ERN: Statistical Decision Theory; Operations Research (Topic)最新文献

{"title":"Queueing systems with rationally inattentive customers","authors":"Caner Canyakmaz, Tamer Boyacı","doi":"10.2139/ssrn.3254813","DOIUrl":"https://doi.org/10.2139/ssrn.3254813","url":null,"abstract":"Problem definition: Classical models of queueing systems with rational and strategic customers assume queues to be either fully visible or invisible, while service parameters are known with certainty. In practice, however, people only have “partial information” on the service environment, in the sense that they are not able to fully discern prevalent uncertainties. This is because assessing possible delays and rewards is costly, as it requires time, attention, and cognitive capacity, which are all limited. On the other hand, people are also adaptive and endogenously respond to information frictions. Methodology: We develop an equilibrium model for a single-server queueing system with customers having limited attention. Following the theory of rational inattention, we assume that customers optimize their learning strategies by deciding the type and amount of information to acquire and act accordingly while internalizing the associated costs. Results: We establish the existence and uniqueness of a customer equilibrium when customers allocate their attention to learn uncertain queue lengths and delineate the impact of service characteristics. We provide a complete spectrum of the impact of information costs on throughput and show numerically that throughput might be nonmonotone. This is also reflected in social welfare if the firm’s profit margin is high enough, although customer welfare always suffers from information costs. Managerial implications: We identify service settings where service firms and social planners should be most cautious for customers’ limited attention and translate our results to advisable strategies for information provision and service design. For example, we recommend firms to avoid partial hindrance of queue-length information when a low-demand service is not highly valued by customers. For a popular service that customers value reasonably highly, however, partial hindrance of information is particularly advisable. Academic/practical relevance: We propose a microfounded framework for strategic customer behavior in queues that links beliefs, rewards, and information costs. It offers a holistic perspective on the impact of information prevalence (and information frictions) on operational performance and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123462587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Product Decoys: A Supply Chain Perspective","authors":"Quan Zheng, X. Pan, A. Vakharia","doi":"10.1111/POMS.13391","DOIUrl":"https://doi.org/10.1111/POMS.13391","url":null,"abstract":"Conventional wisdom suggests that by including a decoy product in the choice set for consumers, a firm can drive consumers to select more profitable non-decoy products. Explanations offered to explain such outcomes are rooted in the psychology of consumer behavior. A scan of retail practice, however, indicates that decoys might also be included in a product assortment for economic reasons. For example, products with very low sales potential are often included in offerings by bricks-and-mortar and online retailers. This leads us to investigate and offer an alternative supply side explanation for the presence of decoy products in a supply chain. \u0000 \u0000More specifically, we show that in a distribution channel with multiple asymmetric manufacturers and a single retailer, there exists the possibility of an equilibrium which includes a decoy product. Such an equilibrium is characterized by the retailer stocking positive quantities of products from a subset of low-cost manufacturers (active manufacturers) and negligible or even zero stock of a decoy product sourced from a higher-cost manufacturer. The retailer includes a decoy product in the assortment since it helps to obtain better contractual terms from the active manufacturers. Recognizing this, upstream active manufacturers not only compete for market share but are induced to cooperate (in setting wholesale prices) so as to ensure that the manufacturer of the decoy product is driven out of the market. We also find that the degree of product substitutability moderates which manufacturer's product is a decoy. Our findings provide theoretical support for industry practice as well as implications for retail assortment decisions.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134339416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Retirement Under Partial Information","authors":"Kexin Chen, Junkee Jeon, H. Y. Wong","doi":"10.2139/ssrn.3683553","DOIUrl":"https://doi.org/10.2139/ssrn.3683553","url":null,"abstract":"The optimal retirement decision is an optimal stopping problem when retirement is irreversible. We investigate the optimal consumption, investment, and retirement decisions when the mean return of a risky asset is unobservable and is estimated by filtering from historical prices. To ensure nonnegativity of the consumption rate and the borrowing constraints on the wealth process of the representative agent, we conduct our analysis using a duality approach. We link the dual problem to American option pricing with stochastic volatility and prove that the duality gap is closed. We then apply our theory to a hidden Markov model for regime-switching mean return with Bayesian learning. We fully characterize the existence and uniqueness of variational inequality in the dual optimal stopping problem, as well as the free boundary of the problem. An asymptotic closed-form solution is derived for optimal retirement timing by small-scale perturbation. We discuss the potential applications of the results to other partial-information settings.