Showing papers in "Operations Research in 2003"
TL;DR: The problem of computing and optimizing the worst-case VaR and various other partial information on the distribution, including uncertainty in factor models, support constraints, and relative entropy information can be cast as semidefinite programs.
Abstract: Classical formulations of the portfolio optimization problem, such as mean-variance or Value-at-Risk (VaR) approaches, can result in a portfolio extremely sensitive to errors in the data, such as mean and covariance matrix of the returns. In this paper we propose a way to alleviate this problem in a tractable manner. We assume that the distribution of returns is partially known, in the sense that onlybounds on the mean and covariance matrix are available. We define the worst-case Value-at-Risk as the largest VaR attainable, given the partial information on the returns' distribution. We consider the problem of computing and optimizing the worst-case VaR, and we show that these problems can be cast as semidefinite programs. We extend our approach to various other partial information on the distribution, including uncertainty in factor models, support constraints, and relative entropy information.
671 citations
TL;DR: In this article, an efficient method based on linear programming for approximating solutions to large-scale stochastic control problems is proposed. But the approach is not suitable for large scale queueing networks.
Abstract: The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.
643 citations
TL;DR: It is demonstrated that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective, which has practical implications for improving the efficiency of supply chains.
Abstract: Although the supply chain management literature is extensive, the benefits and challenges of coordinated decision making within supply chainscheduling models have not been studied. We consider a variety of scheduling, batching, and delivery problems that arise in an arborescent supply chain where a supplier makes deliveries to several manufacturers, who also make deliveries to customers. The objective is to minimize the overall scheduling and delivery cost, using several classical scheduling objectives. This is achieved by scheduling the jobs and forming them into batches, each of which is delivered to the next downstream stage as a single shipment. For each problem, we either derive an efficient dynamic programming algorithm that minimizes the total cost of the supplier or that of the manufacturer, or we demonstrate that this problem is intractable. The total system cost minimization problem of a supplier and manufacturer who make cooperative decisions is also considered. We demonstrate that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective. Finally, we identify incentives and mechanisms for this cooperation, thereby demonstrating that our work has practical implications for improving the efficiency of supply chains.
427 citations
TL;DR: In this paper, the authors consider a consumer-driven substitution problem with an arbitrary number of products under both centralized inventory management and competition, and obtain analytically tractable solutions that facilitate comparisons between centralized and competitive inventory management under substitution.
Abstract: A standard problem in operations literature is optimal stocking of substitutable products. We consider a consumer-driven substitution problem with an arbitrary number of products under both centralized inventory management and competition. Substitution is modeled by letting the unsatisfied demand for a product flow to other products in deterministic proportions. We obtain analytically tractable solutions that facilitate comparisons between centralized and competitive inventory management under substitution. For the centralized problem we show that, when demand is multivariate normal, the total profit is decreasing in demand correlation.
347 citations
TL;DR: This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps, and the phase transition behavior of these models, as far as it is known, is discussed.
Abstract: Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.
294 citations
TL;DR: A perfect coordination mechanism is constructed for a two-echelon distribution system in which a supplier distributes a product toN competing retailers and responds to the retailers' choices by implementing his own cost-minimizing replenishment strategy.
Abstract: We consider a two-echelon distribution system in which a supplier distributes a product toN competing retailers. The demand rate of each retailer depends on all of the retailers' prices, or alternatively, the price each retailer can charge for its product depends on the sales volumes targeted by all of the retailers. The supplier replenishes his inventory through orders (purchases, production runs) from an outside source with ample supply. From there, the goods are transferred to the retailers. Carrying costs are incurred for all inventories, while all supplier orders and transfers to the retailers incur fixed and variable costs. We first characterize the solution to the centralized system in which all retailer prices, sales quantities and the complete chain-wide replenishment strategy are determined by a single decision maker, e.g., the supplier. We then proceed with the decentralized system. Here, the supplier chooses a wholesale pricing scheme; the retailers respond to this scheme by each choosing all of his policy variables. We distinguish systematically between the case of Bertrand and Cournot competition. In the former, each retailer independently chooses his retail price as well as a replenishment strategy; in the latter, each of the retailers selects a sales target, again in combination with a replenishment strategy. Finally, the supplier responds to the retailers' choices by implementing his own cost-minimizing replenishment strategy. We construct a perfect coordination mechanism. In the case of Cournot competition, the mechanism applies a discount from a basic wholesale price, based on thesum of three discount components, which are a function of (1) annual sales volume, (2) order quantity, and (3) order frequency, respectively.
