Avi Herbon

Dynamic pricing vs. acquiring information on consumers’ heterogeneous sensitivity to product freshness

We propose a model of an inventory system in which a perishable product is periodically replenished, and the retailer is unaware of consumer heterogeneity in consumers’ sensitivity to freshness of a perishable product with a fixed shelf life (though it exists). Using an analytical approach, we optimally solve the problem and evaluate the extent to which unawareness is likely to detract from a retailer’s profit and the extent to which it is likely to affect the price that consumers pay. In addition, we evaluate the conditions in which a dynamic pricing policy is beneficial either to the retailer or to the consumer, as compared with a static pricing policy. It is proven that the retailer should assign products a lower price at the early stages of their shelf life and then raise the price as the products approach expiration. A numerical illustration combined with sensitivity analysis demonstrates the applicability of the modelling approach. Key parameters such as volatility of consumer sensitivity to freshness and the retailer’s estimation regarding consumers’ sensitivity are investigated. A conclusion is that, in monetary terms, it is preferable from the retailer’s perspective to invest in dynamic pricing technology rather than in technologies for gathering information on consumers’ purchases.

A supply chain under limited-time promotion: The effect of customer sensitivity

Abstract We consider a two-echelon supply chain with a supplier and a retailer facing stochastic customer demands. The supplier is a leader who determines a wholesale price. In response, the retailer orders products and sets a price which affects customer demands. The goal of both players is to maximize their profits. We find the Stackelberg equilibrium and show that it is unique, not only when the supply chain is in a steady-state but also when it is in a transient state induced by a supplier’s promotion. There is a maximum length to the promotion, however, beyond which the equilibrium ceases to exist. Moreover, if customer sensitivity increases, then the wholesale equilibrium price decreases, product orders increase and product prices drop. This effect, well-observed in real life, does not, however, necessarily imply that the promotion is always beneficial. Conditions for the profitability of a limited-time promotion are shown and analyzed numerically. We discuss both open-loop and feedback policies and derive the conditions necessary for them to remain optimal under stochastic demand fluctuations.

Simulation study of the price differentiation effect in a stochastic deteriorating inventory with heterogeneous consumers -- freshness sensitivity

A fixed price policy regardless of expiration date may result in unsold inventory and sales loss. Price reduction over time as the expiration date approaches motivates customers to purchase all items, including the ones that are left with only a short interval until their expiration. We conduct a discrete event simulation that captures the main characteristics of this phenomenon. Results show that a moderate differentiation of price increases profits by 6%, a larger differentiation reduces profits. Profits are the highest for freshness-oriented customers. A fixed price policy is preferred in an environment of large variance and expected near term expirations.

Optimal dynamic pricing and ordering of a perishable product under additive effects of price and time on demand

When perishable products, such as dairy products, fruits and vegetables, drugs, or batteries are priced uniformly, without taking into consideration the amount of time remaining until the expiration date, consumers may gravitate towards fresher products, leaving some inventory unsold. A dynamic pricing policy, in which products are priced differently as they approach expiration, may encourage customers to buy less-fresh products, potentially increasing revenue and eliminating waste. Following scarce literature on dynamic pricing of storable perishable items, this paper develops a model to determine a products optimal replenishment schedule and dynamic price over time, with the aim of maximizing the retailers profit. Customer demand is assumed to be a pseudo-additive function of price and time since replenishment. Some properties of the optimal pricing and replenishment policy are derived by means of necessary and sufficient conditions of optimality. A number of examples show the dynamics of the optimal policy under different assumptions regarding demand. In particular, we evaluate the extent to which the retailer can benefit from the implementation of a dynamic pricing policy as opposed to a static one, and we show that the optimal policy is highly dependent on the form of demand incorporated into the model.

Optimal piecewise-constant price under heterogeneous sensitivity to product freshness

When perishable products are priced uniformly, regardless of the amount of time remaining until expiration, consumers may gravitate towards fresher products, leaving some inventory unsold. This research considers dynamic pricing policies as well as replenishment policies in the context of perishable products with a fixed shelf life. Consumers are assumed to be heterogeneous in their sensitivity to freshness, i.e. their willingness to pay more for fresher products. We develop a model for identifying an optimal (profit-maximising) dynamic pricing policy and for evaluating the extent to which both the retailer and the consumer benefit from the implementation of a dynamic pricing policy as opposed to a static policy. The model assumes that the retailer is able to utilise knowledge regarding the heterogeneous characteristics of incoming customers (e.g. the retailer can gather specific information about customers’ historical purchases). Unexpectedly, it is proven that in an optimal pricing policy, the retailer should assign a lower price to fresher products and then raise the price as the products approach expiration. A numerical illustration shows that profits are strongly influenced by the volatility of consumer sensitivity to freshness; specifically, this variable has the potential to reduce optimal profits by up to 8%.

