Joint Pricing Research Articles

Joint pricing and lot-sizing for a production model under controllable deterioration and carbon emissions

Carbon emission regulations help firms to develop green inventory systems. Besides, lots of items perish because of deterioration. Therefore, controlling both carbon emissions and the deterioration of items becomes essential. Despite the importance of the contribution of these issues, a few works have attended the concepts simultaneously. To fill this gap, this paper proposes a production system considering carbon emissions and deterioration of items and utilises green and preservation technologies to control them, respectively. Moreover, as determining the selling price of items plays a crucial role in a production system, pricing is another issue that this paper concentrates on it. This paper determines the preservation technology investment and green technology investment with discrete values of the cycle length and selling price for an item which: (a) items deteriorate at a constant rate, and the investment in preservation technology is allowable to mitigate the number of deteriorated items, (b) carbon is emitted due to setup and holding the items and the manufacturer follows carbon cap-and-trade regulation and invests on emission reduction, (c) a price-dependent demand is utilised to evaluate the selling price in optimal value. To validate the mathematical model, numerical examples for all cases are exposed.

Optimal pricing and ordering decisions with reference effect and quick replenishment policy

AbstractThis paper considers a revenue management problem in which a retailer determines joint pricing and ordering decisions for a single product over a two‐period selling horizon. The goal is to investigate the single and combined influences of reference effect (RE) and quick replenishment (QR) policy on the customers' purchasing behaviors, the retailer's optimal decisions, and the total profit of two periods. We first propose a discrete‐time joint pricing and ordering model with RE and QR policy in the presence of strategic customers. Then we extend to the other two models, in which the retailer does not implement the QR policy and the retailer ignores the customers' RE, to, respectively, explore the values of RE and QR policy to the retailer. Several significant results and managerial insights are derived through theoretical analysis and numerical experiments. Implementing the QR policy could help the retailer cut nearly half of the initial order quantity and improve the profit significantly, especially when the strength of RE is large and the storage cost is high. With the QR policy, if the retailer ignores the RE that factually exists in the customers' minds, she would set lower prices, place fewer initial order quantity, and lose much profit, especially when she sells luxury products or the customers' purchasing behaviors are strongly affected by RE.

Multi-commodity price risk hedging in the Atlantic salmon farming industry

Cost management has received limited attention in the aquaculture industry due to historically high profit margins. This trend, however, is not likely to continue. This creates a need for knowledge on optimally managing financial risks. In this study, we address the joint input-output price hedging problem of salmon farmers. Along with salmon, we consider three essential commodities used in fish feed mixtures. We use state-of-the-art copula models to examine multi-commodity hedging strategies. Our results show significant potential in reducing the joint price risk. Our key finding is that multi-commodity hedging improves hedging effectiveness for short horizons and risk-return trade-off for longer horizons. Salmon farmers face a trade-off where longer hedging horizons yield increased effectiveness and lower costs, yet require increased pre-planning of slaughtering volumes.

Inventory replenishment policies for two successive generations price-sensitive technology products

<p style='text-indent:20px;'>The high technology products come in generations, where the demand for newer technology generations is strongly influenced by the installed base of earlier generations (such as computers, cameras, notebooks, etc). However, the effect of technology substitution on inventory replenishment policies has received little attention in the supply chain literature. In the hi-technology market, consumers' purchasing capability, the utility of a product along with the entry of the advanced generation product influence the market expansion/contraction of the products. In this study, the impact of parallel diffusion of two successive generations' products on inventory policies of the monopolist has been analysed. The demand models have been characterised by considering the life-cycle dynamics for a P-type inventory system. The purpose of this paper is to develop a model for joint pricing and replenishment of technology generation products. The model has been solved by using a genetic algorithm technique. The impact of yearly price drop and the price sensitivity of demand on the profit margins vis-à-vis on replenishment policies has also been studied. The paper also brings forward the dynamics of the launch of newer generations and the pricing strategies on optimal inventory replenishment policies. Numerical illustrations have also been covered in the paper.</p>

The Coordinator Role of Trade Credit Contract for Coordinating Integrated Pricing and Periodic Review Inventory Decisions With Stochastic Demand

The purpose of this study is to analytically coordinate joint pricing and periodic review ordering choices for a supply chain (SC) facing stochastic price-dependent demand. In this paper, first, the optimal inventory and pricing strategies made by SC members are obtained under decentralized and centralized models. Thereafter, employing a trade credit contract, it proposes to provide a win–win coordination for the investigated SC. Sensitivity analyses are provided both analytically and numerically which indicate the significance of trade credit contracts in improving both customer service level and customer satisfaction. The results indicate that using trade credit contracts, the coordination of joint pricing and periodic review ordering choices is achievable. Moreover, the proposed trade credit contract has a unique feature in achieving more economic benefit compared to the centralized model under some circumstances. In addition, sensitivity analyses reveal that the coordination of integrated periodic review ordering and pricing choices is beneficial, especially for items with high price sensitivity and high demand uncertainty. Our findings also show the applicability of the trade credit contract for an SC facing highly uncertain demand.