265 citations
TL;DR: The Study Group achieved an understanding of the problem and a plan for further work for solving the set partitioning and covering problem.
Abstract: Airline crew scheduling is concerned with finding a minimum cost assignment of flight crews to a given flight schedule while satisfying restrictions dictated by collective bargaining agreements and...
251 citations
TL;DR: In this paper, a time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times.
Abstract: In this paper a new time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times. While lot-sizing decisions are made sequentially within an internally rolling planning interval (or lot-sizing window), capacities are always considered over the entire planning horizon. For each submodel a model formulation based on the "Simple Plant Location" representation is developed. These mixed-integer linear submodels are solved by standard mathematical programming software even for relatively large test instances. Extensive computational tests show that the heuristic proposed provides a better solution quality than a well-known special purpose heuristic.
201 citations
TL;DR: A new method for calculating explicitly optimal strategies, open-loop equilibria, and closed-loop Equilibria of such nonsmooth problems of asymmetric reference-price effects with loss-aversive consumers is introduced.
Abstract: Models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods. In this study, we introduce a new method for calculating explicitly optimal strategies, open-loop equilibria, and closed-loop equilibria of such nonsmooth problems. Application of this method to the case of asymmetric reference-price effects with loss-aversive consumers leads to the following conclusions: (1) When the planning horizon is infinite, after an introductory stage the optimal price stabilizes at a steady-state price, which is slightly below the optimal price in the absence of reference-price effects. (2) The optimal strategy is the same as in the symmetric case, but with the loss parameter determined by the initial reference-price. (3) Competition does not change the qualitative behavior of the optimal strategy. (4) Adopting an appropriate constant-price strategy results in a minute decline in profits.
199 citations
TL;DR: This work considers a supply chain in which the underlying demand process can be described in a linear state space form, and takes into account the ability of the members to observe subsets of the underlying state vector, and adopt their forecasting and replenishment policies accordingly.
Abstract: We consider a supply chain in which the underlying demand process can be described in a linear state space form. Inventory is managed at various points of the chain (members), based on local information that each member observes and continuously updates. The key feature of our model is that it takes into account the ability of the members to observe subsets of the underlying state vector, and adopt their forecasting and replenishment policies accordingly. This enables us to model situations in which the members are privy to certain explanatory variables of the demand, with the latter possibly evolving according to a vector autoregressive time series. For each member, we identify an associated demand evolution model, for which we propose an adaptive inventory replenishment policy that utilizes the Kalman filter technique. We then provide a simple methodology for assessing the benefits of various types of information-sharing agreements between members of the supply chain. We also discuss inventory positioning and cost performance assessment in the supply chain. Our performance metrics and inventory target levels are usually presented in matrix forms, allowing them to accommodate a relatively large spectrum of linear demand models, and making them simple to implement. Several illustrations for possible applications of our models are provided.
193 citations
TL;DR: The results show that some firms may find it profitable to allocate considerably more hydro production to off-peak periods then they would under perfect competition, highlighting the need to explicitly consider profit-maximizing behavior when examining the impact of regulatory and environmental policies on electricity market outcomes.
Abstract: This paper presents a modeling framework for analyzing competition between multiple firms that each possess a mixture of hydroelectric and thermal generation resources. Based upon the concept of a Cournot oligopoly with a competitive fringe, the model characterizes the Cournot equilibrium conditions of a multiperiod hydrothermal scheduling problem. Using data from the western United States electricity market, this framework is implemented as a mixed linear complementarity model. The results show that some firms may find it profitable to allocate considerably more hydro production to off-peak periods then they would under perfect competition. This strategy is a marked contrast to the optimal hydroschedules that would arise if no firms were acting strategically. These results highlight the need to explicitly consider profit-maximizing behavior when examining the impact of regulatory and environmental policies on electricity market outcomes.
TL;DR: In this paper, the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of systems is large and initial samples from each system have already been taken is addressed.
