Parametric demand learning with limited price explorations in a backlog stochastic inventory system

Bullwhip effect under substitute products

Pricing and inventory replenishment are important operations decisions for firms such as retailers. To make these decisions effectively, a firm needs to know the demand distribution and its dependency on selling price, which is usually estimated using sales data at various testing price levels. Although more testing prices can lead to a better estimation of the demand–price relationship, frequent price changes are costly and come with adverse effect such as customers’ negative perception. In this article, data-driven algorithms are developed that learn the demand structure with constraints on the number of price changes. These algorithms are shown to converge to the optimal clairvoyant solution, and the convergence rates are the best possible in terms of profit loss.

A well-known concept in the marketing literature is that consumers use prices paid in the past or the current market price as a reference point to assess the value of the current price of an item. These 'reference prices' have been shown to have a significant impact on a consumer's purchase decision and a resulting influence on the selling firm's demand of the item. Recently, considerable research has been conducted on coordinated pricing and inventory decisions; however, very little has recognised the existence of reference prices. Thus, a single-period model is developed that incorporates the effects of reference prices, demand uncertainty and price elasticity on the solution. Numeric analysis indicates that accounting for reference prices can have a substantial impact on the pricing and inventory decisions and the resultant profitability, made by a firm.

This paper considers a single-sourcing network design problem for a three-level supply chain. For the first time, a novel mathematical model is presented considering risk-pooling, the inventory existence at distribution centers (DCs) under demand uncertainty, the existence of several alternatives to transport the product between facilities, and routing of vehicles from distribution centers to customer in a stochastic supply chain system, simultaneously. This problem is formulated as a bi-objective stochastic mixed-integer nonlinear programming model. The aim of this model is to determine the number of located distribution centers, their locations, and capacity levels, and allocating customers to distribution centers and distribution centers to suppliers. It also determines the inventory control decisions on the amount of ordered products and the amount of safety stocks at each opened DC, selecting a type of vehicle for transportation. Moreover, it determines routing decisions, such as determination of vehicles' routes starting from an opened distribution center to serve its allocated customers and returning to that distribution center. All are done in a way that the total system cost and the total transportation time are minimized. The Lingo software is used to solve the presented model. The computational results are illustrated in this paper.

In this study, we conduct a comprehensive literature review on the inventory and pricing decisions under the supply chain coordination. To be specific, we review the publications from 1997 to 2017 and divide the papers into six areas for discussion, they are: decisions under integrated supply chain, supply contract, capital-constrained, competition, risk aversion, and information asymmetry. After reviewing the literature, we identify three major future research directions. First, we propose to explore different real world industrial supply contracts and the forms of demand function. Second, limited studies consider risk aversion behaviour of the supply chain members; hence, we also propose to examine the inventory and pricing decisions under supply chain coordination with risk-averse retailer and risk-averse supplier, respectively. Finally, it is also interesting to investigate different types of information asymmetry.

We consider the interdependent decisions on assortment, inventory and pricing of substitutable products that are differentiated by some primary and secondary attributes captured by a nested logit consumer choice. We examine a newsvendor-type setting with several products competing for demand over a single selling season. We assume that all products have equal profit margins. The demand has a multiplicative-additive structure where both variance and coefficient of variation depend on the common profit margin, which adds to the model applicability at the expense of tractability. Under a Taylor series-type approximation, we show that the expected profit is unimodal in the common margin of products in a given assortment. Then, we compare the optimal profit margin to the case under ample inventory, which allows understanding the effect of inventory on pricing. We also study the optimal assortment problem under exogenous pricing. We show that the classic result on the optimality of popular sets holds under tight approximations of the profit function. We finally propose a heuristic for jointly deciding on assortment, pricing, and inventory decisions, which assumes equal profit margins of products, and exploit popular sets only. Our detailed numerical study shows that this equal-margin heuristic produces high quality solutions.

