Showing papers in "Operations Research in 2014"
TL;DR: A unifying framework for modeling and solving distributionally robust optimization problems and introduces standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold.
Abstract: Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.
789 citations
TL;DR: In this paper, the authors consider a general model of such crowdsourcing tasks and pose the problem of minimizing the total price i.e., number of task assignments that must be paid to achieve a target overall reliability, and give a new algorithm for deciding which tasks to assign to which workers and for inferring correct answers from the workers' answers.
Abstract: Crowdsourcing systems, in which numerous tasks are electronically distributed to numerous “information pieceworkers,” have emerged as an effective paradigm for human-powered solving of large-scale problems in domains such as image classification, data entry, optical character recognition, recommendation, and proofreading. Because these low-paid workers can be unreliable, nearly all such systems must devise schemes to increase confidence in their answers, typically by assigning each task multiple times and combining the answers in an appropriate manner, e.g., majority voting.
In this paper, we consider a general model of such crowdsourcing tasks and pose the problem of minimizing the total price i.e., number of task assignments that must be paid to achieve a target overall reliability. We give a new algorithm for deciding which tasks to assign to which workers and for inferring correct answers from the workers' answers. We show that our algorithm, inspired by belief propagation and low-rank matrix approximation, significantly outperforms majority voting and, in fact, is optimal through comparison to an oracle that knows the reliability of every worker. Further, we compare our approach with a more general class of algorithms that can dynamically assign tasks. By adaptively deciding which questions to ask to the next set of arriving workers, one might hope to reduce uncertainty more efficiently. We show that, perhaps surprisingly, the minimum price necessary to achieve a target reliability scales in the same manner under both adaptive and nonadaptive scenarios. Hence, our nonadaptive approach is order optimal under both scenarios. This strongly relies on the fact that workers are fleeting and cannot be exploited. Therefore, architecturally, our results suggest that building a reliable worker-reputation system is essential to fully harnessing the potential of adaptive designs.
379 citations
TL;DR: This work studies a class of assortment optimization problems where customers choose among the offered products according to the nested logit model and develops parsimonious collections of candidate assortments with worst-case performance guarantees for NP-hard cases.
Abstract: We study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model. There is a fixed revenue associated with each product. The objective is to find an assortment of products to offer so as to maximize the expected revenue per customer. We show that the problem is polynomially solvable when the nest dissimilarity parameters of the choice model are less than one and the customers always make a purchase within the selected nest. Relaxing either of these assumptions renders the problem NP-hard. To deal with the NP-hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. We also formulate a convex program whose optimal objective value is an upper bound on the optimal expected revenue. Thus, we can compare the expected revenue provided by an assortment with the upper bound on the optimal expected revenue to get a feel for the optimality gap of the assortment. By using this approach, our computational experiments test the performance of the parsimonious collections of candidate assortments that we develop.
274 citations
TL;DR: In this article, a learning-based algorithm is proposed to dynamically update a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period.
Abstract: A natural optimization model that formulates many online resource allocation problems is the online linear programming LP problem in which the constraint matrix is revealed column by column along with the corresponding objective coefficient. In such a model, a decision variable has to be set each time a column is revealed without observing the future inputs, and the goal is to maximize the overall objective function. In this paper, we propose a near-optimal algorithm for this general class of online problems under the assumptions of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period. Through dynamic learning, the competitiveness of our algorithm improves over the past study of the same problem. We also present a worst case example showing that the performance of our algorithm is near optimal.
257 citations
TL;DR: This work analyzes a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon, and identifies bounds on the optimal order-up-to levels and develops an effective heuristic policy.
Abstract: We analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon. In each period, demand depends on the price of the current period plus an additive random term. Inventories can be intentionally disposed of, and those that reach their lifetime have to be disposed of. The objective is to find a joint pricing, ordering, and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost, inventory holding and backlogging or lost-sales penalty cost, and disposal cost. Employing the concept of L♮-concavity, we show some monotonicity properties of the optimal policies. Our results shed new light on perishable inventory management, and our approach provides a significantly simpler proof of a classical structural result in the literature. Moreover, we identify bounds on the optimal order-up-to levels and develop an effective heuristic policy. Numerical results show that our heuristic policy performs well in both stationary and nonstationary settings. Finally, we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes.
