Quick response policy with Bayesian information updates

In this paper we investigate the quick response (QR) policy with different Bayesian models. Under QR policy, a retailer can collect market information from the sales of a pre-seasonal product whose demand is closely related to a seasonal product’s demand. This information is then used to update the distribution for the seasonal product’s demand by a Bayesian approach. We study two information update models: one with the revision of an unknown mean, and the other with the revision of both an unknown mean and an unknown variance. The impacts of the information updates under both models are compared and discussed. We also identify the features of the pre-seasonal product which can bring more significant profit improvement. We conclude that an effective QR policy depends on a precise information update model as well as a selection of an appropriate pre-seasonal product as the observation target.     

Replenishment Schedule for Deteriorating Items with Time-Proportional Demand

In this paper a heuristic model is presented for determining the ordering schedule when an inventoried item is subject to deterioration and demand changes linearly over time. While the optimizing model developed by researchers fixes the ordering interval and varies the ordering size, the heuristic permits variation in both replenishment-cycle length and the size of the order. As a result, the heuristic produces a better solution than optimizing models in the study presented here.     

A new model for maximal coverage exploiting GIS capabilities

The representation of demand is a key issue which can significantly affect results in several demand covering models. In this paper we concentrate on the well known Maximal Coverage Location Problem and demonstrate that alternative representations of the demand space may lead to largely fluctuating as well as misleading results which seriously overestimate the real coverage achieved by a specified number of servers. We introduce a new model based on the notion of complementary partial coverage and exploit the capabilities of Geographic Information Systems in order to better represent demand. Results of an empirical study indicate that the proposed model is less susceptible to fluctuations for alternative representations of the demand space and that it provides coverage of a larger proportion of demand than traditional models.     

Cellular Network Design Site Selection and Frequency Planning

Deployment of cellular networks involves substantial capital investment. Competition motivates service providers to minimize these costs while maintaining service quality. We develop a cost-minimizing planning model that simultaneously determines three important variables – base station location, power level and frequency group assignments for the antennas at each selected base station. It can represent different antenna configurations and frequency groups commonly used in practice. The integer-programming problem is solved using a Lagrangian relaxation based heuristic and computational tests indicate good solution quality for reasonably large problems. We also note the appropriate role of such optimization models in the overall planning process.     

The multi-hour service system design problem

This paper studies the multi-hour service system design problem that involves locating service facilities, determining their number and capacities and assigning user nodes to those facilities under time varying demand conditions. The goal is to minimize total costs made of the costs of accessing facilities by users and waiting for service at these facilities as well as the cost of setting up and operating the facilities. A unified model is proposed for the problem to exploit the benefits of the non-coincidence of demand across busy-hours. Two Lagrangean relaxation-based heuristic solution procedures are developed and the results of extensive computational experiments are reported.     

Semi-empirical likelihood ratio confidence intervals for the difference of two sample means

We all know that we can use the likelihood ratio statistic to test hypotheses and construct confidence intervals in full parametric models. Recently, Owen (1988,Biometrika,75, 237–249; 1990,Ann. Statist.,18, 90–120) has introduced the empirical likelihood method in nonparametric models. In this paper, we combine these two likelihoods together and use the likelihood ratio to construct confidence intervals in a semiparametric problem, in which one model is parametric, and the other is nonparametric. A version of Wilks's theorem is developed.     

Optimal pricing and advertising in a durable-good duopoly

This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications – linear demand and isoelastic demand – for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.     