Abstract: In this paper we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of systems is large and initial samples from each system have already been taken This problem may be encountered when a heuristic search procedure--perhaps one originally designed for use in a deterministic environment--has been applied in a simulation-optimization context Because of stochastic variation, the system with the best sample mean at the end of the search procedure may not coincide with the true best system encountered during the search This paper develops statistical procedures that return the best system encountered by the search (or one near the best) with a prespecified probability We approach this problem using combinations of statistical subset selection and indifference-zone ranking procedures The subset-selection procedures, which use only the data already collected, screen out the obviously inferior systems, while the indifference-zone procedures, which require additional simulation effort, distinguish the best from the less obviously inferior systems
TL;DR: In this article, a cycle-based neighbourhood structure for metaheuristics aimed at the fixed-charge capacitated multicommodity network design formulation is proposed, which defines moves that explicitly take into account the impact on the total design cost of potential modifications to the flow distribution of several commodities simultaneously.
Abstract: We propose new cycle-based neighbourhood structures for metaheuristics aimed at the fixed-charge capacitated multicommodity network design formulation. The neighbourhood defines moves that explicitly take into account the impact on the total design cost of potential modifications to the flow distribution of several commodities simultaneously. Moves are identified through a shortest-pathlike network optimization procedure and proceed by redirecting flow around cycles and closing and opening design arcs accordingly. These neighbourhoods are evaluated and tested within a simple tabu search algorithm. Experimental results show that the proposed approach is quite powerful and outperforms existing methods reported in the literature.
TL;DR: An eigenfunction expansion approach to pricing options on scalar diffusion processes that develops two applications: pricing vanilla, single- and double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-Ingersoll-Ross (CIR) term-structure model.
Abstract: This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All contingent claims are unbundled into portfolios of primitive securities calledeigensecurities. Eigensecurities are eigenvectors (eigenfunctions) of the pricing operator (present value operator). All computational work is at the stage of finding eigenvalues and eigenfunctions of the pricing operator. The pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications:pricing vanilla, single- and double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-Ingersoll-Ross (CIR) term-structure model.
TL;DR: It is shown that allocation rules in the third stage based on dual solutions, which were used in the ABZ model, may induce the retailers to hold back some of their residual supply/demand.
Abstract: We present and study a three-stage model of a decentralized distribution system consisting ofn retailers, each of whom faces a stochastic demand for an identical product. In the first stage, before the demand is realized, each retailer independently orders her initial inventory. In the second stage, after the demand is realized, each retailer decides how much of her residual supply/demand she wants to share with the other retailers. In the third stage, residual inventories are transshipped to meet residual demands, and an additional profit is allocated. Our model is an extension of the two-stage model of Anupindi et al. (ABZ) (2001), which implicitly assumes that all residuals enter the transshipment stage. We show, however, that allocation rules in the third stage based on dual solutions, which were used in the ABZ model, may induce the retailers to hold back some of their residual supply/demand. In general, we study the effect of implementing various allocations rules in the third stage on the values of the residual supply/demand the retailers are willing to share with others in the second stage, and the trade-off involved in achieving an optimal solution for the corresponding centralized system.
TL;DR: An improved mixed-integer programming model and effective solution strategies for the facility layout problem are presented and an asubstantial increase in the accuracy of the layout produced, while at the same time providing adramatic reduction in computational effort is indicated.
Abstract: This paper presents an improved mixed-integer programming (MIP) model and effective solution strategies for the facility layout problem and is motivated by the work of Meller et al. (1999). This class of problems seeks to determine a least-cost layout of departments having various size and area requirements within a rectangular building, and it is challenging even for small instances. The difficulty arises from the disjunctive constraints that prevent departmental overlaps and the nonlinear area constraints for each department, which existing models have failed to approximate with adequate accuracy. We develop several modeling and algorithmic enhancements that are demonstrated to produce more accurate solutions while also decreasing the solution effort required. We begin by deriving a novel polyhedral outer approximation scheme that can provide as accurate a representation of the area requirements as desired. We also design alternative methods for reducing problem symmetry, evaluate the performance of several classes of valid inequalities, explore the construction of partial convex hull representations for the disjunctive constraints, and investigate judicious branching variable selection priority schemes. The results indicate asubstantial increase in the accuracy of the layout produced, while at the same time providing adramatic reduction in computational effort. In particular, three previously unsolved test problems from the literature for which Meller et al.'s algorithm terminated prematurely after 24 cpu hours of computation (on a SUN Ultra 2 workstation with 390 MB RAM) with respective optimality gaps of 10.14%, 26.45%, and 40%, have been solved to exact optimality with reasonable effort using our proposed approach.
