Problem definition
: A core problem in the area of revenue management is pricing goods in the presence of strategic customers. We study this problem when customers are heterogeneous with respect to ...their initial valuations for the good and their time sensitivities—that is, the customers differ in both their initial valuations and the rates at which their initial valuation decreases with a delay in the purchase.
Academic/practical relevance
: In many settings, especially in fashion and electronic retail, a customer’s valuation for the product is time-sensitive and decreases over time. In these situations, customers are not only different in terms of their initial willingness to pay for these products when they are first introduced to the market, but they are also different in terms of how rapidly they lose interest in these products. We show that when a firm sells products in such settings, it can realize significant benefits by incorporating dynamic pricing, even in the absence of demand uncertainty.
Methodology
: Dynamic mechanism design.
Results
: We characterize the optimal mechanism for selling durable goods when the customers differ in both their initial valuations and the rates at which their initial valuation decreases. We show that delayed allocation and dynamic pricing can be effective screening tools for maximizing firm profit and can also increase social welfare. We also investigate the impact of production and holding costs on the optimal mechanism.
Managerial implications
: Our work shows how firms can exploit scenarios in which their customers have time-sensitive valuations and are forward-looking to achieve a win–win, by both generating additional revenue and improving social welfare.
We study the value of dynamic pricing to maximize revenues in queueing systems with price- and delay-sensitive customers. The system queue length is visible so that upon arrival, customers decide to ...join the system based on the congestion and the price at that time. We analyze this problem in the asymptotic regime of large customer market size and capacity. We find that dynamic pricing performs significantly better than static pricing at mitigating the effect of uncertainty. Asymptotically, the revenue in such systems consists of a positive deterministic component and a negative stochastic component, the latter representing the impact of variability. Static pricing leads to the
n
1/2
-scale effect of variability, i.e., the expected steady-state queue length is
Kn
1/2
for some
K
> 0, where
n
represents the system size. However, dynamic pricing can lower this effect of variability to the
n
1/3
-scale. We further show that a simple policy of using only two prices can achieve most of the benefits of dynamic pricing. We also discuss how our results can apply to other dynamic control problems in queueing systems.
The e-companion is available at
https://doi.org/10.1287/opre.2017.1668
.
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BFBNIB, CEKLJ, IZUM, KILJ, NMLJ, NUK, ODKLJ, PILJ, PNG, SAZU, UL, UM, UPUK
We analyze a service firm that caters to price and delay‐sensitive customers who are differentiated on both their value for the service and the cost of waiting. There is a continuum of customer types ...in our setting and we model each customer's cost of waiting to be linear in the delay incurred with a multiplier that is an increasing linear or sub‐linear function of the customer's value for the service. Using a large system approach, we characterize the firm's revenue maximizing menu of price and delay quotations and the value of customer differentiation. We further characterize the value of offering coarse or few service grades and find that offering two service grades is asymptotically optimal on the typical square‐root scale, relative to the optimal policy.
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BFBNIB, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
4.
The Value of Confession Corona, Carlos; Randhawa, Ramandeep S.
The Accounting review,
05/2018, Volume:
93, Issue:
3
Journal Article
Peer reviewed
Often, firms reveal oversights and bad decisions publicly through their financial reporting (for instance, restating earnings, impairing goodwill, etc.). These "confessions," which usually lead to ...immediate reputation losses, may be attributed to attempts to be perceived as transparent or to attempts to avoid likely litigation costs. In this paper, however, we argue that reputational concerns about perceived ability alone can provide firms with strong enough incentives to confess their mistakes, even in the absence of other non-reputational disciplinary mechanisms. Analyzing the repeated interaction between a firm and an external evaluator who may detect the firm's mistakes, we show that, in equilibrium, a confession places the firm under higher future scrutiny, which is more costly for lower-quality firms. Consequently, in equilibrium, higher-quality firms confess mistakes more often.
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We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the ...model is that the mean arrival rate of work is
random
(in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.
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Problem definition
: We study optimal scheduling of customers in service systems, such as call centers. In such systems, customers typically hang up and abandon the system if their wait for service ...is too long. Such abandonments are detrimental for the system, and so managers typically use scheduling as a tool to mitigate it. In this paper, we study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes.
