Discrete Demand Research Articles

Corporate Social Responsibility and Consumer Choice: Lessons from the Milk Boycott

We study the impact of a boycott on one of the largest Korean dairy producers, triggered by the exposure of the firm’s unethical management practices, on sales of its own and others. We find empirical evidence that the boycott had substantial and long-lasting consequences. First, consumer utility from the boycotted products decreased significantly, reflecting consumers’ strong willingness to take part in collective action. Second, our discrete choice demand model, which addresses both price endogeneity and product substitution, estimates that sales of the boycotted firm decreased by almost 8% or, equivalently, by 8.1 million liters during the 12-month postboycott period. Third, the boycotted firm’s sales and revenue decreases would have been more severe had the firm not cut prices after the boycott outbreak. Our findings emphasize top-level managers’ role in fostering an ethical organizational culture within the firm and taking proper and timely countermeasures to curb losses incurred by a boycott. This paper was accepted by Eric Anderson, marketing. Funding: This work was supported by the Asian Studies Center of Michigan State University [Dr. Delia Koo Faculty Endowment Award] and Sogang University [New Faculty Research Funding Grant 202310031.01]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01062 .

A choice-based approach to dynamic capacitated multi-item lot sizing with demand uncertainty

With the purpose of planning and implementing pricing decisions on a tactical level as well as production decisions on an operational level, we consider – in an integrated form – the capacitated multi-item lot sizing problem with uncertain item demands and price-dependent discrete choice demand. The model is embedded into an overarching rolling horizon procedure allowing for adaptations to changes in demand and cost parameters. We first formulate the static problem version as a nonlinear mathematical program with underlying multinomial logit demand and subsequently linearize it to make it viable for mathematical programming solvers. Uncertainty of demands is taken into account by Monte Carlo simulation. More specifically, we generate random demand scenarios and utilize them as input data for the sample average approximation problem version. We further endow the problem setting with possibilities to incorporate pricing policy requirements such as restricting the number of price adaptations or defining periods without price adaptations. Overall, the developed approach yields a powerful tool for balancing item demands via pricing in a way favorable for adhering to available production capacities and thereby striking a balance between revenues and costs. Computational results confirm that adapting prices to time-dependent demand and cost parameters is exploited effectively to maintain a deliberately controlled production environment. Moreover, the integrated pricing and production setting allows to study the effect of pricing policy restrictions and demand uncertainties upon attainable profits.

Newsvendor problem with discrete demand and constrained first moment under ambiguity

Newsvendor problem with discrete demand and constrained first moment under ambiguity

Data‐driven inventory control involving fixed setup costs and discrete censored demand

AbstractWe investigate a data‐driven dynamic inventory control problem involving fixed setup costs and lost sales. Random demand arrivals stem from a demand distribution that is only known to come out of a vast ambiguity set. Lost sales and demand ambiguity would together complicate the problem through censoring, namely, the inability of the firm to observe the lost portion of the demand data. Our main policy idea advocates periodically ordering up to high levels for learning purposes and, in intervening periods, cleverly exploiting the information gained in learning periods. By regret, we mean the price paid for ambiguity in long‐run average performances. When demand has a finite support, we can accomplish a regret bound in the order of which almost matches a known lower bound as long as inventory costs are genuinely convex. Major policy adjustments are warranted for the more complex case involving an unbounded demand support. The resulting regret could range between and depending on the nature of moment‐related bounds that help characterize the degree of ambiguity. These are improvable to when distributions are light‐tailed. Our simulation demonstrates the merits of various policy ideas.

Mandatory nutrition attributes labeling and consumer demand: a structural approach analysis of the US soft drink market

While soft drinks stand out as a major cause of obesity and overweight worldwide, the USA is the country most concerned with this problem. To reverse the situation, experts have agreed that labels and taxes represent promising policy tools. Focusing on the soda market, this paper investigates how consumer demand for nutrient contents responds to the US revised nutrition facts label policy implemented in 2020. Relying on retail scanner data, the study finds after estimation of a discrete choice logit demand model that the change in nutrition labels caused consumers to modify their purchasing behavior. However, they did not systematically switch from unhealthy beverages to healthy ones. The analysis finds evidence that the label revision policy was mostly impactful in decreasing consumers’ preference for soda with superhigh calories and high sugar content. Surprisingly, the joint effect of label and tax did not decrease the sampled consumers’ preference for unhealthy nutrient contents. They still preferred buying soft drinks superhigh in calorie content inside US cities with a tax on sugar-sweetened beverages (SSB), despite the revision of the facts label. Finally, the new nutrition label has improved the average surplus of consumers and total welfare. However, the gain is lower within the cities implementing the sugar tax.