A graph-pair representation and MIP-model-based heuristic for the unequal-area facility layout problem

Owing to its theoretical as well as practical significance, the facility layout problem with unequal-area departments has been studied for several decades, with a wide range of heuristic and a few exact solution procedures developed by numerous researchers. In one of the exact procedures, the facility layout problem is formulated as a mixed-integer programming (MIP) model in which binary (0/1) variables are used to prevent departments from overlapping with one another. Obtaining an optimal solution to the MIP model is difficult, and currently only problems with a limited number of departments can be solved to optimality. Motivated by this situation, we developed a heuristic procedure which uses a “graph pair” to determine and manipulate the relative location of the departments in the layout. The graph-pair representation technique essentially eliminates the binary variables in the MIP model, which allows the heuristic to solve a large number of linear programming models to construct and improve the layout in a comparatively short period of time. The search procedure to improve the layout is driven by a simulated annealing algorithm. The effectiveness of the proposed graph-pair heuristic is demonstrated by comparing the results with those reported in recent papers. Possible extensions to the graph-pair representation technique are discussed at the end of the paper.     

Limiting Connection between Discrete and Continuous Time Forward Interest Rate Curve Models

We study discrete time Heath–Jarrow–Morton (HJM) type of interest rate curve models, where the forward interest rates – in contrast to the classical HJM models – are driven by a random field. Our main aim is to investigate the relationship between the discrete time forward interest rate curve model and its continuous time counterpart. We derive a general result on the convergence of discrete time models and we give special focus on the nearly unit root spatial autoregression model.     

Computational experience with general equilibrium problems

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5–10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be suitable to estimate equilibria for very large models.Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

Measure of bullwhip effect in supply chains with autoregressive demand process

In supply chain management, one of the most critical problems which require a lot of effort to deal with is how to quantify and alleviate the impact of bullwhip effect – the phenomenon in which information on demand is distorted while moving upstream. Although it is well established that demand forecast, lead time, order batching, shortage gaming and price fluctuation are the main sources that lead to the bullwhip effect, the problem of quantifying bullwhip effect still remain unsolved in many situations due to the complex nature of the problem. In this research, a measure of bullwhip effect will be developed for a simple two-stage supply chain that includes only one retailer and one supplier in the environment where the retailer employs base stock policy for their inventory and demand forecast is performed through the first-order autoregressive model, AR(1). The effect of autoregressive coefficient and lead time on this measure will then be investigated.     

Aggregation error for location models: survey and analysis

Location problems occurring in urban or regional settings may involve many tens of thousands of “demand points,” usually individual private residences. In modeling such problems it is common to aggregate demand points to obtain tractable models. We survey aggregation approaches to a large class of location models, consider and compare various aggregation error measures, identify some effective (and ineffective) aggregation error measures, and discuss some open research areas.     

Maximum likelihood inference for the Cox regression model with applications to missing covariates

In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B 34 (1972) 187–220; D.R. Cox, Partial likelihood, Biometrika 62 (1975) 269–276] both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.     

On the thermodynamic limit for Hartree–Fock type models

We continue here our study [10–13] of the thermodynamic limit for various models of Quantum Chemistry, this time focusing on the Hartree–Fock type models. For the reduced Hartree–Fock models, we prove the existence of the thermodynamic limit for the energy per unit volume. We also define a periodic problem associated to the Hartree–Fock model, and prove that it is well-posed.     

On solution of a class of equilibrium problems

In the article we discuss the question of reducing the Arrow-Debreu model [1, 2] to a problem of mathematical programming; we also study conditions under which the problem is convex. The interest to the question is aroused by the circumstance that the equilibrium problems turn rather difficult for numeric solution. Two approaches are used most frequently. One is based on the monotonicity property (formulated somehow) of the excessive demand [2–5]. If this property is satisfied, then the corresponding differential system, which has the sought equilibrium at the rest point, appears stable. The other approach consists in constructing the so-called heuristic methods (see, for instance, [6]) which have more or less reasonable grounds but in general do not guarantee that a solution is obtainable.The research was supported by the Russian Foundation for Fundamental Research (Grant 93-012-842).Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 990–999, September–October, 1994.     

