Number Of Price Changes Research Articles

Bayesian dynamic learning and pricing with strategic customers

We consider a seller who repeatedly sells a nondurable product to a single customer whose valuations of the product are drawn from a certain distribution. The seller, who initially does not know the valuation distribution, may use the customer's purchase history to learn and wishes to choose a pricing policy that maximizes her long‐run revenue. Such a problem is at the core of personalized revenue management where the seller can access each customer's individual purchase history and offer personalized prices. In this paper, we study such a learning problem when the customer is aware of the seller's policy and thus may behave strategically when making a purchase decision. By using a Bayesian setting with a binary prior, we first show that a popular policy in this setting—the myopic Bayesian policy (MBP)—may lead to incomplete learning of the seller, namely, the seller may never be able to ascertain the true type of the customer and the regret may grow linearly over time. The failure of the MBP is due to the strategic action taken by the customer. To address the strategic behavior of the customers, we first analyze a Stackelberg game under a two‐period model. We derive the optimal policy of the seller in the two‐period model and show that the regret can be significantly reduced by using the optimal policy rather than the myopic policy. However, such a game is hard to analyze in general. Nevertheless, based on the idea used in the two‐period model, we propose a randomized Bayesian policy (RBP), which updates the posterior belief of the customer in each period with a certain probability, as well as a deterministic Bayesian policy (DBP), in which the seller updates the posterior belief periodically and always defers her update to the next cycle. For both the RBP and DBP, we show that the seller can learn the customer type exponentially fast even if the customer is strategic, and the regret is bounded by a constant. We also propose policies that achieve asymptotically optimal regrets when only a finite number of price changes are allowed.

Optimal Inventory Policies for Price and Time Sensitive Demand Under Advertisement

Aims: This article analyzes an inventory system for deteriorating items. The demand is quadratic function of time and is dependent on time, price and advertisement. Shortages are allowed and partially backlogged. Background: Demand and pricing are the two most crucial factors in inventory policy for any business to be successful. In today’s era of competitive circumstances, any product is promoted through advertisement, which plays a vital role in changing the demand pattern among the community. The marketing and demonstration of an item by time-to-time with fashionable advertisements through well-known media such as TV, radio, newspaper, magazine, etc. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this in turn decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsolescence, pilferage. Hence, deterioration effect is a major part in inventory control theory. So in this article demand rate is considered to be a function of selling price, time and occurrence of advertisement instantaneously. Objective: A solution procedure is obtained to find optimal number of price changes and optimal selling price to maximize the total profit. Method: Classical Optimization. Result: From the sensitivity analysis table, it can be seen that the optimal profit is highly sensible to advertisement coefficient and purchase cost. With an increment in rate of deterioration, selling price decreases. Scale demand has reasonable effect on cycle time and selling price. When the value of increase, the cycle length and profit goes on decreasing. Growth in profit is observed if we increase parameter b, higher will be the profit. Price elasticity is sensible parameter with respect to selling price. If backlogging rate increases, the profit will decreases. The inventory parameters holding cost, back order cost and lost sale cost have marginal effect on total profit. Conclusion: In this article, an inventory model is proposed for deteriorating items with variable demand depends upon the advertisement, selling price of the item and time. Shortages are allowed and partially backlogged and backlogging rate depends on the waiting time for the next replenishment. From this article, we can conclude that the parameters are insensible with respect to optimal profit, cycle time and selling price and rest of the parameters have practical output on total profit.

Examination of the Motivations for Equity-based Crowdfunding in an Emerging Market

The purpose of this paper was to identify the most significant factors and issues concerning a successful Pre-Commercial Procurement in the Slovak and Czech markets and to validate a conceptual model developed to describe relations within all procurement phases with more detailed exploratory attributes. Number of price changes within the negotiation phase (generally in electronic dynamic pricing environment) and volume of procurement were identified as the most crucial determinants of savings, with a positive and negative effect on the success of Pre-Commercial Procurement respectively. Selection of auction type affects the number of participants and number of new participants in the auction, with less transparent auction types being more attractive for suppliers than transparent types. Further, Pre-Commercial Procurement was compared to traditional procurement of common products and services, identifying differences in number of participants and total volume of auctions. A survey conducted identified the critical need to improve innovation driven sourcing ecosystem to make the market more transparent for identification of suitable suppliers but also for the procurer to be more visible on the market when procurement is taking the place. The developed conceptual framework with tested relations can be a guide to proper Pre-Commercial Procurement procurement setting.

What Is the Long-Term Impact of an Implant Stewardship Program on Orthopaedic Trauma Implant Pricing?