Optimal two-level piecewise-constant price discrimination for a storable perishable product

Price differentiation over time is an additional policy that firms might consider when determining prices for perishable products. The common policy of a fixed price regardless of freshness might result in leaving some expired inventory unsold. Price differentiation can impact the demand for perishable products, which declines as the expiration date approaches. We develop an optimisation model with the goal of evaluating the monetary effectiveness of the strategy of simultaneously combining price discrimination across heterogeneous consumers with price differentiation over time for perishable inventory under separable multiplicative demand factors of price and time. Necessary optimality equations are derived, and their solutions are proved to constitute a unique global optimal solution. It is proved that an optimal pricing policy is to implement price discrimination with respect to consumers’ sensitivity to freshness, while dynamically changing the price over time, starting with a lower price at the early stages of the product’s shelf life and increasing it at a later stage. The monetary benefit that the retailer and consumer can derive from the suggested pricing policy is evaluated by comparing the model to other models in which price discrimination or dynamic pricing are not implemented. A numerical example that illustrates the significance is introduced. From the analysis of a numerical illustration of the model, it is concluded that a dynamic price discrimination policy can be approximated by an identical-to-all dynamic pricing policy in order to maximise the retailer’s profit and thus, mitigate the retailer’s risk from failing in the process of implementing price discrimination.

Dynamic weights approach for off‐line sequencing of supplier selection over a finite planning horizon

Purpose – The purpose of this paper is to develop a user‐oriented decision‐supporting applicable tool for selection of a single supplier out of a group of potential suppliers in a dynamic business environment over a finite planning horizon.Design/methodology/approach – A qualitative and quantitative description of the impact of a change in one or several business environment parameters on current and future supplier choice; the methodology is accompanied by a visual representation of those impacts for the decision maker. The paper presents extended simulation experiments to test the proposed methodology.Findings – A strategy of replacing suppliers over a definite planning horizon based on a forecast of the business environment is significantly (2‐9 per cent) more efficient than a strategy of relying on a single leading supplier throughout the planning horizon. This efficiency gain is greater the more the business environment is dynamic.Practical implications – The proposed methodology is applicable to a b...

Production under periodic demand update prior to a single selling season: A decomposition approach

This paper focuses on dynamic, continuous-time production control problems in the fashion industry. Similar to the classical news-vendor problem, we consider a single product-type and the cumulative demand for items is not known until the end of the production horizon and therefore must be forecasted. Since there are periodic updates before a single selling season, actual demand during a period of time can only be determined by the end of the period. If the overall demand is overestimated, excessive inventory holding and production costs are paid and surpluses are sold at low prices at the end of the production horizon. If it is under-estimated, then sales are lost. The objective is to dynamically determine production orders which minimize overall expected costs. Since the optimal feedback for such a problem is characterized by thresholds evolving with time and system states, there is a significant computational burden in determining them. With the aid of the variational analysis and a decomposition, we derive a closed-form solution for the thresholds. A numerical study carried out to compare the decomposition and straightforward simulation-based solutions indicates the high accuracy of the suggested approach while the computational burden is dramatically reduced.

Reduction of future information required for optimal control of dynamic systems: a pseudostochastic model

This note develops a pseudostochastic model for optimal control of dynamic systems over a given planning horizon. The obtained results reflect the extent to which reduction of future information impacts upon the performance and optimal control of dynamic systems. The main results indicate that, when using only partial information for determining optimal control, the performance of the dynamic system is almost identical to that when using full information. When ignoring the information expected beyond the planning horizon, a significant performance loss and a possible violation of feasibility of the optimal control can occur.

Using a pseudo-stochastic approach for multiple-parts scheduling on an unreliable machine

Abstract In this paper we follow previous “pseudo-stochastic” approaches that solve stochastic control problems by using deterministic optimal control methods. In a similar manner to the certainty equivalence principle, the suggested model maximizes a given profit function of the expected system outcome. However, unlike the certainty equivalence principle, we model the expected influences of all future events (including those that are expected beyond the planning horizon), as encapsulated by their density functions and not only by their mean values. The model is applied to the optimal scheduling of multiple part-types on a single machine that is subject to random failures and repairs. The objective of the scheduler is to maximize the profit function of the produced multiple-part mix. A numerical study is performed to evaluate the suggested pseudo-stochastic solutions under various conditions. These solutions are compared to a profit upper bound of the stochastic optimal control solutions.