226 citations
TL;DR: It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order T in the former case and of order log T inthe latter case.
Abstract: We consider a monopolist who sells a set of products over a time horizon of T periods. The seller initially does not know the parameters of the products' linear demand curve, but can estimate them based on demand observations. We first assume that the seller knows nothing about the parameters of the demand curve, and then consider the case where the seller knows the expected demand under an incumbent price. It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order T in the former case and of order log T in the latter case. To derive pricing policies that are practically implementable, we take as our point of departure the widely used policy called greedy iterated least squares ILS, which combines sequential estimation and myopic price optimization. It is known that the greedy ILS policy itself suffers from incomplete learning, but we show that certain variants of greedy ILS achieve the minimum asymptotic loss rate. To highlight the essential features of well-performing pricing policies, we derive sufficient conditions for asymptotic optimality.
210 citations
TL;DR: The results suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially, and that the values of information on both the parametric form of the demand function as well as each customer's exact reservation price are less important than prior literature suggests.
Abstract: We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer such as price adjustment, sales commission, advertisement intensity, etc.. The relationship between the action and the demand rate is not known in advance. However, the retailer is able to learn the optimal action on the fly as she maximizes her total expected revenue based on the observed demand reactions.
Using the pricing problem as an example, we propose a dynamic learning-while-doing algorithm that only involves function value estimation to achieve a near-optimal performance. Our algorithm employs a series of shrinking price intervals and iteratively tests prices within that interval using a set of carefully chosen parameters. We prove that the performance of our algorithm is among the best of all possible algorithms in terms of the asymptotic regret the relative loss compared to the full information optimal solution. Our result closes the performance gaps between parametric and nonparametric learning and between the post-price mechanism and the customer-bidding mechanism. Important managerial insight from this research is that the values of information on both the parametric form of the demand function as well as each customer's exact reservation price are less important than prior literature suggests. Our results also suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially.
183 citations
TL;DR: This work develops appointment scheduling models that take into account the patient preferences regarding when they would like to be seen and proposes a heuristic solution procedure to maximize the expected net “profit” per day.
Abstract: Motivated by the rising popularity of electronic appointment booking systems, we develop appointment scheduling models that take into account the patient preferences regarding when they would like to be seen. The service provider dynamically decides which appointment days to make available for the patients. Patients arriving with appointment requests may choose one of the days offered to them or leave without an appointment. Patients with scheduled appointments may cancel or not show up for the service. The service provider collects a “revenue” from each patient who shows up and incurs a “service cost” that depends on the number of scheduled appointments. The objective is to maximize the expected net “profit” per day. We begin by developing a static model that does not consider the current state of the scheduled appointments. We give a characterization of the optimal policy under the static model and bound its optimality gap. Building on the static model, we develop a dynamic model that considers the current state of the scheduled appointments, and we propose a heuristic solution procedure. In our computational experiments, we test the performance of our models under the patient preferences estimated through a discrete choice experiment that we conduct in a large community health center. Our computational experiments reveal that the policies we propose perform well under a variety of conditions.
157 citations
TL;DR: In this article, the authors considered the multi-product pricing problem under the general nested logit model with product-differentiated price sensitivities and arbitrary nest coefficients and showed that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all the products within a nest at optimality.
Abstract: We study firms that sell multiple substitutable products and customers whose purchase behavior follows a nested logit model, of which the multinomial logit model is a special case. Customers make purchasing decisions sequentially under the nested logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multiproduct pricing problem under the general nested logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all the products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multiproduct price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and we show that similar techniques can be used to significantly simplify the corresponding pricing problems.
140 citations
TL;DR: A novel interpretation of the inverse formulation as the dual of the well-known Benson's method is provided and by doing so a new connection between inverse optimization and Pareto surface approximation techniques is developed.