To analyze the effectiveness of an implant stewardship program on implant cost containment and to estimate surgeons' responsiveness to implant price changes. Interrupted time series. Level I trauma center. Monitored usage of 5 trauma constructs by 10 surgeons over a 5-year period. Red-Yellow-Green (RYG) implant pricing comparison chart. Primary outcomes were changes in the mean price, minimum price, and the number of price changes. The secondary outcome was surgeons' responsiveness to RYG/cost changes. The study consisted of 2468 procedures. A mean construct price decrease of $66 per year [95% confidence interval (CI), $-170 to $-151], with distal femoral plates demonstrating the largest mean annual price decline ($486; 95% CI, $-540 to $-432). The minimum construct price decreased by $131 per year (95% CI, $-155 to $-111), with the largest reductions observed for distal femoral plates (-$436 per year; 95% CI, $-516 to $-354) and external fixators (-$122 per year; 95% CI, $-258 to $-136). The median price decrease was $407 (range: $6 to $2491) or 12.5% of the previous price. Positive changes in RYG levels increased surgeons' usage of tibial nails by 115%, femoral nails by 106%, and external fixators by 104%. Surgeons' implant selection was insensitive to RYG changes for distal femoral plates [RYG elasticity (ERYG): -0.74] and proximal tibia plates (ERYG: -0.21). The implant stewardship program was associated with substantial implant price reductions. Surgeons' implant selection was especially sensitive to price changes for intramedullary nails and external fixators.

Technical Note—Data-Based Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes

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.

An agent-based model of intra-day financial markets dynamics

We develop an agent-based model of a financial market which is able to jointly reproduce many of the stylised facts at different time scales. These include properties related to returns (leptokurtosis, absence of linear autocorrelation, volatility clustering), trading volumes (volume clustering, correlation between volume and volatility), and timing of trades (number of price changes, autocorrelation of durations between subsequent trades, heavy tails in their distribution, order-side clustering). Our model combines heterogeneous boundedly rational agents, endogenously activating on the basis of market events, with realistic assumptions on market microstructure. In particular, we introduce a strict event scheduling borrowed from the Euronext exchange. We study the model in a bottom-up fashion under alternative scenarios regarding the sophistication of agents’ strategies. These scenarios allow us to disentangle the role of microstructure characteristics from trading behaviour in the emergence of market statistical properties. Our results reveal that traders’ endogenous activation is crucial to jointly reproduce most of these properties. The ability of the model to replicate the main stylised facts of financial markets proves that it can be fruitfully used by policymakers as a test-bed for regulatory experiments aimed at improving market outcomes at different time-scales.

How do firms set prices? Narrative evidence from corporate filings

We quantify narrative evidence from archived corporate filings to construct a novel dataset on the price-setting behavior of public companies. Our approach is closely related to that of survey-based studies on price setting, but we collect data from twenty-five years instead of one specific point in time. This allows us to investigate variation over time and to establish that qualitative information provided directly by firms is informative about the aggregate variables macroeconomists are fundamentally interested in. Our findings suggest that (i) price setting is asymmetric and has a strong state-dependent component, (ii) real rigidities in the form of strategic pricing complementarities are very common, and (iii) an increase in the number of price changes does not necessarily reflect a decrease in price rigidity. We discuss to what extent our results can be explained by strategic reporting behavior and consider their implications in the context of widely-used price-setting models.

Network Revenue Management with Limited Switches: Known and Unknown Demand Distributions

Our work is motivated by a common business constraint in online markets. While firms respect the advantages of dynamic pricing and price experimentation, they must limit the number of price changes (i.e., switches) to be within some budget due to various practical reasons. We study both the classical price-based network revenue management problem in the distributionally-unknown setup, and the bandits with knapsacks problem. In these problems, a decision-maker (without prior knowledge of the environment) has finite initial inventory of multiple resources to allocate over a finite time horizon. Beyond the classical resource constraints, we introduce an additional switching constraint to these problems, which restricts the total number of times that the decision-maker makes switches between actions to be within a fixed switching budget. For such problems, we show matching upper and lower bounds on the optimal regret, and propose computationally-efficient limited-switch algorithms that achieve the optimal regret. Our work reveals a surprising result: the optimal regret rate is completely characterized by a piecewise-constant function of the switching budget, which further depends on the number of resource constraints --- to the best of our knowledge, this is the first time the number of resources constraints is shown to play a fundamental role in determining the statistical complexity of online learning problems. We conduct computational experiments to examine the performance of our algorithms on a numerical setup that is widely used in the literature. Compared with benchmark algorithms from the literature, our proposed algorithms achieve promising performance with clear advantages on the number of incurred switches. Practically, firms can benefit from our study and improve their learning and decision-making performance when they simultaneously face resource and switching constraints.