The newsvendor problem with GHG emissions from waste disposal under cap-and-trade regulation

We study a newsvendor problem with greenhouse gas (GHG) emissions at the disposal stage regulated by a cap-and-trade policy. We first consider a synchronous version of the problem where the replenishment period and the emission assessment period are the same. For this problem, we propose simple algorithms to derive the optimal quantity and cost for both continuous and discrete demand distributions. We show that ignoring the carbon tax may lead to large overcost, especially when the GHG quota is small. For a normally distributed demand, we also show that the demand standard deviation has a non-linear and non-monotonic effect on the order quantity. We then investigate an asynchronous version of the problem where replenishment decisions occur at a higher frequency than the quota allocation. We formulate this lot sizing problem as a Markov decision process and solve it with a dynamic programming algorithm whose complexity is assessed. Through a numerical experimentation and theoretical results, we demonstrate how and when the flexibility of the optimal dynamic replenishment decisions allows to reduce costs. When approaching the end of the time horizon, the uncertainty reduction allows the decision maker to adopt a riskier policy and order larger quantities.

Nationwide Demand Modeling for an Urban Air Mobility Commuting Mission

In this paper, we present a comprehensive and reproducible urban air mobility (UAM) demand model centered around publicly available data and open source tools capable of demand estimation at the national level. A discrete mode-choice demand model is developed using longitudinal origin–destination employment statistics flow data, American community survey economic data, and the Open Source Routing Machine (OSRM) to identify the utility of a UAM commuter service relative to other modes of transportation. Using the implemented model, we identify New York City, San Francisco, and Los Angeles as cities with the highest potential commuter demand, and Seattle as the city most resilient to increases in delay time. A sensitivity study of demand is performed and shows that strong demand exists for short trips with low total delay times and for longer trips with a low ticket price per kilometer, with the former showing resilience to increases in operational costs and the latter showing resilience to increases in delays. The demand model is supported by a speed-flow model, which fuses highway performance monitoring system data with OpenStreetMap data to provide traffic-adjusted road segment speeds to OSRM. The speed-flow model has the capability of providing congestion data for road segments across the United States without the use of commercial data sets or routing services and is shown to improve routing duration accuracy in congested regions.

Getting off track: Cortical feedback processing network modulated by continuous error signal during target-feedback mismatch

Performance monitoring and feedback processing – especially in the wake of erroneous outcomes – represent a crucial aspect of everyday life, allowing us to deal with imminent threats in the short term but also promoting necessary behavioral adjustments in the long term to avoid future conflicts. Over the last thirty years, research extensively analyzed the neural correlates of processing discrete error stimuli, unveiling the error-related negativity (ERN) and error positivity (Pe) as two main components of the cognitive response. However, the connection between the ERN/Pe and distinct stages of error processing, ranging from action monitoring to subsequent corrective behavior, remains ambiguous. Furthermore, mundane actions such as steering a vehicle already transgress the scope of discrete erroneous events and demand fine-tuned feedback control, and thus, the processing of continuous error signals – a topic scarcely researched at present. We analyzed two electroencephalography datasets to investigate the processing of continuous erroneous signals during a target tracking task, employing feedback in various levels and modalities. We observed significant differences between correct (slightly delayed) and erroneous feedback conditions in the larger one of the two datasets that we analyzed, both in sensor and source space. Furthermore, we found strong error-induced modulations that appeared consistent across datasets and error conditions, indicating a clear order of engagement of specific brain regions that correspond to individual components of error processing.

A Random Coefficients Model of Seafood Demand: Implications for Consumer Preferences and Substitution Patterns

Discrete choice models of demand are growing in popularity for understanding markets for seafood, but have thus far been limited to applications using individual-level choice data. The random coefficients logit model is a discrete choice demand model designed for aggregate sales data and imparts a number of theoretical and empirical advantages. Instrumental variables account for price endogeneity, which can arise when there are unobserved product characteristics. Furthermore, correlated preferences can be accommodated in the random coefficients as well as through demographic interactions, which is especially important for seafood where product characteristics are primarily qualitative. We estimate this model for salmon fillets using four years of county-level seafood sales in California, and demonstrate the insights that can be drawn regarding consumer preferences and substitution patterns. Although the model is computationally burdensome, it offers considerable potential for further seafood demand analysis.