Abstract: We generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible. In multiobjective linear optimization, given a solution that is not a weakly efficient solution to the forward problem, our method generates objective function weights that make the given solution a near-weakly efficient solution. Our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem. We provide a novel interpretation of our inverse formulation as the dual of the well-known Benson's method and by doing so develop a new connection between inverse optimization and Pareto surface approximation techniques. We apply our method to prostate cancer data obtained from Princess Margaret Cancer Centre in Toronto, Canada. We demonstrate that clinically acceptable treatments can be generated using a small number of objective ...
117 citations
TL;DR: This work in a nonprofit setting solves the sequential resource allocation problem with an objective function aimed at equitable and effective service and describes the structure of the optimal allocation policy for a given sequence of customers when demand follows continuous probability distributions.
Abstract: This paper studies a sequential resource allocation problem motivated by distribution operations of a nonprofit organization. The alternate objectives that arise in nonprofit as opposed to commercial operations lead to new variations on traditional problems in operations research and inventory management. Specifically, we consider the problem of distributing a scarce resource to meet customers' demands that are observed sequentially. An allocation policy that seeks to maximize profit may lead to inequitable distributions among customers. Our work in a nonprofit setting solves the sequential resource allocation problem with an objective function aimed at equitable and effective service. We define service in terms of fill rate the ratio of the allocated amount to observed demand and develop an objective function to maximize the expected minimum fill rate among customers, which balances equity in fill rates with effectiveness in the use of resources low waste. Through a dynamic programming framework, we characterize the structure of the optimal allocation policy for a given sequence of customers when demand follows continuous probability distributions. We use that optimal structure to develop a heuristic allocation policy for instances with discrete demand distribution. In addition, we identify customer demand properties to consider when sequencing customer visits to optimize the fill rate objective. For both inventory allocation and customer sequencing decisions, the proposed heuristic methods yield near-optimal solutions.
TL;DR: This paper provides a method to measure the overall uncertainty while simultaneously reducing the influence of simulation estimation error due to output variability, and summarizes overall uncertainty via a credible interval for the mean.
Abstract: When we use simulation to estimate the performance of a stochastic system, the simulation often contains input models that were estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance estimates. In this paper, we provide a method to measure the overall uncertainty while simultaneously reducing the influence of simulation estimation error due to output variability. To reach this goal, a Bayesian framework is introduced. We use a Bayesian posterior for the input-model parameters, conditional on the real-world data, to quantify the input-parameter uncertainty; we propagate this uncertainty to the output mean using a Gaussian process posterior distribution for the simulation response as a function of the input-model parameters, conditional on a set of simulation experiments. We summarize overall uncertainty via a credible interval for the mean. Our framework is fully Bayesian, makes more effective use of the simulation budget than other Bayesian approaches in the stochastic simulation literature, and is supported with both theoretical analysis and an empirical study. We also make clear how to interpret our credible interval and why it is distinctly different from the confidence intervals for input uncertainty obtained in other papers.
TL;DR: A matheuristic solution methodology integrating slope scaling, a dynamic block-generation mechanism, long-term-memory-based perturbation strategies, and ellipsoidal search, a new intensification mechanism to thoroughly explore very large neighborhoods of elite solutions restricted using information from the history of the search are proposed.
Abstract: This paper addresses the scheduled service network design problem for freight rail transportation. The proposed model integrates service selection and scheduling, car classification and blocking, train makeup, and routing of time-dependent customer shipments based on a cyclic three-layer space--time network representation of the associated operations and decisions and their relations and time dimensions. This paper also proposes a matheuristic solution methodology integrating slope scaling, a dynamic block-generation mechanism, long-term-memory-based perturbation strategies, and ellipsoidal search, a new intensification mechanism to thoroughly explore very large neighborhoods of elite solutions restricted using information from the history of the search. Experimental results show that the proposed solution method is efficient and robust, yielding high-quality solutions for realistically sized problem instances.
TL;DR: A new matching algorithm is introduced and it is shown that if the number of couples grows slower than the size of the market, a stable matching will be found with high probability, if however, the numberof couples grows at a linear rate, with constant probability not depending on the market size, no stable matching exists.