Joint Pricing and Inventory Model for Deteriorating Items with Maximum Lifetime and Controllable Carbon Emissions under Permissible Delay in Payments

Reducing carbon emissions plays a significant role in developing sustainable inventory systems. In a seller-buyer relationship, an allowable delay in payment is considered for the buyer to manage the stock and simulate the demand. Deteriorating items that usually have specific maximum lifetimes have become a challenge for most firms. Contrary to the importance of these issues, very little research has studied the impact of carbon emissions on deteriorating inventory systems. This paper provides a price-dependent demand for perishable items when carbon cap-and-trade regulation fills the mentioned gap. This model provides a carbon reduction investment scheme and illustrates this investment’s effect on the inventory system. This paper determines the optimal replenishment cycle and selling price, in which: (a) perishable items have specific maximum lifetimes, (b) a specific period of delay in payment is allowed for the buyer to accumulate revenue, (c) carbon is emitted due to ordering and storage operations and carbon cap and trade is regulated along with allowable carbon reduction investment. After developing the model, optimal values are obtained from necessary and sufficient conditions of optimality. Numerical experiments are proposed to validate the model. By developing an algorithm, the optimal values of replenishment cycle, selling price, and carbon reduction technology investment are obtained, and the impact of carbon emissions and efforts to control emissions are outlined. Finally, some managerial applications are mentioned, and future research directions are exposed.

Collaborative innovation in supply chain systems: Value creation and leadership structure

In the information age, collaborative innovation in process and product is critically important. In this paper, we study the value of a supply chain innovation in which one upstream supplier and one downstream manufacturer may co-develop a product that includes several innovative elements. The supplier is responsible for process innovation to optimise the production system and reduce unit production costs, and the manufacturer is responsible for product innovation. We study innovation leadership and consider the supplier-led (SL) and manufacturer-led (ML) innovation games. We find that in both SL and ML innovation games, if the manufacturer has sufficient resources and capability to invest in product innovation, the manufacturer is always willing to invest in product innovation, but not the supplier. We identify the value of co-innovation and innovation leadership. We find that the product with higher innovation level will be provided under the ML innovation game. When selling the technological and innovative products (as they usually have a larger profit margin ratio), the manufacturer should invest more in product innovation. When product innovation efficiency is large (small), the manufacturer's profit is convex (concave) in the profit margin ratio. We identify the optimal value creation of joint pricing and innovation in a supply chain and the impacts of “process-product innovation dependence”. Our results (i) highlight the value of manufacturer-led innovation and the importance of considering the product's profit margin ratio in co-innovation, (ii) indicate that the manufacturer should be the leader to invest in product innovation, and (iii) the co-innovated products should be sold at a high profit margin.

Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand

We consider a joint pricing and inventory control problem in which the customer’s response to selling price and the demand distribution are not known a priori. Unsatisfied demand is lost and unobserved, and the only available information for decision making is the observed sales data (also known as censored demand). Conventional approaches, such as stochastic approximation, online convex optimization, and continuum-armed bandit algorithms, cannot be employed, because neither the realized values of the profit function nor its derivatives are known. A major challenge of this problem lies in that the estimated profit function constructed from observed sales data is multimodal in price. We develop a nonparametric spline approximation–based learning algorithm. The algorithm separates the planning horizon into a disjoint exploration phase and an exploitation phase. During the exploration phase, a spline approximation of the demand-price function is constructed based on sales data, and then the corresponding surrogate optimization problem is solved on a sparse grid to obtain a pair of recommended price and target inventory level. During the exploitation phase, the algorithm implements the recommended strategies. We establish a (nearly) square-root regret rate, which (almost) matches the theoretical lower bound.