Cycling for Education? Heterogeneous Preferences for Academic Tracks at Secondary School

Using a unique data set from the Netherlands, I estimate a discrete choice demand model under congestion effects to recover preferences for secondary school tracks between parents with different socioeconomic status (SES) but equally proficient children. I find that highly educated parents are willing to let their offspring commute longer distances to attend tracks that grant direct admission to university. Valuation heterogeneity for such options explains more than half of the observed enrollment gap between students from different SES divides. These results suggest that low-SES children sort into academic tracks with lower economic prospects, even in schooling systems with negligible choice restrictions.

Dynamic Scheduling and Optimization of AGV in Factory Logistics Systems Based on Digital Twin

At present, discrete workshops demand higher transportation efficiency, but the traditional scheduling strategy of the logistics systems can no longer meet the requirements. In a transportation system with multiple automated guided vehicles (multi-AGVs), AGV path conflicts directly affect the efficiency and coordination of the whole system. At the same time, the uncertainty of the number and speed of AGVs will lead to excessive cost. To solve these problems, an AGVs Multi-Objective Dynamic Scheduling (AMODS) method is proposed which is based on the digital twin of the workshop. The digital twin of the workshop is built in the virtual space, and a two-way exchange and real-time control framework based on dynamic data is established. The digital twin system is adopted to exchange data in real time, create a real-time updated dynamic task list, determine the number of AGVs and the speed of AGVs under different working conditions, and effectively improve the efficiency of the logistics system. Compared with the traditional scheduling strategy, this paper is of practical significance for the scheduling of the discrete workshop logistics systems to improve the production efficiency, utilization rate of resources, and dynamic response capability.

Pricing-inventory model with discrete demand and delivery orders

This paper aims to develop an inventory model considering discrete demand, coordinated pricing, and multiple delivery policy in a single-buyer single-supplier production-inventory system. The shortage is not allowed and the planning horizon is considered to be infinite. The main objective of the framework is to equip the decision-maker with optimal order, pricing, and shipment quantities to maximize the total profit of the system. The results obtained from the numerical example reveal that the proposed approach with an average selling price equal to about 94% of the classical model, has resulted in an average profit increase of about 16% and an average order increase of about 34% compared to the classical approach

An exact algorithm for the static pricing problem under discrete mixed logit demand

Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that includes customer specific variables and parameters in the utility specification, our pricing problem reflects well the discrete choice models used in practice. To solve this pricing problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a “good” feasible solution and approximate the problem from below. A convex optimization problem is designed using a convexification technique to approximate the optimization problem from above. Then, using a branching method, we tighten the optimality gap. The effectiveness of our algorithm is illustrated on several cases, and compared against solvers and existing state-of-the-art methods in the literature.

A Dantzig-Wolfe decomposition-based algorithm for capacitated passenger assignment problem with time-varying demand in high-speed railway networks

This paper proposes an algorithm for solving the schedule-based passenger assignment problem, with explicit consideration of continuous time-varying demand and tight capacity constraints for large-scale high-speed railway (HSR) networks. We construct the space–time travel network and formulate the assignment model by destination-based arc flow variables, then design a Dantzig-Wolfe (D-W) decomposition-based algorithm to solve the large-scale model of this problem with less memory requirement and computational complexity. The sub-problem in each iteration can be solved as a single-source (destination) minimum cost flow problem without capacity constraint by the “rooftops” method, which provides an effective technique to tackle both continuous and discrete time-varying demand in the assignment problem. It is further demonstrated that the assignment solutions for discrete time-varying demand can converge to that for continuous time-varying demand with the increase of demand discretization number. Three real case studies with different HSR network scales show that the proposed algorithm is efficient in memory and computational complexity, especially when highly accurate solutions for passenger assignment on large-scale HSR networks are needed.

