Pricing, assortment, and inventory decisions under nested logit demand and equal profit margins

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

We study a multi-period stochastic inventory system with backlogs. Demand in each period is random and price sensitive, but the firm has little or no prior knowledge about the demand distribution and how each customer responds to the selling price, so the firm has to learn the demand process when making periodic pricing and inventory replenishment decisions to maximize its expected total profit. We consider the scenario where the firm is faced with the business constraint that prevents it from conducting extensive price exploration, and develop parametric data-driven algorithms for pricing and inventory decisions. We measure the performances of the algorithms by regret, which is the profit loss compared with a clairvoyant who has complete information about the demand distribution. We analyze the cases where the number of price changes is restricted to a given number or a small number relative to the planning horizon, and show that the regrets for the corresponding learning algorithms converge at the best possible rates in the sense that they reach the theoretical lower bounds. Numerical results indicate that these algorithms empirically perform very well. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transaction, for datasets, additional tables, detailed proofs, etc.

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.

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.

Beyond Plain Vanilla: Modeling Joint Product Assortment and Pricing Decisions

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

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.

Many enterprises that participate in dynamic markets need to make product pricing and inventory resource utilization decisions in real time. We describe a family of statistical models that addresses these needs by combining characterization of the economic environment with the ability to predict future economic conditions to make tactical (short-term) decisions, such as product pricing, and strategic (long-term) decisions, such as level of finished goods inventories. Our models characterize economic conditions, called economic regimes, in the form of recurrent statistical patterns that have clear qualitative interpretations. We show how these models can be used to predict prices, price trends, and the probability of receiving a customer order at a given price. These “regime” models are developed using statistical analysis of historical data and are used in real time to characterize observed market conditions and predict the evolution of market conditions over multiple time scales. We evaluate our models using a testbed derived from the Trading Agent Competition for Supply Chain Management, a supply chain environment characterized by competitive procurement, sales markets, and dynamic pricing. We show how regime models can be used to inform both short-term pricing decisions and long-term resource allocation decisions. Results show that our method outperforms more traditional short- and long-term predictive modeling approaches.

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.

This paper aims to develop a new bi-level game model for joint pricing and inventory decisions in a competitive supply chain consisting of a dominant manufacturer, who produces single perishable product from deteriorating raw materials, and two follower retailers who face nonlinear price-dependent demand and operate under Cournot assumptions. Three levels of warehousing including raw material warehouse, final product warehouse, and retail warehouses with exponential deterioration rates are considered to explore the joint impact of deterioration rate and price elasticity on the equilibrium inventory decisions. A Stackelberg–Nash–Cournot model is developed to seek the equilibrium prices, quantities, and replenishment cycles and is solved through an exact methodology. A numerical example is presented to validate the proposed model and comprehensive sensitivity analyses are carried out to measure the impact of the model’s key parameters including the deterioration rate in the producer’s and the retailers’ warehouses, the retail and competitor price elasticity, and the market scale on the equilibrium.

When Demand Projections are Too Optimistic: A Structural Model of Product Line and Pricing Decisions

Purpose – The purpose of this paper is to evaluate the interaction between inventory availability (scarcity) and pricing levels (price-leadership (PL)), and its effect on product returns in the internet retail supply chain. Specifically, this paper investigates how supply chain managers can use inventory (seller-induced scarcity) and pricing (PL) levers to control product returns. Design/methodology/approach – Empirical data of sales and product returns from an internet retailer is analyzed to identify the scale of the effect that product scarcity and PL has on product returns. These factors are considered in developing a sales-return process model which is used with empirical data in a simulation study. The study evaluates changes in product returns for different policy settings related to PL and inventory levels. Findings of the simulation study are validated using statistical analysis of empirical data. Findings – PL and seller-induced product scarcity affect the rate of product returns; however, the scale of this effect depends on inventory and pricing decisions. The results identify an inflection boundary based on scarcity and PL levels which reverses this effect. This reversal is explained by underlying principles at play regarding buyers’ valuation of the sale and corresponding product attributes. Practical implications – Supply chain managers in internet retail can leverage lower inventory under the seller-induced scarcity approach to improve revenues. However, reducing inventory levels beyond a threshold is counterproductive, due to an associated increase in product returns. Similarly, setting market competitive prices (PL) can help reduce product returns. Under the seller-induced scarcity condition, this effect is reversed for inventory levels below a threshold. Retailers can implement the methodology developed in this paper to identify the inventory-price threshold that can help increase revenues while keeping the rate of product returns at a manageable level. Originality/value – This research extends prior work regarding the role of product scarcity and pricing on product returns and develops a deeper understanding of how these factors can be managed to control product returns in the internet retail setting.

This paper studies the impact of supply reliability on a retail firm's performance under joint marketing and inventory decisions. The firm sells a product in a single selling season and can exert marketing effort to influence consumer demand. We develop a modeling framework to quantify the value of improving supply reliability and investigate how this value depends on different model parameters. Our results provide useful insights into how firms should make investment decisions on adopting new technologies to improve supply reliability. First, we establish a necessary and sufficient condition under which the maximum unit cost a firm is willing to pay to improve supply reliability increases in product price. We further show that this condition would hold in most practical situations. Thus, with some caveats, our result supports the intuition that a firm is willing to pay more to improve supply reliability for products with a higher price. Next, we show that for two products with the same price, a firm is willing to pay more to improve supply reliability for the product with a higher product cost. This implies that it is not necessarily true that emerging technologies for improving supply reliability should be first adopted for products with the highest unit contribution margin. Finally, we show that a product with a lower marketing cost function always benefits more from improved supply reliability than a product with a higher marketing cost function. This finding suggests that the priority of adopting new technologies should be given to situations where the firm can effectively induce greater demand through promotional effort.

Gross margin management is a complex task as gross margin can’t be too high or too low in order to deliver maximum sales and profit.Objective of the article is to present framework which allows understanding and managing gross margin and gross profit in companies with large assortment of products. The framework has defined basic margin variances – pricing, cost, volume and mix. These variances enable to understand and interpret strategic and merchandising decisions of the company. Formulas are presented which translate specific merchandising decisions impact on gross margin and gross profit, formulas allow to simplify calculations without the need to recalculate all assortment on product by product basis multiple times.Derivations of algebraic formulas are used to obtain gross margin variances impact on gross margin and gross profit. Cause and effect model is used as a method to integrate gross margin variance into the gross margin management framework. Boston Consulting Group matrix principle is used to establish and analyse typical gross margin management situations and interpret behavior of customers.Conclusions – companies with large assortment of products have to manage financial results and gross profit through gross margin management by evaluating merchandising decisions impact on both gross profit and gross margin. Four gross profit and margin variances – price, cost, volume and mix, need to be used to understand business situations related to gross margin management and these four variances can be used as building blocks to analyse specific merchandising offers and strategic decisions.The type of the article: Methodological articleJEL Classification: G39, M49.DOI: http://dx.doi.org/10.5755/j01.em.18.1.4116