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130425354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Intertemporal Content Variation with Customer Learning","authors":"Fernando Bernstein, Soudipta Chakraborty, R. Swinney","doi":"10.2139/ssrn.3489425","DOIUrl":"https://doi.org/10.2139/ssrn.3489425","url":null,"abstract":"Problem definition: We analyze a firm that sells repeatedly to a customer population over multiple periods. Although this setting has been studied extensively in the context of dynamic pricing—selling the same product in each period at a varying price—we consider intertemporal content variation, wherein the price is the same in every period, but the firm varies the content available over time. Customers learn their utility on purchasing and decide whether to purchase again in subsequent periods. The firm faces a budget for the total amount of content available during a finite planning horizon, and allocates content to maximize revenue. Academic/practical relevance: A number of new business models, including video streaming services and curated subscription boxes, face the situation we model. Our results show how such firms can use content variation to increase their revenues. Methodology: We employ an analytical model in which customers decide to purchase in multiple successive periods and a firm determines a content allocation policy to maximize revenue. Results: Using a lower bound approximation to the problem for a horizon of general length T, we show that, although the optimal allocation policy is not, in general, constant over time, it is monotone: content value increases over time if customer heterogeneity is low and decreases otherwise. We demonstrate that the optimal policy for this lower bound problem is either optimal or very close to optimal for the general T period problem. Furthermore, for the case of T = 2 periods, we show how two critical factors—the fraction of “new” versus “repeat” customers in the population and the size of the content budget—affect the optimal allocation policy and the importance of varying content value over time. Managerial implications: We show how firms that sell at a fixed price over multiple periods can vary content value over time to increase revenues.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"2020 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132540912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Eliciting Human Judgment for Prediction Algorithms","authors":"Rouba Ibrahim, Song-Hee Kim, Jordan D. Tong","doi":"10.2139/ssrn.3606633","DOIUrl":"https://doi.org/10.2139/ssrn.3606633","url":null,"abstract":"Even when human point forecasts are less accurate than data-based algorithm predictions, they can still help boost performance by being used as algorithm inputs. Assuming one uses human judgment indirectly in this manner, we propose changing the elicitation question from the traditional direct forecast (DF) to what we call the private information adjustment (PIA): how much the human thinks the algorithm should adjust its forecast to account for information the human has that is unused by the algorithm. Using stylized models with and without random error, we theoretically prove that human random error makes eliciting the PIA lead to more accurate predictions than eliciting the DF. However, this DF-PIA gap does not exist for perfectly consistent forecasters. The DF-PIA gap is increasing in the random error that people make while incorporating public information (data that the algorithm uses) but is decreasing in the random error that people make while incorporating private information (data that only the human can use). In controlled experiments with students and Amazon Mechanical Turk workers, we find support for these hypotheses. This paper was accepted by Charles Corbett, operations management.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129828106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient Simulation of Stochastic Differential Equations Based on Markov Chain Approximations With Applications","authors":"Zhenyu Cui, J. Kirkby, D. Nguyen","doi":"10.2139/ssrn.3665661","DOIUrl":"https://doi.org/10.2139/ssrn.3665661","url":null,"abstract":"We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local volatility (SLV) models arising in finance, which includes the Heston and the stochastic alpha beta rho (SABR) models as special cases. \u0000 \u0000Our simulation algorithm is constructed based on approximating the latent stochastic variance process by a CTMC. Compared with time-discretization schemes, our method exhibits several advantages, including flexible boundary condition treatment, weak continuity conditions imposed on coefficients, and a second order convergence rate in the spatial grids of the approximating CTMC under suitable regularity conditions. Replacing the stochastic variance process with a discrete-state approximation greatly simplifies the direct sampling of the integrated variance, thus enabling a highly efficient simulation scheme. \u0000 \u0000Extensive numerical examples illustrate the accuracy and efficiency of our estimator, which outperforms textit{both biased and unbiased} simulation estimators in the literature in terms of root mean squared error (RMSE) and computational time. This paper is focused primarily on the simulation of SDEs which arise in finance, but this new simulation approach has potential for applications in other contextual areas in operations research, such as queuing theory. Note: this is an earlier version of the work \"Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models based on Markov Chain Approximations\".","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127403683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Economic Order Quantity (EOQ) – An Extension","authors":"S. Senthilnathan","doi":"10.2139/ssrn.3665757","DOIUrl":"https://doi.org/10.2139/ssrn.3665757","url":null,"abstract":"The aim of this paper is to illustrate the determination of the Economic Order Quantity (EOQ) or Economic Number of Orders (ENO) when the Total Ordering Cost (TOC) and Total Handling Cost (THC) are not equally the same. For this purpose, two assumptions of the basic EOQ model - (a) the constant unit handling cost, and (b) the constant per order cost - are relaxed; and instead, their varying conditions are considered. Hence, this paper presents two exhibits to make the readers understand the EOQ at the condition where the Total Handling Cost is not equal to the Total Ordering Cost (THC ≠ TOC). Accordingly, Exhibit 1 relaxes the assumption of 'constant per order cost' and considers the concepts of fixed cost and variable cost for placing an order. Also, Exhibit 2 relaxes the assumption of 'constant unit handling cost' and illustrates with the varying handling cost per unit for the ordering quantity (Q) in an order. These exhibits support the situations where the EOQ (or ENO) can be determined at the condition where THC ≠ TOC. Notably, for both exhibits, appropriate tables and figures are also presented for the readers’ convenience to understand the presentation of the paper.