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

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.

The Effects of the Market Transparency Unit for Fuels in Germany

The authors analyse how the market transparency unit for fuels in Germany affects both supplier and consumer behaviour. The number of price changes has increased, mainly due to increasing price cuts, as has the spread between the lowest and the highest price of the day — both indicators of intensified competition. The concern that the introduction of the market transparency unit would facilitate collusion appears not to be warranted. In contrast, competition has intensified and consumers are increasingly making use of the price differences. The analysis also reveals that consumers purchased more gasoline in times of low prices (so-called price valleys) in 2015 than they did in 2012. The change in consumer behaviour is an indicator that at least some drivers tend to use fuel price comparison apps fed by data from the market transparency unit.

DTER and DTTER as High-Frequency Trading Efficiency Ratios

The aim of this paper is to present new transaction efficiency ratios mainly aimed for High-Frequency Trading - ratios which in general are available in very scarce numbers. I present here two dynamic efficiency ratios that are based on simple price changes and not on external benchmarks or returns, such as the rate of return of competing entities or the risk-free rate - as most of the generally applied ratios do. The proposed ratios are based on assumptions, different than the general portfolio theory, and on the fact that the entity itself does not have the capacity or does not want to affect prices through order placement. These assumptions rely on the fact that higher rates of return for HFT are not dependent on a higher price volatility, and therefore, higher risk. In the end, for HFT trading, risk is in large scope related to time and not volatility, since the longer it takes for prices to change, the higher the risk (and costs) the HFT entity takes. This means that higher rates of return are directly dependent on variability (volatility) in prices - not price amplitude but the number of price changes, and risk is related to time, since the longer it takes for prices to change the higher the risk (and costs) the HFT entity may be exposed to. As such, the proposed ratios take into consideration such elements as the number of price innovations (changes), the number of transactions performed or the time between transactions.

A continuous approximation method for dynamic pricing problem under costly price modifications

This paper presents a heuristic method to solve a dynamic pricing problem under costly price modifications. This is an extremely difficult nonlinear problem that has been solved only for a few special instances. Here we provide a new approach that involves an approximate reformulation of the problem, which can subsequently be solved in closed-form using elementary calculus techniques. Numerical results show that the approach is quite accurate; approximating the optimal revenue with errors usually much less than 1%. Moreover, the accuracy rapidly improves as the optimal number of price changes increases, which are precisely the cases conventional approaches would fail.

Multi-sector specific factors model with two mobile factors

This paper is an extension of the specific factors model to the study of relative wages by considering a multi-industry model with skilled and unskilled labor as the only mobile factors. We show that for changes in the price of a single industry, the impact on the skill premium is usually modest and sometimes the sign is the reverse of expectations. The elasticity of substitution between factors is critical for single-sector price changes. To generate a Stolper-Samuelson magnification effect, it is necessary to have a large number of price changes across industries intensive in either skilled or unskilled labor.

Bayesian Dynamic Learning and Pricing with Strategic Customers

We consider a seller who repeatedly sells a nondurable product to a single customer whose valuations of the product are drawn from a certain distribution. The seller, who initially does not know the valuation distribution, may use the customer's purchase history to learn, and wishes to choose a pricing policy that maximizes her long-run revenue. Such a problem is at the core of personalized revenue management where the seller can access each customer's individual purchase history and offer personalized prices.In this paper, we study such a learning problem when the customer is aware of the seller's policy, and thus may behave strategically when making a purchase decision. By using a Bayesian setting with a binary prior, we first show that a naive myopic Bayesian policy (MBP) by the seller may lead to incomplete learning -- the seller may never be able to ascertain the true type of the customer and the regret may grow linearly in time. The failure of the MBP is due to the strategic action taken by the customer. To resolve this issue, we propose a randomized Bayesian policy (RBP), which updates the posterior belief of the customer in each period with a certain probability. We show that the seller can learn the customer type exponentially fast with the RBP even if the customer is strategic, and the regret is bounded by a constant. We also propose policies that achieve asymptotically optimal regrets when only a finite number of price changes is allowed.

Data-Driven Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes

A firm sells a product over T periods. Demand in each period is random and price sensitive, and unsatisfied demands are lost and unobservable. The firm has limited prior knowledge about the demand process and needs to learn it through historical sales data. We consider the scenario where the firm is faced with the business constraint that prevents it from conducting extensive price experimentation. We develop data-driven algorithms for pricing and inventory decisions and evaluate their effectiveness using regret, which is the profit loss compared to a clairvoyant who has complete information about the demand process. We study three distinct scenarios and design algorithms that achieve the lowest possible regret rates: First, in a quite general case, when the number of price changes is bounded by a given number, the regret is O(T1/2). Second, in a special so-called well-separated case, when the number of price changes is limited to m, the regret is O(T1/m 1). Third, in the well-separated case allowing more frequent price changes that is limited to O(logT), the regret is O(logT). Numerical results show that these algorithms empirically perform very well.