Economic Order Quantity with Discrete Demand and Delivery Orders

کاهش هزینه‏‌های مرتبط با موجودی از مهم‌ترین استراتژی‌‏های هر بنگاه اقتصادی برای بقا و سوددهی در شرایط رقابتی امروزی است. در این راستا مدل‏‌های موجودی کلاسیک برای کاهش این هزینه‏‌ها مطرح شده‌اند؛ اما مدل‏‌های کلاسیک در کنار مزایای فراوان دارای فرضیه‌های محدودکننده‌ای هستند. در این پژوهش، یک زنجیره سه­‌سطحی لجستیکی شامل یک تولیدکننده، یک توزیع‌‏کننده و یک خرده‏‌فروش در نظر گرفته می‏‌شود و مسئله بهینه‌سازی مدل موجودی برای توزیع‌کننده موردبررسی قرار می‏‌گیرد. در مسئله موردنظر، توزیع‏‌کننده محصولات موردنیاز خود را از تولیدکننده درخواست می‌کند؛ اما به علت عدم‌­امکان ارسال محصولات درخواستی هر دوره به‌صورت یکجا، تولیدکننده محصولات را به‌صورت گسسته در چند مرحله ارسال می‌کند؛ به‌عبارت‌دیگر از استراتژی دریافت چندگانه استفاده می‌شود؛ همچنین تقاضای خرده‌‏فروش گسسته بوده و برابر مقدار ثابتی در فاصله‏‌های زمانی برابر است. در چنین حالتی، توزیع‌کننده در نظر دارد مقدار بهینه هر بار سفارش و مقدار بهینه ارسالی هر مرحله تولیدکننده را به‌گونه‌ای تعیین کند که هزینه‌های سیستم حداقل شود. درنهایت با بیان یک مثال عددی مسئله پیشنهادی بررسی و تحلیل شده و نتایج با مدل کلاسیک موجودی مقایسه می‌شود. نتایج نشان می­‌دهد با افزایش هزینه‌های نگهداری و سفارش­‌دهی، مدل پیشنهادی دارای کارایی بهتری است.

A sequential choice model for multiple discrete demand

A sequential choice model for multiple discrete demand

Dynamic Inventory Control with Fixed Setup Costs and Unknown Discrete Demand Distribution

When a new product has just been introduced or the economy has just entered a new phase, a firm is often at a loss as to what the underlying demand pattern has become let alone how best to respond to it. In “Dynamic Inventory Control with Fixed Setup Costs and Unknown Discrete Demand Distribution,” Davoodi, Katehakis, and Yang faced off this challenging problem by tailoring ordering decisions to empirical distributions formed out of past demand observations. In the presence of fixed setup costs, however, an (s,S) policy optimal in the conventional known-distribution setting would take many periods for its long-term benefit to be realized. Therefore, a good online policy has to balance between letting ordering decisions settle for long periods and adjusting them frequently to take advantage of newly available information. When properly balanced, such policies could indeed achieve tight bounds for the performance measure of regret.

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context.

In the continuous review reorder point, base-stock (s, S) policy, the replenishment order is launched when the inventory position reaches the reorder point, s. It is commonly assumed that the inventory position is exactly equal to the reorder point at the moment the order is launched, when actually it could be lower at that moment. This implies neglecting the possible undershoots at the reorder point, which has a direct impact on the calculation of the expected shortages per replenishment cycle. This article presents a method for an exact calculation of the fill rate (fraction of demand that is immediately satisfied from shelf) which takes explicit account of the existence of undershoots and is applicable to any discrete demand distribution function in a context of lost sales. This method is based on the determination of the stock probability vector at the moment the replenishment order is launched. Furthermore, neglecting the undershoots is shown to lead to an overestimation of the fill rate, particularly when we move farther away from the unitary demand assumption. From a practical point of view, this behaviour involves underestimating the base-stock level, S, when a target fill rate is set for its determination. The method proposed in this paper overcomes these shortcomings.

Identification and Estimation of Discrete Choice Demand Models When Observed and Unobserved Characteristics are Correlated

Identification and Estimation of Discrete Choice Demand Models When Observed and Unobserved Characteristics are Correlated

Bertrand competition under asymmetric conditions

Abstract Analyzing price competition through game theory is one of the most important frameworks of oligopoly theory, especially in industrial organizations. Numerous studies have been conducted in this direction, as companies are forced to adjust their sustainable pricing policy to operate in the long term. Thus, the players make a regular adjustment of the pricing strategy. Of all the models developed based on Bertrand’s reference model (1883), the most analyzed were those in which informational symmetry predominated. Since informational symmetry presents only a theoretical framework, economists have turned their attention to information asymmetry. This type of information best describes a complex economic game, as it creates an information gap between players and generates opportunities in the decision-making process. Thus, asymmetric information is the main parameter of the decision-making process that determines decision makers to resort to different decision strategies than those assumed by the analytical model. Any asymmetric Bertrand model predicts competitive and efficient market outcomes, a direct relationship between a firm’s conduct, market structure and finally market performance. This paper undertakes an analysis of the Bertrand model in the case of demand and asymmetric costs. We determine the Bertrand-Nash equilibrium under the scenario in which close, but not perfect substitutes exist for the differentiated product with hypothetical data. Then we highlight what happens with profits when we consider that discrete cross marginal demand gradually increases. For more research, there are numerous studies based on sequential games, Bayesian games and signaling games both in discrete time and in continuous time.