The supply chain literature analyzing supplier–retailer contracts and channel coordination has typically focused on profit or revenue maximization as the members’ sole objective. In such settings, it ...is well known that a simple wholesale price contract is not effective in coordinating the channel due to double marginalization. Recently, Cui et al. Cui, T.H., Raju, J.S., Zhang, Z.J., 2007. Fairness and channel coordination. Management Science 53 (8) 1303–1314 introduced the members’ fairness concerns into channel coordination. Assuming a linear demand function, the authors show that a coordinating wholesale price contract can be designed when only the retailer or both parties are concerned about fairness. In this paper, we extend the authors’ results to other nonlinear demand functions that are commonly used in the literature. Our analysis reveals that, compared to the linear demand, the exponential demand function requires less stringent conditions to achieve coordination when only the retailer is fairness-concerned.
An increasing number of omnichannel retailers operate physical and online channels and implement various strategies that integrate both channels. For example, some retailers have begun offering ...consumers the option to purchase online and return items to physical stores if necessary (i.e., buy-online, return-to-physical store (BORP) option). Such cross-channel return policies can be competitive tools while online retail sales continue to grow and return rates from these sales remain high. We investigate the retailers’ strategic decisions on the adoption of the BORP policy from a competitive perspective. In a duopoly setting, we incorporate model elements, including retailers’ price and online return fee decisions and customers’ heterogeneity and forward-looking purchase behavior. We adopt a multistage, non-cooperative game framework and find that the adoption of the BORP policy by one or both retailers can be sustained in equilibrium if the retailers are sufficiently differentiated and when they can recover significantly larger salvage values from items returned in-store than those returned online. Neither retailer offers the BORP option under intense competition and/or when the retailers’ physical channels lose the aforementioned advantages. Furthermore, in the equilibrium with asymmetric adoption of the BORP policy, both retailers are better off compared with that without adoption. However, the retailer who offers the BORP policy is not guaranteed of a larger profit gain than its rival. We provide a systematic explanation for the mechanisms underlying these results and generate further managerial insights by exploring scenarios with free online return service and retailer heterogeneity.
The classical risk-neutral newsvendor problem is to decide the order quantity that maximizes the one-period expected profit. In this note, we consider a risk-averse newsvendor with stochastic ...price-dependent demand. We adopt Conditional Value-at-Risk (CVaR), a risk measure commonly used in finance, as the decision criterion. The aim of our study is to investigate the optimal pricing and ordering decisions in such a setting. For both additive and multiplicative demand models, we provide sufficient conditions for the uniqueness and existence of the optimal policy. Comparative statics show the monotonicity properties and other characteristics of the optimal pricing and ordering decisions. We also compare our results with those of the newsvendor with a risk-neutral attitude and a general utility function.
A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., 1 year). Such ...contracts are widely used in industries, because they provide the buyer with flexibility in terms of the timing and size of each order and the supplier with a guaranteed total order volume. Previous studies on such contracts have focused primarily on the firm's inventory decisions, and none of them has considered the coordination of inventory and pricing decisions. In this study, we fill this gap by studying dynamic inventory and pricing problems under a commitment contract. Under a general demand model with backlogging and zero lead time, we prove that the optimal policy is a committed‐inventory‐position‐dependent base‐stock list‐price policy and characterize its structural properties. We also conduct an extensive numerical study to derive further managerial insights. In particular, we find that dynamic pricing can substantially improve the firm's profitability and enables it to select contracts with large committed quantities and price discount rates, and that ignoring the commitment in joint pricing and ordering decisions can result in substantial profit loss. Finally, we partly extend our results to a lost‐sales model and a backlogging model with lead times.
We consider a stochastic inventory control problem in which a buyer makes procurement decisions while facing periodic random demand and two supply sources, namely, a long-term contract supplier and a ...spot market. The contract between the buyer and the supplier partially shields the latter from the vicissitudes of the spot market, in that the price paid by the buyer to the supplier is only partially linked to the spot price at the moment. After fulfilling the minimum-order commitment with the supplier, the buyer has the full freedom to source from both the supplier and the market. Procurement from the spot market also incurs a fixed setup cost. We show that an optimal policy consists of three different policy forms, with the realization of each depending on the buyer's inventory level and the prevalent spot price. Certain conditions are identified under which monotone trends exist between policy parameters and the current spot price.
We consider the coordination of a supply chain with a long leadtime and demand information updating. In such a supply chain the initial production or key material procurement decision has to be made ...when there is limited information about the market demand. When it is the time for the final production and/or shipment decision, more accurate demand information is available, which allows the modification of the initial decision so that some costs can be saved. We consider a two-stage supply chain in which the manufacturer decides the initial production quantity in the first stage, and the retailer specifies her order quantity in the second stage after the demand forecast is improved. In this setting, the conventional return mechanism needs to be modified to coordinate the supply chain. We propose a risk sharing contract that requests the retailer to partially compensate for the manufacturer's loss that is attributable to the overproduction in the first stage, and the manufacturer to provide a partial credit for the retailer's loss that results from overstocking in the second stage. Such a contract not only extracts the maximal supply-chain profit, but can also improve the profit of each supply-chain member by tuning the contract parameters.
We study a coordination contract for a supplier–retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product’s selling season is short, and ...the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract permits any agreed-upon division of the supply-chain profit between the channel members.
We study a risk‐averse newsvendor problem where demand distribution is unknown. The focal product is new, and only the historical demand information of related products is available. The newsvendor ...aims to maximize its expected profit subject to a profit risk constraint. We develop a model with a value‐at‐risk constraint and propose a data‐driven approximation to the theoretical risk‐averse newsvendor model. Specifically, we use machine learning methods to weight the similarity between the new product and the previous ones based on covariates. The sample‐dependent weights are then embedded to approximate the expected profit and the profit risk constraint. We show that the data‐driven risk‐averse newsvendor solution entails a closed‐form quantile structure and can be efficiently computed. Finally, we prove that this data‐driven solution is asymptotically optimal. Experiments based on real data and synthetic data demonstrate the effectiveness of our approach. We observe that under data‐driven decision‐making, the average realized profit may benefit from a stronger risk aversion, contrary to that in the theoretical risk‐averse newsvendor model. In fact, even a risk‐neutral newsvendor can benefit from incorporating a risk constraint under data‐driven decision‐making. This situation is due to the value‐at‐risk constraint that effectively plays a regularizing role (via reducing the variance of order quantities) in mitigating issues of data‐driven decision‐making, such as sampling error and model misspecification. However, the above‐mentioned effects diminish with the increase in the size of the training data set, as the asymptotic optimality result implies.
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