Optimal fences and joint price and inventory decisions in distinct markets with demand leakage

Problem definition: In high-product-variety businesses like fashion, mass production (MP) systems create environmental waste in the form of overproduction on a colossal scale. Mass customization (MC) has been proposed—without solid evidence—as a solution. In this paper, we analyze whether MC can indeed offer a win-win solution that helps both the bottom line and the environment. We also study the impact of three real policy options: promoting MC, charging a disposal fee for overproduction, and recycling. Academic/practical relevance: There is increasing interest in mass-customizing fashion goods, not only because consumers value customization, but also because MC is perceived to be environmentally friendly. Our paper puts this advocacy for MC to the test. We contribute to the literature, which has been largely silent on the issue, by uncovering when MC offers a win-win and relating such market outcomes to policy ideas. Methodology: We develop an analytical model of an MP firm adopting MC (going hybrid). The firm’s profit-maximizing variety, price, and inventory decisions then form the basis of our understanding the environmental impact of adopting MC and assessing various policy options. Results: Adopting MC can be a win-win, but it can also increase overproduction and hurt the environment. Our policy analyses reveal two kinds of insights. The first kind is about whether a policy expands win-win outcomes—encouraging sustainable adoption of MC. Among the policy ideas we explore, only promoting MC so as to increase consumers’ tolerance for waiting for mass-customized products can do that unambiguously. The second kind of insight is about whether a policy reduces the hybrid firm’s environmental impact. Only a disposal fee and costly recycling programs can do that unambiguously. Managerial implications: For MC adoption to be a win-win, policy makers must (1) work on convincing consumers to wait for bespoke fashion; (2) target MP firms with low cost of variety (high product-mix flexibility) with disposal fees or costly recycling programs; and (3) encourage those with relatively higher cost of variety to develop/acquire technology that would make recycling profitable. History: This paper has been accepted for the Manufacturing & Service Operations Management Special Section on Responsible Research in Operations Management. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1088 .

Newsvendor Inventory and Pricing Decisions in the Presence of Stochastic Purchase Return

We consider a periodic review, joint inventory and pricing control problem for a firm that faces general random price‐dependent demands. Any unsatisfied demand can be either backordered or lost immediately. The objective is to maximize the expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period. For both the backorder model and the lost sales model, we derive some quite general sufficient conditions to ensure the optimality of a base‐stock list price (BSLP) policy based on the strict monotonicity of demand functions in the realizations of random noises. We are among the first to utilize the strict monotonicity of demand functions in the realizations of random noises for deriving the sufficient conditions. We derive the sufficient conditions in both the backorder model and the lost‐sales model by utilizing the new concept of upper‐set and lower‐set decreasing properties (USDP/LSDP), which is a generalized version of the first‐order stochastic dominance. This study reveals that the optimality of a BSLP policy is robust to more general business environments than what we previously thought. Finally, we also apply the USDP/LSDP in other inventory management problems.

A specific integral, which is used in insurance mathematics for the determination of a stop-loss premium, corresponds to the definition of a performance characteristic of an inventory management decision problem. It is investigated whether the operational management problem might benefit from specific results obtained in the actuarial world. In the case little information is available on the demand distribution during the lead-time, which is relevant in inventory decision-making, interesting results might be used from the actuarial problem where limited information (e.g., only a few moments of the claim size distribution) is known. With a limited transformation of the actuarial results, upper and lower bounds may be determined for the safety stock in the inventory management problem. Also a numerical approximation using linear programming is shown to be equivalent to the problem under study.

Technology products often experience a life‐cycle demand pattern that resembles a diffusion process, with weak demand in the beginning and the end of the life cycle and high demand intensity in between. The customer price‐sensitivity also changes over the life cycle of the product. We study the prespecified pricing decision for a product that exhibits such demand characteristics. In particular, we determine the optimal set of discrete prices and the times to switch from one price to another, when a limited number of price changes are allowed. Our study shows that the optimal prices and switching times show interesting patterns that depend on the product's demand pattern and the change in the customers' price sensitivity over the life cycle of the product. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Multi-sector specific factors model with two mobile factors

Revenue management involves the use of pricing and inventory control strategies to balance supply and demand in a revenue-maximising manner. Although pricing and inventory control decisions are closely related, they have historically been considered in isolation in both industry and academic work. This paper adds to the recent research stream on joint pricing and inventory control by investigating static deterministic optimisation models for firms managing multiple products sharing multiple resources. Firms must manage both sales (demand rationing) and pricing decisions in order to maximise profits. This paper shows that, under standard regularity assumptions on demand, the deterministic joint price–inventory control problem with substitutable products can be reduced to a pure pricing problem. This is not true if demand is uncertain and/or products exhibit complementary effects, in which case demand rationing can be profitable. Illustrative examples that consider linear demand with and without substitution effects are provided. In this case, the price–inventory control problem can be solved by optimising a concave quadratic objective function with linear constraints. Practical applications of the models, which have been successfully used by several industries, are presented.

Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty