OPER: Analytical (Topic)最新文献

{"title":"Stochastic and Strategy-Proof Auctions for Statistical Inferences","authors":"Yoji Tomita","doi":"10.2139/ssrn.3711187","DOIUrl":"https://doi.org/10.2139/ssrn.3711187","url":null,"abstract":"We study a stochastic auction in a multi-items and unit-demand setting where bidders have one-dimensional type spaces. In a usual Pareto-efficient auction such as the VCG auction, items are allocated deterministically to bidders depending on their bids. However, even if an auctioneer implements a deterministic auction repeatedly, data that the auctioneer and bidders can get from the auction would be limited because the bidder with the highest bid gets the best item, the bidder with second highest bid gets the second best item, and so on surely. Then, for example, the auctioneer cannot infer what happens if the best item was allocated to the other bidder. We consider a stochastic auction which allocates items stochastically to bidders according to their bids in order to get rich data. We introduce a stochastic auction rule that is strategy-proof and individual rational. Moreover, we show that our stochastic auction can be used to get rich data, and yields relatively high revenue compared to the VCG auction in a computer experiment.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"226 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132408938","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 Impact of Committing to Customer Orders in Online Retail","authors":"G. Figueira, W. Jaarsveld, P. Amorim, J. Fransoo","doi":"10.2139/ssrn.3641875","DOIUrl":"https://doi.org/10.2139/ssrn.3641875","url":null,"abstract":"Problem definition: Online retailers are on a consistent drive to increase on-time delivery and reduce customer lead time. However, in reality, an increasing share of consumers places orders early. Academic/practical relevance: Such advance demand information can be deployed strategically to reduce costs and improve the customer service experience. This requires inventory and allocation policies that make optimal use of this information and that induce consumers to place their orders early. An increasing number of online retailers not only offer customers a choice of lead time but also, actively back-order missing items from a consumer basket. Methodology: We develop new allocation policies that commit to a customer order upon arrival of the order rather than at the moment the order is due. We provide analytical results for the performance of these allocation policies and evaluate their behavior with real data from a large food retailer. Results: Our policy leads to a higher fill rate at the expense of a slight increase in average delay. The analysis based on real-life data suggests a sizeable impact that should impact current best practices in online retail. Managerial implications: With the changing landscape in online retail, customers increasingly place baskets of orders that they would like to receive at a planned and confirmed moment in time. Especially in grocery, this has grown fast. This fundamentally changes the strategic management of inventory. We demonstrate that online retailers should commit early to customer orders to enhance the customer service experience and eventually, to also create opportunities for reducing the cost of operations.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123740908","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":"A Simple Heuristic Policy for Stochastic Distribution Inventory Systems with Fixed Shipment Costs","authors":"Han Zhu, Frank Y. Chen, Ming Hu, Yi Yang","doi":"10.2139/ssrn.2921743","DOIUrl":"https://doi.org/10.2139/ssrn.2921743","url":null,"abstract":"We study a classic one-warehouse multi-retailer distribution system, in which any inventory replenishment at each location incurs a fixed-plus-variable cost and takes a constant lead time. The optimal policy is unknown and even if it exists, must be extremely complicated. The goal of this paper is to identify an easy-to-compute heuristic policy within the class of modified echelon (r, Q) policies that does not require an integer-ratio property or a synchronized, nested ordering property, yet has certain performance bounds. We first develop a cost upper bound for any given modified echelon (r, Q) policy. Computation of the bound does not require an exact evaluation of the system-wide cost, which is notoriously difficult. We next adopt parameters of the heuristic by minimizing the cost upper bound, which is equivalent to solving a set of independent single-stage (r, Q) systems. With a cost lower bound that has been established in the literature, we then develop easy-to-compute performance bounds for the heuristic policy. Finally, using those bounds, we show that the proposed modified echelon (r, Q) heuristic policy is asymptotically optimal as a pair of system parameters is scaled up, e.g., when the ratios of the fixed cost of the warehouse over those of the retailers become large. Numerical study demonstrates that our proposed heuristic performs well and tends to outperform the echelon-stock (r, nQ) heuristic policy studied in the literature.