Abstract: Labor markets can often be viewed as many-to-one matching markets. It is well known that if complementarities are present in such markets, a stable matching may not exist. We study large random matching markets with couples. We introduce a new matching algorithm and show that if the number of couples grows slower than the size of the market, a stable matching will be found with high probability. If however, the number of couples grows at a linear rate, with constant probability not depending on the market size, no stable matching exists. Our results explain data from the market for psychology interns.
TL;DR: This study presents new exact algorithms for the clustered vehicle routing problem CluVRP, a generalization of the capacitated vehicle routingProblem CVRP in which the customers are grouped into clusters, based on an exponential time preprocessing scheme and a polynomial time graph reduction scheme.
Abstract: This study presents new exact algorithms for the clustered vehicle routing problem CluVRP. The CluVRP is a generalization of the capacitated vehicle routing problem CVRP, in which the customers are grouped into clusters. As in the CVRP, all the customers must be visited exactly once, but a vehicle visiting one customer in a cluster must visit all the remaining customers therein before leaving it. Based on an exponential time preprocessing scheme, an integer programming formulation for the CluVRP is presented. The formulation is enhanced by a polynomial time graph reduction scheme. Two exact algorithms for the CluVRP, a branch and cut as well as a branch and cut and price, are presented. The computational performances of the algorithms are tested on benchmark instances adapted from the vehicle routing problem literature as well as real-world instances from a solid waste collection application.
TL;DR: This paper proposes a new exact method that solves a large number of the open benchmark instances within a limited computational effort and shows that the proposed algorithm provides a substantial breakthrough with respect to previously published algorithms.
Abstract: We study the strip packing problem, in which a set of two-dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height, with the aim of minimizing the height used. The problem is important because it models a large number of real-world applications, including cutting operations where stocks of materials such as paper or wood come in large rolls and have to be cut with minimum waste, scheduling problems in which tasks require a contiguous subset of identical resources, and container loading problems arising in the transportation of items that cannot be stacked one over the other. The strip packing problem has been attacked in the literature with several heuristic and exact algorithms, nevertheless, benchmark instances of small size remain unsolved to proven optimality. In this paper we propose a new exact method that solves a large number of the open benchmark instances within a limited computational effort. Our method is based on a Benders' decomposition, in whi...
TL;DR: A fluid model is used to examine how different definitions of “overload” affect the long-term behavior of the system and provides insight into the impact of using speedup, and introduces a state-dependent queuing network where service times and return probabilities depend on the ‘overloaded’ and “underloaded” state of thesystem.
Abstract: In a number of service systems, there can be substantial latitude to vary service rates. However, although speeding up service rate during periods of congestion may address a present congestion issue, it may actually exacerbate the problem by increasing the need for rework. We introduce a state-dependent queuing network where service times and return probabilities depend on the “overloaded” and “underloaded” state of the system. We use a fluid model to examine how different definitions of “overload” affect the long-term behavior of the system and provide insight into the impact of using speedup. We identify scenarios where speedup can be helpful to temporarily alleviate congestion and increase access to service. For such scenarios, we provide approximations for the likelihood of speedup to service. We also identify scenarios where speedup should never be used; moreover, in such a situation, an interesting bi-stability arises, such that the system shifts randomly between two equilibria states. Hence, our analysis sheds light on the potential benefits and pitfalls of using speedup when the subsequent returns may be unavoidable.
TL;DR: A multinomial logit model for estimating historical passenger travel and a previously developed greedy reaccommodation heuristic for estimating the resulting passenger delays are developed.
Abstract: Many of the existing methods for evaluating an airline's on-time performance are based on flight-centric measures of delay. However, recent research has demonstrated that passenger delays depend on many factors in addition to flight delays. For instance, significant passenger delays result from flight cancellations and missed connections, which themselves depend on a significant number of factors. Unfortunately, lack of publicly available passenger travel data has made it difficult for researchers to explore the nature of these relationships. In this paper, we develop methodologies to model historical travel and delays for U.S. domestic passengers. We develop a multinomial logit model for estimating historical passenger travel and extend a previously developed greedy reaccommodation heuristic for estimating the resulting passenger delays. We report and analyze the estimated passenger delays for calendar year 2007, developing insights into factors that affect the performance of the National Air Transportat...