TL;DR: This work considers a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic, and proposes a simple policy, called ( s, k, S), which works extremely well and is very easy to compute.
Abstract: We consider a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic. The deterministic demand must be met immediately in each period. However, the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales. At each decision epoch, one has to decide not only whether an order should be placed and how much to order, but also how much demand to fill from the stochastic source. The firm has the option to ration inventory to the stochastic source (i.e., not satisfy all customer demand even though there is inventory in the system).We first characterize the structure of the optimal policy. We show that, in general, the optimal order quantity and rationing policy are state dependent and do not have a simple structure. We then propose a simple policy, called ( s, k, S) policy, wheres andS (ordering policy) determine when and how much to order, whilek (rationing policy) specifies how much of the stochastic demand to satisfy. We report the results of a numerical study, which shows that this simple policy works extremely well and is very easy to compute.
TL;DR: The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.
Abstract: In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.
TL;DR: This work presents an extended crew pairing model that integrates crew scheduling and maintenance routing decisions and discusses how to solve the model both heuristically and to optimality, providing the user with the flexibility to trade off solution time and quality.
Abstract: Crew costs are the second-largest operating expense faced by the airline industry, after fuel. Thus, even a small improvement in the quality of a crew schedule can have significant financial impact. Decisions made earlier in the airline planning process, however, can reduce the number of options available to the crew scheduler. We address this limitation by delaying some of these earlier planning decisions--specifically, key maintenance routing decisions--and incorporating them within the crew scheduling problem. We present anextended crew pairing model that integrates crew scheduling and maintenance routing decisions. We prove theoretical results that allow us to improve the tractability of this model by decreasing the number of variables needed and by relaxing the integrality requirement of many of the remaining variables. We discuss how to solve the model both heuristically and to optimality, providing the user with the flexibility to trade off solution time and quality. We present a computational proof-of-concept to support the tractability and effectiveness of our approach.
TL;DR: This work develops recourse approximation schemes representing different decentralization schemes, which vary in information requirements and complexity and shows that it is possible to arrive at near optimal solutions with information decentralization while using a fraction of the computer time.
Abstract: We study strategic capacity planning in the semiconductor industry. Working with a major US semiconductor manufacturer on the configuration of their worldwide production facilities, we identify two unique characteristics of this problem as follows: (1) wafer demands and manufacturing capacity are both main sources of uncertainty, and (2) capacity planning must consider the distinct viewpoints from marketing and manufacturing. We formulate a multi-stage stochastic program with demand and capacity uncertainties. To reconcile the marketing and manufacturing perspectives, we consider a decomposition of the planning problem resembling decentralized decision-making. We develop recourse approximation schemes representing different decentralization schemes, which vary in information requirements and complexity. We show that it is possible to arrive at near optimal solutions (within 6.5%) with information decentralization while using a fraction (16.2%) of the computer time.
TL;DR: This work analyzes an assemble-to-order system with stochastic leadtimes for component replenishment as a set of queues driven by a common, multiclass batch Poisson input, and derives the joint queue-length distribution.
Abstract: We study an assemble-to-order system with stochastic leadtimes for component replenishment. There are multiple product types, of which orders arrive at the system following batch Poisson processes. Base-stock policies are used to control component inventories. We analyze the system as a set of queues driven by a common, multiclass batch Poisson input, and derive the joint queue-length distribution. The result leads to simple, closed-form expressions of the first two moments, in particular the covariances, which capture the dependence structure of the system. Based on the joint distribution and the moments, we derive easy-to-compute approximations and bounds for the order fulfillment performance measures. We also examine the impact of demand and leadtime variability, and investigate the value of advance demand information.
TL;DR: A canonical setting that illustrates the need for explicitly modeling interactions between manufacturing and marketing/sales decisions in a firm is presented and it is proved that the optimal sales plan is indeed of the "build-up" type.