Academic/practical relevance
: Call centers constitute a large industry that has a global spending of around $300 billion and employs more than 15 million people worldwide. Our work focuses on improving call center operations, which can reduce costs and improve customer satisfaction. Mathematically, customer patience is typically modeled as exponentially distributed for tractability. Our work makes inroads into relaxing this restrictive assumption to allow modeling more realistic call center situations.
Methodology
: We use heavy traffic–motivated asymptotic queueing machinery that provides us the traction to successfully capture and incorporate the customer impatience distribution into the scheduling problem. In our approach, the scheduling problem reduces to a diffusion control problem, which we solve to propose near-optimal scheduling policies.
Results
: We propose near-optimal scheduling policies that can be implemented by call centers to improve their quality-of-service metrics. One of our main results is that, for a class of parameters, we establish sufficient conditions for both the optimality and nonoptimality of threshold policies.
Managerial implications
: Threshold policies are widely used for scheduling. Our work provides additional insight into whether these may be suboptimal. Our work provides an easy-to-implement alternative that can reduce customer abandonments considerably; for instance, our numerical results indicate that for a system with two customer types, the abandonment rate of one class can be lowered by 30% by using our policy relative to the best threshold policy.
The online appendix is available at
https://doi.org/10.1287/msom.2017.0642
.
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CEKLJ, IZUM, KILJ, NUK, PILJ, SAZU, UL, UM, UPUK
We consider a setting in which consumers experience distinct instances of need for a durable product at random intervals. Each instance of need is associated with a random utility and the consumers ...are differentiated according to the frequency with which they experience such instances of need. We use our model of consumer utility to characterize the firm's optimal strategy of whether to sell, rent, or do a combination of both in terms of the transaction costs and consumers' usage characteristics. We find that the two modes of operation serve different roles in allowing the firm to price discriminate. While sales allow the firm to discriminate among consumers of different usage frequencies, rentals allow it to discriminate according to consumers' realized valuations. Consequently, even when transaction costs are negligible, it is often optimal for the firm to simultaneously rent and sell its product. In addition, we find that although sales and rentals are substitutes and that the offering of sales weakly increases rental prices, it is possible that the introduction of rentals to a pure selling operation can either increase or decrease the optimal sales prices.
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In complex systems, it is quite common to resort to approximations when optimizing system performance. These approximations typically involve selecting a particular system parameter and then studying ...the performance of the system as this parameter grows without bound. In such an asymptotic regime, we prove that if the approximation to the objective function is accurate up to O(1), then under some regularity conditions, the prescriptions that are derived from this approximation are o(1)-optimal, i.e., their optimality gap is asymptotically zero. A consequence of this result is that the well-known square-root staffing rules for capacity sizing in M / M / s and M/M/s+M queues to minimize the sum of linear expected steady-state customer waiting costs and linear capacity costs are o(1)-optimal. We also discuss extensions of this result for the case of nonlinear customer waiting costs in these systems.
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CEKLJ, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We consider queueing systems in which customers arrive according to a Poisson process and have exponentially distributed service requirements. The customers are impatient and may abandon the system ...while waiting for service after a generally distributed amount of time. The system incurs customer-related costs that consist of waiting and abandonment penalty costs. We study capacity sizing in such systems to minimize the sum of the long-term average customer-related costs and capacity costs. We use fluid models to derive prescriptions that are asymptotically optimal for large customer arrival rates. Although these prescriptions are easy to characterize, they depend intricately upon the distribution of the customers' time to abandon and may prescribe operating in a regime with offered load (the ratio of the arrival rate to the capacity) greater than 1. In such cases, we demonstrate that the fluid prescription is optimal up to
O
(1). That is, as the customer arrival rate increases, the optimality gap of the prescription remains bounded.
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BFBNIB, CEKLJ, IZUM, KILJ, NMLJ, NUK, ODKLJ, PILJ, PNG, SAZU, UL, UM, UPUK
We consider revenue optimization in an
M
/
M
/1 queue with price and delay sensitive customers, and we study the performance of demand-independent pricing that does not require any arrival rate ...information. We formally characterize the optimal demand-independent price and its performance relative to pricing with precise arrival rate knowledge. We find that demand-independent pricing can perform remarkably well and its performance improves as customers become more delay sensitive. In particular, for uniformly distributed customer valuations, under a large set of parameters, we find that demand-independent prices can capture more than 99% of the optimal revenue. We also study social optimization and find that demand-independent pricing can perform quite well; however, the performance is better under revenue optimization.
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