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125357635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Column-Randomized Linear Programs: Performance Guarantees and Applications","authors":"Yi-Chun Chen, V. Mišić","doi":"10.2139/ssrn.3656704","DOIUrl":"https://doi.org/10.2139/ssrn.3656704","url":null,"abstract":"We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by column generation, which is often still computationally challenging due to the intractability of the subproblem in many applications. Instead of iteratively introducing one column at a time as in column generation, our proposed method involves sampling a collection of columns according to a user-specified randomization scheme and solving the linear program consisting of the sampled columns. While similar methods for solving large-scale linear programs by sampling columns (or, equivalently, sampling constraints in the dual) have been proposed in the literature, in this paper we derive an upper bound on the optimality gap that holds with high probability and converges with rate $1/sqrt{K}$, where $K$ is the number of sampled columns, to the value of a linear program related to the sampling distribution. To the best of our knowledge, this is the first paper addressing the convergence of the optimality gap for sampling columns/constraints in generic linear programs without additional assumptions on the problem structure and sampling distribution. We further apply the proposed method to various applications, such as linear programs with totally unimodular constraints, Markov decision processes, covering problems and packing problems, and derive problem-specific performance guarantees. We also generalize the method to the case that the sampled columns may not be statistically independent. Finally, we numerically demonstrate the effectiveness of the proposed method in the cutting-stock problem and in nonparametric choice model estimation.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132995355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of a Dummy Guided Formulation and Exact Solution Method for TSP","authors":"E. Munapo","doi":"10.15587/1729-4061.2020.203865","DOIUrl":"https://doi.org/10.15587/1729-4061.2020.203865","url":null,"abstract":"A traveling salesman problem (TSP) is a problem whereby the salesman starts from an origin node and returns to it in such a way that every node in the network of nodes is visited once and that the total distance travelled is minimized. An efficient algorithm for the TSP is believed not to exist. The TSP is classified as NP-hard and coming up with an efficient solution for it will imply NP = P . The paper presents a dummy guided formulation for the traveling salesman problem. To do this, all sub-tours in a traveling salesman problem (TSP) network are eliminated using the minimum number of constraints possible. Since a minimum of three nodes are required to form a sub-tour, the TSP network is partitioned by means of vertical and horizontal lines in such a way that there are no more than three nodes between either the vertical lines or horizontal lines. In this paper, a set of all nodes between any pair of vertical lines or horizontal lines is called a block. Dummy nodes are used to connect one block to the next one. The reconstructed TSP is then used to formulate the TSP as an integer linear programming problem (ILP). With branching related algorithms, there is no guarantee that numbers of sub-problems will not explode to unmanageable levels. Heuristics or approximating algorithms that are sometimes used to make quick decisions for practical TSP models have serious economic challenges. The difference between the exact solution and the approximated one in terms of money is very big for practical problems such as delivering household letters using a single vehicle in Beijing, Tokyo, Washington, etc. The TSP model has many industrial applications such as drilling of printed circuit boards (PCBs), overhauling of gas turbine engines, X-Ray crystallography, computer wiring, order-picking problem in warehouses, vehicle routing, mask plotting in PCB production, etc.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126912484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Variance Learning Curve","authors":"Hessam Bavafa, J. Jónasson","doi":"10.2139/ssrn.3635676","DOIUrl":"https://doi.org/10.2139/ssrn.3635676","url":null,"abstract":"The expansive learning curve literature in operations management has established how various facets of prior experience improve average performance. In this paper, we explore how increased cumulative experience affects performance variability or consistency. We use a two-stage estimation method of a heteroskedastic learning curve model to examine the relationship between experience and performance variability among paramedics at the London Ambulance Service. We find that, for paramedics with lower experience, an increase in experience of 500 jobs reduces the variance of task completion time by 8.7%, in addition to improving average completion times by 2.7%. Similar to prior results on the average learning curve, we find a diminishing impact of additional experience on the variance learning curve. We provide an evidence base for how to model the learning benefits of cumulative experience on performance in service systems. Our findings imply that the benefits of learning are substantially underestimated if the consistency effect is ignored. Specifically, our estimates indicate that queue lengths (or wait times) might be overestimated by as much as 4% by ignoring the impact of the variance learning curve in service systems. Furthermore, our results suggest that previously established drivers of productivity should be revisited to examine how they affect consistency, in addition to average performance. This paper was accepted by Charles Corbett, operations management.","PeriodicalId":200007,"journal":{"name":"ERN: Statistical Decision Theory; Operations Research (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127733928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}