Abstract: In this paper we present a canonical setting that illustrates the need for explicitly modeling interactions between manufacturing and marketing/sales decisions in a firm. We consider a firm that sells an innovative product with a given market potential. The firm may not be able to meet demand due to capacity constraints. For such firms, we present a new model of demand, modified from the original model of Bass, to capture the effect of unmet past demand on future demand. We use this model to find production and sales plans that maximize profit during the lifetime of the product in a firm with a fixed production capacity. We conduct an extensive numerical study to establish that the trivial, myopic sales plan that sells the maximal amount possible at each time instant is not necessarily optimal. We show that a heuristic "build-up" policy, in which the firm does not sell at all for a period of time and builds up enough inventory to never lose sales once it begins selling, is a robust approximation to the optimal policy. Specializing to a lost-sales setting, we prove that the optimal sales plan is indeed of the "build-up" type. We explicitly characterize the optimal build-up period and analytically derive the optimal initial inventory and roll-out delay. Finally, we show that the insights obtained in the fixed capacity case continue to hold when the firm is able to dynamically change capacity.
TL;DR: This paper develops a fast, linear-programming-based, approximation scheme that exploits the decomposable structure and is guaranteed to produce feasible solutions for a stochastic capacity expansion problem.
Abstract: Planning for capacity expansion forms a crucial part of the strategic-level decision making in many applications. Consequently, quantitative models for economic capacity expansion planning have been the subject of intense research. However, much of the work in this area has been restricted to linear cost models and/or limited degree of uncertainty to make the problems analytically tractable. This paper addresses a stochastic capacity expansion problem where the economies-of-scale in expansion costs are handled via fixed-charge cost functions, and forecast uncertainties in the problem parameters are explicitly considered by specifying a set of scenarios. The resulting formulation is a multistage stochastic integer program. We develop a fast, linear-programming-based, approximation scheme that exploits the decomposable structure and is guaranteed to produce feasible solutions for this problem. Through a probabilistic analysis, we prove that the optimality gap of the heuristic solution almost surely vanishes asymptotically as the problem size increases.
TL;DR: Two classes of optimization models to maximize revenue in a restaurant (while controlling average waiting time as well as perceived fairness) that may violate the first-come-first-serve (FCFS) rule are developed.
Abstract: We develop two classes of optimization models to maximize revenue in a restaurant (while controlling average waiting time as well as perceived fairness) that may violate the first-come-first-serve (FCFS) rule. In the first class of models, we use integer programming, stochastic programming, and approximate dynamic programming methods to decide dynamically when, if at all, to seat an incoming party during the day of operation of a restaurant that does not accept reservations. In a computational study with simulated data, we show that optimization-based methods enhance revenue relative to the industry practice of FCFS by 0.11% to 2.22% for low-load factors, by 0.16% to 2.96% for medium-load factors, and by 7.65% to 13.13% for high-load factors, without increasing, and occasionally decreasing, waiting times compared to FCFS. The second class of models addresses reservations. We propose a two-step procedure: Use a stochastic gradient algorithm to decide a priori how many reservations to accept for a future time and then use approximate dynamic programming methods to decide dynamically when, if at all, to seat an incoming party during the day of operation. In a computational study involving real data from an Atlanta restaurant, the reservation model improves revenue relative to FCFS by 3.5% for low-load factors and 7.3% for high-load factors.
TL;DR: The paper presents several structural properties of the problem and develops a polynomial time algorithm for computing the optimal solution, applicable in the general context of coordinating inventory and outbound transportation decisions.
Abstract: This paper presents a model for computing the parameters of an integrated inventory replenishment and outbound dispatch scheduling policy under dynamic demand considerations The optimal policy parameters specify (i) how often and in what quantities to replenish the stock at an upstream supply chain member (eg, a warehouse), and (ii) how often to release an outbound shipment to a downstream supply-chain member (eg, a distribution center) The problem is represented using a two-echelon dynamic lot-sizing model with pre-shipping and late-shipping considerations, where outbound cargo capacity constraints are considered via a stepwise cargo cost function Although the paper is motivated by a third-party warehousing application, the underlying model is applicable in the general context of coordinating inventory and outbound transportation decisions The problem is challenging due to the stepwise cargo cost structure modeled The paper presents several structural properties of the problem and develops a polynomial time algorithm for computing the optimal solution
TL;DR: This work considers a queueing system, commonly found in inbound telephone call centers, that processes two types of work, and determines the structure of effective routing policies that are optimal within the class of priority policies.