Vacation models in discrete time

A class of single server vacation queues which have single arrivals and non-batch service is considered in discrete time. It is shown that provided the interarrival, service, vacation, and server operational times can be cast with Markov-based representation then this class of vacation model can be studied as a matrix–geometric or a matrix-product problem – both in the matrix–analytic family – thereby allowing us to use well established results from Neuts (1981). Most importantly it is shown that using discrete time approach to study some vacation models is more appropriate and makes the models much more algorithmically tractable. An example is a vacation model in which the server visits the queue for a limited duration. The paper focuses mainly on single arrival and single unit service systems which result in quasi-birth-and-death processes. The results presented in this paper are applicable to all this class of vacation queues provided the interarrival, service, vacation, and operational times can be represented by a finite state Markov chain.An erratum to this article can be found at     

A two-warehouse production model for deteriorating inventory items with time-dependent demands

A two-warehouse inventory model for deteriorating items with time-dependent demand has been developed. Compared with previous models, the model involves a free form time-dependent demand and a finite replenishment rate within a finite planning horizon. Rather than the heuristic approach of equal production cycle times adopted by Lee and Ma, an approach which permits variation in production cycle times is adopted to determine the number of production cycles and the times for replenishment during a finite planning horizon. Numerical examples are provided to illustrate the application of the model and the results indicate that the performance of the proposed approach is superior to that of the heuristic approach of Lee and Ma.     

Mixed Integer Programming Approaches to Treatment Planning for Brachytherapy – Application to Permanent Prostate Implants

Mixed integer programming models and computational strategies developed for treatment planning optimization in brachytherapy are described. The problem involves the designation of optimal placement of radioactive sources (seeds) inside a tumor site. Two MIP models are described. The resulting MIP instances are difficult to solve, due in large part to dense constraint matrices with large disparities in the magnitudes of the nonzero entries. A matrix reduction and approximation scheme is presented as a computational strategy for dealing with the dense matrices. Penalty-based primal heuristic and branching strategies to assist in the solution process are also described. Numerical results are presented for 20 MIP instances associated with prostate cancer cases. Compared to currently used computer-aided planning methods, plans derived via the MIP approach use fewer seeds (20–30 fewer) and needles, and provide better coverage and conformity – measures commonly used to assess the quality of treatment plans. Good treatment plans are returned in 15 CPU minutes, suggesting that incorporation of this MIP-based optimization module into a real-time comprehensive treatment planning system is feasible.     

GARCH option pricing: A semiparametric approach

Option pricing based on GARCH models is typically obtained under the assumption that the random innovations are standard normal (normal GARCH models). However, these models fail to capture the skewness and the leptokurtosis in financial data. We propose a new method to compute option prices using a nonparametric density estimator for the distribution of the driving noise. We investigate the pricing performances of this approach using two different risk neutral measures: the Esscher transform pioneered by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1994a. Option pricing by Esscher transforms (with discussions). Trans. Soc. Actuar. 46, 99–91], and the extended Girsanov principle introduced by Elliot and Madan [Elliot, R.J., Madan, D.G., 1998. A discrete time equivalent martingale 9 measure. Math. Finance 8, 127–152]. Both measures are justified by economic arguments and are consistent with Duan’s [Duan, J.-C., 1995. The GARCH option pricing model. Math. Finance 5, 13–32] local risk neutral valuation relationship (LRNVR) for normal GARCH models. The main advantage of the two measures is that one can price derivatives using skewed or heavier tailed innovations distributions to model the returns. An empirical study regarding the European Call option valuation on S&P500 Index shows: (i) under both risk neutral measures our semiparametric algorithm performs better than the existing normal GARCH models if we allow for a leverage effect and (ii) the pricing errors when using the Esscher transform are quite small even though our estimation procedure is based only on historical return data.     

Building and Solving Large-Scale Stochastic Programs on an Affordable Distributed Computing System

We present an integrated procedure to build and solve big stochastic programming models. The individual components of the system – the modeling language, the solver and the hardware – are easily accessible, or a least affordable to a large audience. The procedure is applied to a simple financial model, which can be expanded to arbitrarily large sizes by enlarging the number of scenarios. We generated a model with one million scenarios, whose deterministic equivalent linear program has 1,111,112 constraints and 2,555,556 variables. We have been able to solve it on the cluster of ten PCs in less than 3 hours.