product supply chain with price-sensitive demand

A manufacturer wholesaling to a retailer a ‘newsvendor-type’ product such as a seasonal/fashion good or a perishable food item is considered here. It is known that such a manufacturer/retailer channel has difficulties in fully realizing the market's profit potential. We study a theoretical construct of such a channel and present practically useful results for a manufacturer trying to design more profitable pricing schemes. Specifically, we consider a ‘dominant’ manufacturer supplying a newsvendor-type product to a retailer. The retail market volume varies with the unit retail price according to a stochastic demand curve. We study the design and performance of ‘price-only’, ‘buyback’ and ‘manufacturer-imposed retail price’ schemes. All these schemes have been considered in earlier works. The first part of this paper studies some important but previously overlooked aspects of price-only and buyback schemes. We show that the performance of these schemes is strongly and somewhat counter-intuitively affected by the specific form of demand curve and of demand randomization. Thus, we identify hitherto neglected factors that must be carefully considered when designing pricing schemes for actual implementation. The second part of this paper demonstrates the practicality and merit of using buyback in conjunction with a manufacturer-imposed retail price—an arrangement overlooked in the literature because it is widely mistaken as illegal. Overall, the paper shows how a manufacturer can better realize the market's potential by: (i) modifying slightly the well-known buyback arrangement; and (ii) carefully modelling certain hitherto neglected aspects of the price/demand relationship—a conclusion quite contrary to what one might surmise from the current theoretical literature.     

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

We consider a two-stage supply chain with one supplier and one manufacturer. The manufacturer faces a Poisson demand process where the arrival rate depends on the selling price, the announced delivery time, and the delivery reliability defined as the probability of satisfying the announced delivery time. Such a demand model generalizes the works in the literature by simultaneously considering the above three demand sensitivity factors. The main purpose of this paper is to study the equilibrium decisions in the supply chain with an all-unit quantity discount contract. We consider four scenarios regarding whether the leadtime standard, the delivery reliability standard, and the manufacturer’s capacity are endogenous, and whether the manufacturer’s production cost is its private information. We find that an all-unit quantity discount scheme can coordinate the supply chain for most cases. Managerial insights are observed regarding the impact of the three demand sensitivity factors. For example, the breakpoint in an optimal quantity discount contract always increases with the delivery reliability sensitivity under an exogenous delivery reliability, but may decrease under an endogenous delivery reliability; with asymmetric information, a higher variance of the manufacturer’s unit production costs leads to a lower unit wholesale price for the low-cost manufacturer.     

Integrated inventory models considering the two-level trade credit policy and a price-negotiation scheme

This paper develops the integrated inventory models with permissible delay in payment, in which customers’ demand is sensitive to the buyer’s price. The models consider the two-level trade credit policy in the vendor–buyer and buyer–customer relationships in supply chain management. A simple recursive solution procedure is proposed for the integrated models to determine the buyer’s optimal pricing and production/order strategy. Although the total profit from the buyer and vendor increases together, the buyer’s share lessens. To compensate the buyer’s loss due to the cooperative relationship, a negotiation system is presented in order to allocate the profit increase to the vendor and buyer to determine the pricing and production/order strategy. A numerical example and sensitivity analysis are provided to illustrate the proposed model. The results indicate that the total profit from the buyer and vendor together can increase, although a price discount is given to the buyer in the proposed models.     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

考虑产品环境质量和消费者惯性的电动汽车供应链策略分析

按是否拥有传统汽车将潜在消费者分成两类,基于不同购买行为的消费者,根据消费者购买行为理论,针对每一类消费者分别建立效用模型,运用斯坦伯格博弈理论求解得到厂商的最优定价策略和政府的最优补贴策略,进而分析政府考虑包括厂商收益、消费者剩余、政府支出以及环境效益在内的社会福利最大化时电动汽车的环境质量、传统汽车原拥有比例以及消费者惯性三因素对电动汽车普及率、政府补贴以及生产商收益的影响。研究结果表明:当生产成本小于某阀值时,电动汽车的市场需求随电动汽车的环境质量的增加而增大,传统汽车的市场需求则随之减小,反之亦然。电动汽车的生产效率较高时,政府的最优补贴随产品环境质量的增加而增大,生产效率较低时,最优补贴随之减小,政府通过增大补贴的方式鼓励生产商提高生产效率。最后通过数值实验验证了以上结论,并分析得到以上三方面因素对生产商收益的影响。     