Abstract: We consider a queueing system, commonly found in inbound telephone call centers, that processes two types of work. Type-H jobs arrive at rate ? H , are processed at rate I»i¾µ H, and are served first come, first served within class. Aservice-level constraint of the form E[delay] = a orP {delay = I²} = limits the delay in queue that these jobs may face. An infinite backlog of type-L jobs awaits processing at rate I»L , and there is no service-level constraint on this type of work. A pool ofc identical servers processes all jobs, and a system controller must maximize the rate at which type-L jobs are processed, subject to the service-level constraint placed on the type-H work.We formulate the problem as a constrained, average-cost Markov decision process and determine the structure of effective routing policies. When the expected service times of the two classes are the same, these policies are globally optimal, and the computation time required to find the optimal policy is about that required to calculate the normalizing constant for a simpleM/M/c system. When the expected service times of the two classes differ, the policies are optimal within the class of priority policies, and the determination of optimal policy parameters can be determined through the solution of a linear program with O( c3) variables and O( c2) constraints.
TL;DR: This paper revisits the serial multiechelon inventory system of Clark and Scarf and extends the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times and autocorrelation on the performance of the serial inventory system.
Abstract: Since Clark and Scarf's pioneering work, most advances in multiechelon inventory systems have been based on demand processes that are time independent. This paper revisits the serial multiechelon inventory system of Clark and Scarf and develops three key results. First, we provide a simple lower-bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of Clark and Scarf. Second, we show that the structure of the optimal stocking policy of Clark and Scarf holds under time-correlated demand processes using a Martingale model of forecast evolution. Third, we extend the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times and autocorrelation on the performance of the serial inventory system.
TL;DR: A broadcast scheduling system developed for a precision marketing firm specialized in location-sensitive permission-based mobile advertising using SMS (Short Message Service) text messaging is described, which significantly reduced the time required to schedule the broadcasts, and resulted both in increased customer response and revenues.
Abstract: We describe a broadcast scheduling system developed for a precision marketing firm specialized in location-sensitive permission-based mobile advertising using SMS (Short Message Service) text messaging. Text messages containing advertisements were sent to registered customers when they were shopping in one of two shopping centers in the vicinity of London. The ads typically contained a limited-time promotional offer. The company's problem was deciding which ads to send out to which customers at what particular time, given a limited capacity of broadcast time slots, while maximizing customer response and revenues from retailers paying for each ad broadcast. We solved the problem using integer programming with an interface in Microsoft Excel. The system significantly reduced the time required to schedule the broadcasts, and resulted both in increased customer response and revenues.
TL;DR: The value of a tight upper bound on the achievable capacity is deduced by equating the capacity of the queueing network model with that of a limiting deterministic fluid model.
Abstract: This paper is concerned with the design of dynamic server assignment policies that maximize the capacity of queueing networks with flexible servers. Flexibility here means that each server may be capable of performing service at several different classes in the network. We assume that the interarrival times and the service times are independent and identically distributed, and that routing is probabilistic. We also allow for server switching times, which we assume to be independent and identically distributed. We deduce the value of a tight upper bound on the achievable capacity by equating the capacity of the queueing network model with that of a limiting deterministic fluid model. The maximal capacity of the deterministic model is given by the solution to a linear programming problem that also provides optimal allocations of servers to classes. We construct particular server assignment policies, called generalized round-robin policies, that guarantee that the capacity of the queueing network will be arbitrarily close to the computed upper bound. The performance of such policies is studied using numerical examples.
TL;DR: In this paper, a periodic review inventory system with fast and slow delivery modes, fixed ordering cost, and regular demand forecast updates is considered, and a forecast-update-dependent ( s,S)-type policy is shown to be optimal.
Abstract: This paper is concerned with a periodic review inventory system with fast and slow delivery modes, fixed ordering cost, and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current period and at the end of the next period, respectively. A forecast-update-dependent ( s,S)-type policy is shown to be optimal. Also shown are some monotonicity properties of the policy parameters with respect to the costs and information updates.