Joint pricing strategies of multi-product retailer with reference-price and substitution-price effect

Joint pricing strategies of multi-product retailer with reference-price and substitution-price effect

Multiperiod Dynamic Pricing and Inventory Control Decisions for an Omnichannel BOPS Retailer with Reference Price Effects

This paper utilizes the consumers’ reference price in prospect theory to analyze an omnichannel retailer’s multiperiod pricing and inventory management problem in which consumers can cancel their orders before payment and return the products after payment if the products do not meet their expectation. The omnichannel retailer’s optimal equilibrium pricing and ending inventory level are derived under reference price effects by maximizing the discounted total profit over the infinite planning horizon, where the optimal decisions we discussed under two scenarios: loss neutrality and loss aversion. The analysis shows that the convergence of the pricing and ending inventory level toward their equilibrium is from above or below, depending on the relative location of the initial reference price with respect to the unique equilibrium price. Moreover, a set of sensitivity analyses is discussed to characterize the impacts of system parameters on the optimal decisions. This research fills the gap of behavioral operation in the field of omnichannel joint pricing and inventory management.

Pricing strategy in the product and service market

Existing studies have mainly focused on pricing in either primary markets or aftermarkets. However, in practice, prices in primary markets and aftermarkets are closely correlated. This study examines the joint pricing strategy in both primary markets and aftermarkets based on customer utility and establishes a pricing model for profit-maximization firms. Our results show that overpricing in the aftermarket is caused by customer myopia, while the motivation of the firm to avoid customer myopia depends on its pricing strategy. A quantity–price contract in the aftermarket is designed to raise the firm’s profit.

Joint Innovation Investment and Pricing Decisions in Retail Supply Chains with Customer Value

In the retail industry, customer value has become the key to maintaining competitive advantages. In the era of new retail, customer value is not only affected by the product price, but it is also closely related to innovations, such as value-added services and unique business models. In this paper, we study the joint innovation investment and pricing decisions in a retailer–supplier supply chain based on revenue sharing contracts and customer value. We first find that, in the non-cooperative game, equilibrium only exists in the supplier Stackelberg game. However, revenue sharing contracts cannot coordinate the supply chain in the non-cooperative game. By considering supply chain members’ bargaining power, we find that there exists a unique equilibrium for the Nash bargaining product. In addition, revenue sharing contracts can coordinate the supply chain and achieve the optimal consumer surplus. When the supply chain is coordinated, supply chain profit is allocated to the supply chain members based on their bargaining powers.

A Statistical Learning Approach to Personalization in Revenue Management

We consider a logit model-based framework for modeling joint pricing and assortment decisions that take into account customer features. This model provides a significant advantage when one has insufficient data for any one customer and wishes to generalize learning about one customer’s preferences to the population. Under this model, we study the statistical learning task of model fitting from a static store of precollected customer data. This setting, in contrast to the popular learning and earning paradigm, represents the situation many business teams encounter in which their data collection abilities have outstripped their data analysis capabilities. In this learning setting, we establish finite-sample convergence guarantees on the model parameters. The parameter convergence guarantees are then extended to out-of-sample performance guarantees in terms of revenue, in the form of a high-probability bound on the gap between the expected revenue of the best action taken under the estimated parameters and the revenue generated by a decision maker with full knowledge of the choice model. We further discuss practical implications of these bounds. We demonstrate the personalization approach using ticket purchase data from an airline carrier. This paper was accepted by J. George Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics.

Dynamic pricing and lot sizing for a newsvendor problem with supplier selection, quantity discounts, and limited supply capacity

This study considers the joint pricing and sourcing decision problem for a buyer purchasing a product from a set of suppliers who offer quantity discounts. The suppliers’ supply and/or the buyer’s warehouse capacities are bounded, causing the buyer to split its order over multiple suppliers and periods. This study assumes that demand is random over the planning horizon, divided into several periods, and dependent on price and time. The buyer, in each period, has to determine its retail price and the order quantities from the suppliers that maximize its expected profit. The problem is, therefore, formulated as mixed-integer nonlinear programming one, and an algorithm is developed to solve it. Numerical results show that the buyer may not buy up to the maximum capacity of a supplier with the lowest price when its order quantity exceeds the supply capacity of that supplier. In this case, the buyer needs to assign the remaining quantity to a more expensive supplier given that it exceeds that supplier’s minimum order quantity. The buyer could consider, as another option, convincing the low-priced supplier to increase its supply capacity in return for accepting a higher wholesale price, which only applies to the portion of an order exceeding the original supply capacity. For this to work, it should be economical for both players. Many numerical examples are provided with their results discussed to draw some insights and concluding remarks.