TL;DR: Computational tests show that the solution algorithms developed and imbedded in the decision support system DSS outperform the manual planning method that Baosteel used to use by a significant margin both in terms of tundish utilization for almost every case, and in total cost for most cases.
Abstract: We study an integrated charge batching and casting width selection problem arising in the continuous casting operation of the steelmaking process at Shanghai, China based Baosteel. This decision-making problem is not unique to Baosteel; it exists in every large iron and steel company in the world. We collaborated with Baosteel on this problem from 2006 to 2008 by developing and implementing a decision support system DSS that replaced their manual planning method. The DSS is still in active use at Baosteel. This paper describes the solution algorithms we developed and imbedded in the DSS. For the general problem that is strongly NP-hard, a column generation-based branch-and-price B&P solution approach is developed to obtain optimal solutions. By exploiting the problem structure, efficient dynamic programming algorithms are designed to solve the subproblems involved in the column generation procedure. Branching strategies are designed in a way that ensures that after every stage of branching the structure of the subproblems is preserved such that they can still be solved efficiently. We also consider a frequently occurring case of the problem where each steel grade is incompatible with any other grade. For this special case, a two-level polynomial-time algorithm is developed to obtain optimal solutions. Computational tests on a set of real production data as well as on a more diverse set of randomly generated problem instances show that our algorithms outperform the manual planning method that Baosteel used to use by a significant margin both in terms of tundish utilization for almost every case, and in terms of total cost for most cases. Consequently, by replacing their manual method with our DSS, the estimated benefits to Baosteel include an annual cost saving of about US $1.6 million and an annual revenue increase of about US $3.25 million.
TL;DR: New analytical models of controlled hospital census are developed that can, for the first time, be incorporated into a mixed-integer programming model to optimally solve the strategic planning/scheduling portion of the HASC.
Abstract: Hospitals typically lack effective enterprise level strategic planning of bed and care resources, contributing to bed census levels that are statistically "out of control." This system dysfunction manifests itself in bed block, surgical cancelation, ambulance diversions, and operational chaos. This is the classic hospital admission scheduling and control HASC problem, which has been addressed in its entirety only through inexact simulation-based search heuristics. This paper develops new analytical models of controlled hospital census that can, for the first time, be incorporated into a mixed-integer programming model to optimally solve the strategic planning/scheduling portion of the HASC. Our new solution method coordinates elective admissions with other hospital subsystems to reduce system congestion. We formulate a new Poisson-arrival-location model PALM based on an innovative stochastic location process that we developed and call the patient temporal resource needs model. We further extend the PALM approach to the class of deterministic controlled-arrival-location models d-CALM and develop linearizing approximations to stochastic blocking metrics. This work provides the theoretical foundations for an efficient scheduled admissions planning system as well as a practical decision support methodology to stabilize hospital census.
TL;DR: This is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs and shows that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation.
Abstract: Airline operations are subject to frequent disruptions typically due to unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights and increasing cruise stage speed when possible in an effort to contain the delays. However, there is a critical trade-off between fuel consumption and its adverse impact on air quality and greenhouse gas emissions and cruise speed. Here we consider delays caused by such disruptions and propose a flight rescheduling model that includes adjusting cruise stage speed on a set of affected and unaffected flights as well as swapping aircraft optimally.
To the best of our knowledge, this is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs. The proposed model allows one to investigate the trade-off between flight delays and the cost of recovery. We show that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation.
Flight time controllability, nonlinear delay, fuel burn and CO2 emission cost functions, and binary aircraft swapping decisions complicate the aircraft recovery problem significantly. In order to mitigate the computational difficulty we utilize the recent advances in conic mixed integer programming and propose a strengthened formulation so that the nonlinear mixed integer recovery optimization model can be solved efficiently. Our computational tests on realistic cases indicate that the proposed model may be used by operations controllers to manage disruptions in real time in an optimal manner instead of relying on ad-hoc heuristic approaches.
TL;DR: A framework for robustifying convex, law invariant risk measures is introduced and it is shown that under mild conditions, the infinite dimensional optimization problem of finding the worst-case risk can be solved analytically and closed-form expressions for the robust risk measures are obtained.