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114154703","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":"High-Dimensional Dynamic Stochastic Model Representation","authors":"Aryan Eftekhari, S. Scheidegger","doi":"10.2139/ssrn.3603294","DOIUrl":"https://doi.org/10.2139/ssrn.3603294","url":null,"abstract":"We propose a generic and scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within an MPI–TBB parallel time-iteration framework, we approximate economic policy functions using an adaptive, high-dimensional model representation scheme, combined with adaptive sparse grids. With increasing dimensions, the number of points in this efficiently-chosen combination of low-dimensional grids grows much more slowly than standard tensor product grids, sparse grids, or even adaptive sparse grids. Moreover, the adaptivity within the individual component functions adds an additional layer of sparsity, since grid points are added only where they are most needed — that is to say, in regions of the computational domain with steep gradients or at non-differentiabilities. Second, we introduce a performant vectorization scheme of the interpolation compute kernel. Third, we validate our claims with numerical experiments conducted on “Piz Daint\" (Cray XC50) at the Swiss National Super-computing Center. We observe significant speedups over the state-of-the-art techniques, and almost ideal strong scaling up to at least 1, 000 compute nodes. Fourth, to demonstrate the broad applicability of our method, we compute global solutions to two different versions of a dynamic stochastic economic model: a high-dimensional international real business cycle model with capital adjustment costs, and with or without irreversible investment. We solve these models up to 300 continuous state variables globally.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129822231","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":"M-natural-Convexity and its Applications in Operations","authors":"Xin Chen, Menglong Li","doi":"10.2139/ssrn.3431474","DOIUrl":"https://doi.org/10.2139/ssrn.3431474","url":null,"abstract":"M-natural-convexity, one of the main concepts in discrete convex analysis, possesses many salient structural properties and allows for the design of efficient algorithms. In this paper, we establish several new fundamental properties of M-natural-convexity and its variant SSQM- natural-convexity (semistrictly quasi M-natural-convexity). We show that in a parametric maximization model, the optimal solution is nonincreasing in the parameters when the objective function is SSQM- natural-concave and the constraint is a box, and illustrate when SSQM- natural-convexity and M-natural-convexity are preserved. A sufficient and necessary characterization of twice continuously differentiable M- natural-convex function is provided. We then utilize them to analyze two important operations models: a classical multi-product dynamic stochastic inventory model, and a portfolio contract model where a buyer reserves capacities in blocks from multiple competing suppliers. We illustrate that looking from the lens of M-natural-convexity allows to simplify the complicated analysis in the literature for each model and extend the results to more general settings.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121809162","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":"Dynamic Inventory Repositioning in On-Demand Rental Networks","authors":"S. Benjaafar, Daniel R. Jiang, Xiang Li, Xiaobo Li","doi":"10.2139/ssrn.2942921","DOIUrl":"https://doi.org/10.2139/ssrn.2942921","url":null,"abstract":"We consider a rental service with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers can decide on how long to keep a unit and where to return it. Because of the randomness in demand and in returns, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where, the system manager balances potential lost sales with repositioning costs. Although the problem is increasingly common in applications involving on-demand rental services, not much is known about the nature of the optimal policy for systems with a general network structure or about effective approaches to solving the problem. In this paper, first, we show that the optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory, whereas, outside the region, it is optimal to reposition but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We also provide a simple check for when a state is in the no-repositioning region. Second, we leverage the features of the optimal policy, along with properties of the optimal cost function, to propose a provably convergent approximate dynamic programming algorithm to tackle problems with a large number of dimensions. This paper was accepted by David Simchi-Levi, optimization.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129571007","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":"Modeling Inequality and Mobility with Stochastic Processes","authors":"Thomas G. Fischer","doi":"10.2139/ssrn.3090904","DOIUrl":"https://doi.org/10.2139/ssrn.3090904","url":null,"abstract":"This paper presents tractable two parameter stochastic processes of the drift-diffusion class in order to model economic processes with a focus on income. Starting from the resulting closed-form, cross-sectional distributions, easy-to-interpret expressions for mobility and inequality (including the popular Gini-coefficient) are derived. The general processes are applied to discuss income mobility and inequality and fitted to US evidence. Heteroscedasticity is crucial to explaining skewed distributions of log-income, while multiplicative risk is necessary for generating Pareto tails. Furthermore, introducing Poisson death jumps also generates Pareto tails in the low end of the distribution and therefore fits the evidence best. Finally, we develop a micro-founded model for income inequality that fits the current US evidence and permits discussing the welfare effects of tax reforms given that individuals also adjust their labor supply and human capital accumulation. According to the model current US taxation is close to its welfare optimum.