Bullwhip effect under substitute products

Using a large-scale, product-level dataset collected from a supply chain dyad, we examine the effect of own and substitute products on a focal product's bullwhip effect and estimate the existence and magnitude of the bullwhip effect at the product level. We find that, under substitute products, the bullwhip effect is not only affected by a product's own factors but also by those of its substitute products. An increase in the number of own price changes is associated with a decrease in the bullwhip effect in terms of the direct effect but with an increase in the bullwhip effect in terms of the total effect, and increases in the number of price changes of substitute products and own stockouts are associated with increases in the bullwhip effect. The potential effects for own price changes, price changes of substitute products and own stockouts are as much as 59.51%, 95.06% and 66.11%. We also find that the bullwhip effect is prevalent and very intensive at the product level. We discuss the theoretical and managerial implications of the findings.

A comparative study of optimal replenishment policy for a retailer in declining market

The aim of this article is to provide an analytical solution to a retailer whether to adopt positive stock on hand or stockless inventory policy. Mathematical models are developed for both the policies for a product with price and time sensitive demand to maximise the profit functions. Here, unlike the conventional inventory models with pricing strategy, which were restricted to pre-specified replenishment or pricing cycle times and hence fixed number of price changes over the finite time horizon, we allow the number of price changes to be a decision variable for both policies. Within a fixed planning horizon, existence and uniqueness of optimal solutions are verified. A solution procedure is presented to determine optimal inventory policy and corresponding optimal prices, optimal number of pricing cycles, optimal lot size and optimal profit simultaneously. Numerical examples are provided to illustrate the development of the models.

The Effects of Gasoline Price Regulations: Experimental Evidence

Petrol prices tend to be subject to regular changes, often changing more than once a day in many countries, and the number of changes appears to increase. For example, a recent sector inquiry by Germany’s competition authority has found that the number of price changes has almost tripled between 2007 and 2010. At the same time, economic theory suggests that gasoline retail markets are prone to collusive behavior. Oligopoly market structures prevail, market interactions occur frequently, prices are highly transparent, and demand is rather inelastic. As a result, a public debate has emerged whether or not to adopt regulatory pricing rules for gas stations similar to those implemented in Austria, parts of Australia, Luxembourg or parts of Canada. In order to increase consumer welfare these rules either restrict the number of price changes per day or they limit the mark-up for gasoline retail prices. As theoretical predictions about the impact of these measures are mixed and empirical studies rare, we analyze the effects, using an experimental gasoline market in the lab. Our results reveal that two of the suggested rules rather decrease consumer welfare: The Austrian rule which only allows one price increase per day (while price cuts are always possible) and the Luxembourg rule which introduces a maximum markup for retailers. While no rule tends to induce lower retail prices, the Western Australian rule which allows at most one daily price change (no matter whether up or down) does at least not harm consumers.

Costly price changes with dynamic pricing and lot-sizing

In this article, we address the profit maximization version of the dynamic economical problem where we charge a cost per price change. This model makes an explicit link between the number of price changes and the cost of changing prices. Hence, this new cost can determine the number of different possible prices, especially when all others costs are constant, as well as it reflects the real cost of changing prices (labor, communication and so on). To solve our model, we describe a simple heuristic that strongly outperforms state-of-art solvers even for medium-size instances. Furthermore, we give numerical evidence that charging a cost per price change does not impact setups in general, even if it deeply modifies the pricing.

Pricing and Lot Sizing for Seasonal Products in Price Sensitive Environment

Some seasonal products have limited sales season, and the demand of such products over the sales season is of increasing-steady-decreasing type. Customers are highly sensitive to the prices of the products. In such situation, adjustment of unit selling price is needed to accelerate inventory depletion rate and for determining order quantity for the sales season. In this paper, we focus on the issue by jointly determining optimal unit selling prices and optimal lot size over the sales season. Unlike the conventional inventory models with pricing strategy, which were restricted to prespecified pricing cycle lengths, that is, fixed number of price changes over the time horizon, we allow the number of price changes to be a decision variable. The mathematical model is developed and existence of optimal solution is verified. A solution procedure is developed to determine optimal prices, optimal number of pricing cycles, and optimal lot size. The model is illustrated by a numerical example. Sensitivity analysis of the model is also carried out.