Abstract: This paper introduces a framework for robustifying convex, law invariant risk measures. The robustified risk measures are defined as the worst case portfolio risk over neighborhoods of a reference probability measure, which represent the investors' beliefs about the distribution of future asset losses. It is shown that under mild conditions, the infinite dimensional optimization problem of finding the worst-case risk can be solved analytically and closed-form expressions for the robust risk measures are obtained. Using these results, robust versions of several risk measures including the standard deviation, the Conditional Value-at-Risk, and the general class of distortion functionals are derived. The resulting robust risk measures are convex and can be easily incorporated into portfolio optimization problems, and a numerical study shows that in most cases they perform significantly better out-of-sample than their nonrobust variants in terms of risk, expected losses, and turnover.
TL;DR: This paper proposes a bet-and-run approach to actually turn erraticism to one's advantage and results are presented, showing the potential of this approach even when embedded in a proof-of-concept implementation.
Abstract: High sensitivity to initial conditions is generally viewed as a drawback of tree search methods because it leads to erratic behavior to be mitigated somehow. In this paper we investigate the opposite viewpoint and consider this behavior as an opportunity to exploit. Our working hypothesis is that erraticism is in fact just a consequence of the exponential nature of tree search that acts as a chaotic amplifier, so it is largely unavoidable. We propose a bet-and-run approach to actually turn erraticism to one's advantage. The idea is to make a number of short sample runs with randomized initial conditions, to bet on the “most promising” run selected according to certain simple criteria, and to bring it to completion. Computational results on a large testbed of mixed integer linear programs from the literature are presented, showing the potential of this approach even when embedded in a proof-of-concept implementation.
TL;DR: This work presents a new sequential elimination IZ procedure, called BIZ Bayes-inspired indifference zone, whose lower bound on worst-case probability of correct selection in the preference zone is tight in continuous time, and nearly tight in discrete time.
Abstract: We consider the indifference-zone IZ formulation of the ranking and selection problem with independent normal samples. In this problem, we must use stochastic simulation to select the best among several noisy simulated systems, with a statistical guarantee on solution quality. Existing IZ procedures sample excessively in problems with many alternatives, in part because loose bounds on probability of correct selection lead them to deliver solution quality much higher than requested. Consequently, existing IZ procedures are seldom considered practical for problems with more than a few hundred alternatives. To overcome this, we present a new sequential elimination IZ procedure, called BIZ Bayes-inspired indifference zone, whose lower bound on worst-case probability of correct selection in the preference zone is tight in continuous time, and nearly tight in discrete time. To the author's knowledge, this is the first sequential elimination procedure with tight bounds on worst-case preference-zone probability of correct selection for more than two alternatives. Theoretical results for the discrete-time case assume that variances are known and have an integer multiple structure, but the BIZ procedure itself can be used when these assumptions are not met. In numerical experiments, the sampling effort used by BIZ is significantly smaller than that of another leading IZ procedure, the KN procedure, especially on the largest problems tested 214 = 16,384 alternatives.
TL;DR: This work provides a simple explanation for nonmonotonic queue-joining strategies that emerge for discrete as well as continuously distributed priors on the expected service time with positively correlated service value by relaxing the informational assumptions in Naor's model.
Abstract: In the operations research literature, the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these nonmonotonic queue-joining strategies by relaxing the informational assumptions in Naor's model. Instead of imposing that the expected service time and service value are common knowledge, we assume that they are unknown to consumers, but positively correlated. Under such informational assumptions, the posterior expected waiting cost and service value increase in the observed queue length. As a consequence, we show that queue-joining equilibria may emerge for which the joining probability increases locally in the queue length. We refer to these as “sputtering equilibria.” We discuss when and why such sputtering equilibria exist for discrete as well as continuously distributed priors on the expected service time with positively correlated service value.
TL;DR: A dynamic traveling salesman problem TSP with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which the cost of a decision is known only probabilistically beforehand but is revealed dynamically before the decision is executed is proposed.