具有Weibull生存死亡特征的冷链品库存补货定价策略研究

建立了无限期内冷链品具有Weibull生存死亡特征、随机需求且受售价影响的库存补货定价模型,其中售价是连续变化的,需求率是售价的指数函数,变质率服从的三参数Weibull分布,提前期固定。系统以利润最大化为目标函数,在(r,Q)库存策略下,建立库存模型,采用直接法,对模型近似求解,得到最优补货定价策略。利用Matlab进行算例模拟和灵敏度分析发现:补货提前期和单位仓储成本对补货定价策略影响较大,二者增大会导致系统利润降低;单位处理成本的增加,在一定程度上使得系统降低最优补货量,使系统利润增加;保鲜期固定的前提下,受冷链品的流动环境因子和存储环境因子影响的变质率对补货定价策略影响较大,它的增大会使系统利润降低。这些发现能够帮助优化系统模型,对现实问题具有一定的指导意义。     

随机产出环境下联产品的产量及价格策略研究

基于制造商生产主产品的过程中会随机产出两类存在替代关系的副产品的联产品系统,采用清仓定价模型,研究了不同需求函数(线性需求和指数需求)下,制造商对于主产品和副产品的最优产量与定价策略。通过两阶段优化模型的建立和求解,确定了主产品的最优产量和价格。借助数值分析,归纳出产品替代度和产出波动性对最优产量和利润的影响。研究结果表明,随着产品替代度的增加,制造商的产量上升;随着波动性的增加,制造商的产量下降。最后,将模型扩展到市场非出清的情况,并得出制造商的最优生产决策。     

考虑保质期的非即时易腐品最优订购与定价决策

针对有保质期约束的非即时易腐品,零售商可以在产品非腐败阶段和腐败阶段进行差异化定价来调整市场需求。即零售商可以调整产品非腐败阶段的定价策略,使得非即时易腐品在进入腐败阶段之前全部售出;或者在产品腐败阶段降低零售价格以刺激市场需求。因此,在需求依赖价格的假设下,本文研究了零售商关于有保质期约束的非即时易腐品的最优订购与定价决策。通过分析零售商单位时间利润函数的理论性质,得到了零售商的最优订购与定价策略。基于线性和指数型两种需求函数形式进行数值算例,可以发现针对保质期较长或者非腐败阶段较长的易腐品,零售商会延长订货周期来增加销售收入。特别是在指数型需求函数情境下,当市场需求与零售价格高度相关时,零售商更有意愿降价来刺激销量,从而使得易腐品在非腐败阶段内销售完毕。     

Price markdown scheme in a multi-echelon supply chain in a high-tech industry

This paper studies the price markdown scheme in a supply chain that consists of a supplier, a contract manufacturer (CM), and a buyer (retailer). The buyer subcontracts the production of the final product to the CM. The CM buys the components from the supplier and charges the buyer a service fee for the final product produced. The price markdown is made possible by the supplier with the development of new manufacturing technologies that reduce the production cost for the sourced component. Consequently, the buyer adjusts the retail price in order to possibly stimulate stronger demand that may benefit both the supplier and the buyer. Under this scenario, we identify the optimal discount pricing strategies, capacity reservation, and the stocking policies for the supplier and the buyer. We also investigate the optimal inventory decision for the CM to cope with the price discount by considering both demand and delivery uncertainties. Our results suggest that higher production cost accelerates the effects of higher price sensitivity on lowering the optimal capacity and stocking policies in the supply chain. The effect of mean demand error on the optimal prices is relatively marginal compared with that from price sensitivity. We also found that increasing the standard deviation of the random demand does not necessarily increase the stocking level as one would predict. The results show that delivery uncertainty plays an important role in the inventory carried beyond the price break. We discuss potential extensions for future research.     

Joint pricing and inventory replenishment decisions with returns and expediting

We study a single-item periodic-review model for the joint pricing and inventory replenishment problem with returns and expediting. Demand in consecutive periods are independent random variables and their distributions are price sensitive. At the end of each period, after the demand is realized, a buyer can return excess stocks to a supplier. Or, if there are stockouts, the buyer can place an expediting order at the supplier to reduce the amount of shortage. Unfilled demands are fully backlogged. We characterize the optimal dynamic policy that determines the pricing, inventory replenishment, and adjustment decisions in each period so that the total expected discounted profit is maximized. For a very general stochastic demand function, we can show that the optimal replenishment policy is a modified base-stock policy, the optimal pricing policy is a modified base-stock-list-price policy, and the optimal policy for inventory adjustment follows a dual-threshold policy. We further study the operational effect of returns and expediting. Analytical and numerical results demonstrate that returns and expediting lead to a significant profit increase in a number of situations, including limited supply capacity, sufficient flexibility of the expediting order, high demand uncertainty, and a price-sensitive market.     

Loss-averse newsvendor problem with supply risk

Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor’s loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker’s optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.