Joint Pricing and Inventory Control Decisions for Fashion Apparel with Considering Fashion Level and Partial Backlogging

Apparel inventories have been crawling up for decades. The fashion level of clothing drops over time, resulting in a continuous decline in market value, a rapid reduction in demand, and unsold inventory. Poor inventory management weighs down the apparel industry. Inventory planning decisions are crucial for a fashion apparel retailer. When the good is highly perishable, the retailer may need to backlog demand in order to market the good at a reasonable price and reduce inventory costs. This study formulates a finite horizon inventory model for fashion apparel under deteriorating fashion level and partial backlogging conditions. This model jointly optimizes the selling price, length of inventory-holding period, and length of shortage period by maximizing the average profit. The conditions that characterize the optimal solution are established and an algorithm is proposed to search for the optimal solutions. A numerical example is provided to illustrate the algorithm and the solution procedure. Furthermore, sensitivity analysis of the key system parameters is carried out and some interesting managerial insights are presented. Findings clearly suggest that the presence of shortage has got an affirmative effect on ordering policy of the fashion apparel retailer.

Joint Strategy of Dynamic Ordering and Pricing for Competing Perishables with Q‐Learning Algorithm

We use Machine Learning (ML) to study firms’ joint pricing and ordering decisions for perishables in a dynamic loop. The research assumption is as follows: at the beginning of each period, the retailer prices both the new and old products and determines how many new products to order, while at the end of each period, the retailer decides how much remaining inventory should be carried over to the next period. The objective is to determine a joint pricing, ordering, and disposal strategy to maximize the total expected discounted profit. We establish a decision model based on Markov processes and use the Q‐learning algorithm to obtain a near‐optimal policy. From numerical analysis, we find that (i) the optimal number of old products carried over to the next period depends on the upper quantitative bound for old inventory; (ii) the optimal prices for new products are positively related to potential demand but negatively related to the decay rate, while the optimal prices for old products have a positive relationship with both; and (iii) ordering decisions are unrelated to the quantity of old products. When the decay rate is low or the variable ordering cost is high, the optimal orders exhibit a trapezoidal decline as the quantity of new products increases.

A General Framework for Resource Constrained Revenue Management with Demand Learning and Large Action Space

This paper proposes a general framework/meta-policy to solve Revenue Management (RM) problems with demand learning and potentially large action space, constrained by initial unreplenishable resources. This framework combines the technique of primal-dual method in optimization and Upper-Confidence-Bound (UCB) algorithm in learning. Three important RM applications are discussed in this paper to illustrate the general framework: network revenue management (NRM), dynamic assortment selection with multinomial- logit (MNL) choice model, and joint pricing and assortment optimization problems. This paper demonstrates how to adapt the framework to each application by designing application-specific subroutines. Theoretical results show that the adapted algorithms in all three applications are effective in achieving low regrets, and numerical experiments using the example of dynamic assortment selection demonstrate that our algorithm has great empirical performance and it is computationally efficient.

Solving a Joint Pricing and Inventory Control Problem for Perishables via Deep Reinforcement Learning

We study a joint pricing and inventory control problem for perishables with positive lead time in a finite horizon periodic‐review system. Unlike most studies considering a continuous density function of demand, in our paper the customer demand depends on the price of current period and arrives according to a homogeneous Poisson process. We consider both backlogging and lost‐sales cases, and our goal is to find a simultaneously ordering and pricing policy to maximize the expected discounted profit over the planning horizon. When there is no fixed ordering cost involved, we design a deep reinforcement learning algorithm to obtain a near‐optimal ordering policy and show that there are some monotonicity properties in the learned policy. We also show that our deep reinforcement learning algorithm achieves a better performance than tabular‐based Q‐learning algorithms. When a fixed ordering cost is involved, we show that our deep reinforcement learning algorithm is effective and efficient, under which the problem of “curse of dimension” is circumvented.

Joint Pricing and Inventory Decisions

Joint Pricing and Inventory Decisions

Implied Asset Return Profiles, Firm Fundamentals, and Stock Returns

We introduce a novel approach to ascertain firms’ unobserved asset return distribution implied by the joint pricing of equity and credit securities within a structural framework. Motivated by Q-theory, we propose a two-factor model that captures asset growth and risk-shifting effects on stock returns. We show that strong asset returns representing systematic growth options predict higher stock returns, whereas shifting risk from equity to credit forecasts lower stock returns. We also find that the performance of many popular stock market factors (that overlook the optionality of equity) are significantly improved after controlling for asset-level risk-shifting exposure.