Abstract: We propose a dynamic traveling salesman problem TSP with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which the cost of a decision is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate this as a dynamic program DP and compare it to static counterparts to demonstrate the advantage of the dynamic paradigm over an a priori approach. We then apply approximate linear programming ALP to overcome the DP's curse of dimensionality, obtain a semi-infinite linear programming lower bound, and discuss its tractability. We also analyze a rollout version of the price-directed policy implied by our ALP and derive worst-case guarantees for its performance. Our computational study demonstrates the quality of a heuristically modified rollout policy using a computationally effective a posteriori bound.
TL;DR: A simple improvement of the popular static price control known in the literature is introduced, which only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all, which provides an advantage over the potentially heavy computational burden of re Optimization.
Abstract: We consider a standard dynamic pricing problem with finite inventories, finite selling horizon, and stochastic demands, where the objective of the seller is to maximize total expected revenue. We introduce a simple improvement of the popular static price control known in the literature. The proposed heuristic only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all. This provides an advantage over the potentially heavy computational burden of reoptimization, especially for very large applications with frequent price adjustments. In addition, our heuristic can be implemented in combination with a few reoptimizations to achieve a high-level revenue performance. This hybrid of real-time adjustment and reoptimization allows the seller to enjoy the benefit of reoptimization without overdoing it.
TL;DR: This paper studies DPs that have a convex structure and considers gradient penalties that are based on first-order linear approximations of approximate value functions that can provide tight bounds for convex DPs and can be used to improve on bounds provided by other relaxations, such as Lagrangian relaxation bounds.
Abstract: We consider the information relaxation approach for calculating performance bounds for stochastic dynamic programs DPs. This approach generates performance bounds by solving problems with relaxed nonanticipativity constraints and a penalty that punishes violations of these nonanticipativity constraints. In this paper, we study DPs that have a convex structure and consider gradient penalties that are based on first-order linear approximations of approximate value functions. When used with perfect information relaxations, these penalties lead to subproblems that are deterministic convex optimization problems. We show that these gradient penalties can, in theory, provide tight bounds for convex DPs and can be used to improve on bounds provided by other relaxations, such as Lagrangian relaxation bounds. Finally, we apply these results in two example applications: first, a network revenue management problem that describes an airline trying to manage seat capacity on its flights; and second, an inventory management problem with lead times and lost sales. These are challenging problems of significant practical interest. In both examples, we compute performance bounds using information relaxations with gradient penalties and find that some relatively easy-to-compute heuristic policies are nearly optimal.
TL;DR: Examination of a more general situation in which two or more retailers engage in Cournot competition under complete information enables a new rule called competitive allocation to be constructed that can eliminate the gaming effect.
Abstract: When retailers' orders exceed the supplier's available capacity, the supplier allocates his capacity according to some allocation rule. When retailers are local monopolists, uniform allocation eliminates the “gaming effect” so that each retailer orders her ideal allocation. However, when two retailers engage in Cournot competition under complete information, a recent study has shown that uniform allocation fails to eliminate the gaming effect so that some retailer may inflate her order strategically. By examining a more general situation in which two or more retailers engage in Cournot competition under complete information, we establish exact conditions under which uniform allocation fails to eliminate the gaming effect. These exact conditions enable us to construct a new rule called competitive allocation that can eliminate the gaming effect. Without inflated orders from the retailers, the supplier's profit could be lower under competitive allocation than under uniform allocation when certain restrictive conditions hold. In contrast, competitive allocation generates higher average profits for the retailers and for the supply chain; hence, it reduces the inefficiency of the decentralized supply chain.
TL;DR: The Fast Algorithm for the Scenario Technique is introduced, a variant of the scenario optimization algorithm with reduced sample complexity, to obtain feasible solutions to chance-constrained optimization problems based on random sampling.
Abstract: The scenario approach is a recently introduced method to obtain feasible solutions to chance-constrained optimization problems based on random sampling. It has been noted that the sample complexity of the scenario approach rapidly increases with the number of optimization variables and this may pose a hurdle to its applicability to medium- and large-scale problems. We here introduce the Fast Algorithm for the Scenario Technique, a variant of the scenario optimization algorithm with reduced sample complexity. Subject classifications: stochastic programming; chance-constrained optimization; randomized algorithms; sample-based methods; scenario approach. Area of review: Optimization.