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131237052","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":"Managing Customer Churn via Service Mode Control","authors":"Yashodhan Kanoria, I. Lobel, J. Lu","doi":"10.2139/SSRN.3188226","DOIUrl":"https://doi.org/10.2139/SSRN.3188226","url":null,"abstract":"We introduce a novel stochastic control model for the problem of a service firm interacting over time with one of its customers who probabilistically churns depending on the customer’s satisfaction. The firm has two service modes available, and they determine the drift and volatility of the Brownian reward process. The firm’s objective is to maximize the rewards generated over the customer’s lifetime. Meanwhile, the customer might churn probabilistically if the customer’s satisfaction, modeled as an Orstein–Uhlenbeck process controlled by the firm’s service mode, is below a certain threshold. We build upon Markov processes with spatial delay to solve this problem, and we explicitly characterize the firm’s optimal policy, which is either myopic or a sandwich policy. A sandwich policy is one in which the firm deploys the service mode with inferior reward rate when the customer satisfaction level is in a specific interval near the satisfaction threshold and uses the myopically optimal service mode for all other satisfaction levels. Specifically, we find that the firm should use the safe service mode when the customer is marginally satisfied and the risky service mode when the customer is marginally unsatisfied. We find numerically that the customer lifetime value under the optimal policy is large relative to that under the myopic policy. Our results are robust to a variety of alternative model specifications. Funding: J. Lu gratefully acknowledges financial support from Natural Science Foundation of China (NSFC) [Project 72192805]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0179 .","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"28 20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125809360","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 Stochastic Feedback in Asymmetric Dynamic Contests","authors":"Jochen Schlapp, Jürgen Mihm","doi":"10.2139/ssrn.3134386","DOIUrl":"https://doi.org/10.2139/ssrn.3134386","url":null,"abstract":"Contests, in which contestants compete at their own expenses for prizes offered by a contest holder, have become the foundational primitive of many theories of competition. Recently, the focus in contest research has turned to the role of in-contest performance feedback. The extant literature on feedback has focused on specific ad-hoc policies and hence failed to more broadly characterize optimal feedback policies. In this note we solve a general formulation of a contest involving feedback, and thus characterize the optimal feedback policy in a very wide class of (stochastic) feedback policies. We find that, in many settings where informative feedback is useful, feedback is optimal when it is both truthful and fully informative.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121612566","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":"Stochastic Differential Equation for Approval Ratings and Scoring Systems","authors":"Saugata Giri","doi":"10.2139/ssrn.3108861","DOIUrl":"https://doi.org/10.2139/ssrn.3108861","url":null,"abstract":"Feedback and rating/scoring systems are used almost everywhere nowadays. Generally customers are being asked to rate a product on a scale of 1 to 10, or 1 to 5 or on any other positive real number scale. The average score then would provide for the qualitative assessment of the product. For example Movies would be rated by their viewers and critics alike. The mean or some king of weighted mean of there feedback scores would then become their \"APPROVAL RATING\" or \"AR\" for short. Approval ratings thus are measures of central tendency for approval/disapproval for a product. But these approval ratings keep changing as new feedback data is punched into the system. Hence they are dynamic (stochastic in nature) with their value changing as and when more feedback data keep flowing in. The most simple feedback system is where a customer is just asked whether they liked/disliked a product. The sequence of responses then would look like the output of a coin toss experiment (with heads/approval would be scored as 1 and tails/disapproval would be 0). At any point of time the overall mean would then be reported as the Approval Rating Score. The sequence of all running means, updated with the latest feedback data from customers, would form the \"APPROVAL RATING VECTOR\" or \"ARV\" for short. If we take a look at a sequence of evolution of the approval rating score with newer feedbacks, we would realise that even though we are using the last available data as the latest rating the whole path and the data hidden behind that path is never actually used. In Finance for example a measure called IRR (Internal Rate of Return) would describe the whole yield curve. While IRR is a single number, it is derived by using the information from the whole path followed by the yield curve. Similar mechanism is also present in the field of quantitative finance where the zero coupon bond prices would be calculated from the expected value of the continuous compounding of the rates which could be described by any popular short rate model. The short rate model parameters are calculated by taking in information of whole path of evolution of the interest rate. While the future is predicted by calculating the expectation over all possible future paths that the interest rate could take. The point is that the expectation is taken over the whole path. The prevailing interest rate today is not the only component used for pricing the zero coupon bond. Approval ratings however are just described by the present mean/weighted mean, and do not use the information provided by the path it took to reach to the present value, devoiding us the power to predict its future.","PeriodicalId":103032,"journal":{"name":"OPER: Analytical (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129089013","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}