A continuous model for dynamic pricing under costly price modifications

This paper presents a heuristic method to solve a dynamic pricing problem under costly price modifications. This is a remarkably difficult problem that is solvable only under very few special cases. The method is applied to a more general form of the problem and is numerically tested for a variety of demand functions in the literature. The results show that the method is quite accurate, approximating the optimal profit within usually much less than 1\%. A more important result is that the accuracy tend to be much greater as the number of price changes increases, precisely when the underlying optimization problem becomes much harder, which makes this approach particularly desirable

Linear integrated location-inventory models for service parts logistics network design

We present two integrated network design and inventory control problems in service-parts logistics systems. Such models are complicated due to demand uncertainty and highly nonlinear time-based service level constraints. Exploiting unique properties of the nonlinear constraints, we provide an equivalent linear formulation under part-warehouse service requirements, and an approximate linear formulation under part service requirements. Computational results indicate the superiority of our approach over existing approaches in the literature

An integrated model for cash transfer system design problem

This paper presents an integrated model that incorporates strategic, tactical, and operational decisions for a cash transfer management system of a bank. The aim of the model is to decide on the location of cash management centers, number and routes of vehicles, and the cash inventory management policies to minimize the cost of owning and operating a cash transfer system while maintaining a pre-defined service level. Owing to the difficulty of finding optimal decisions in such integrated models, an iterative solution approach is proposed in which strategic, tactical, and operational problems are solved separately via a feedback mechanism. Numerical results show that such an approach is quite effective in reaching greatly improved solutions with just a few iterations, making it a promising approach for similar integrated models

A two-level facility location and sizing problem for maximal coverage

This paper presents a two-stage hierarchical location problem for systems where the lower level facilities act as the first points contact for the customers while the upper level facilities act as suppliers of the lower level facilities that either serve them or provide advanced services to customers. Furthermore, more recent and realistic coverage constructs such as gradual and cooperative covering are included in our setting. Although our problem can be applicable in various settings, the most fitting application is in wireless telecommunication networks to determine the location of base stations and mobile switching centers. We have developed two competing formulations for the problem, each of which involve nonlinear components that are difficult to deal with. We then develop their respective linearizations and tested their performances. These formulations are solved by commercial optimizers for a set of reasonably large problem instances and it is found that majority of the problems can be solved within a maximum of 10% optimality gap within a short time

A continuous approximation method for dynamic pricing problem under costly price modifications

This paper presents a heuristic method to solve a dynamic pricing problem under costly price modifications. This is an extremely difficult nonlinear problem that has been solved only for a few special instances. Here we provide a new approach that involves an approximate reformulation of the problem, which can subsequently be solved in closed-form using elementary calculus techniques. Numerical results show that the approach is quite accurate; approximating the optimal revenue with errors usually much less than 1\%. Moreover, the accuracy rapidly improves as the optimal number of price changes increases, which are precisely the cases conventional approaches would fail

Joint optimization of energy storage sizing and transmission line capacities for an island system

In this work, we present a stochastic mixed-integer programming model to optimize the sizes of two different kinds of energy storage systems and the capacity of the transmission lines for an island system. We consider an island where the main generation source is wind and alternative source is diesel. The primary aim of this study is to investigate the investment decisions in storage and to determine energy capacities and power rates of the storage systems while minimizing the construction, O&M, and diesel costs. By deploying two different storage types at different places, we investigate the circumstances where installation decisions change. Stochastic renewable energy generation and demand are taken into account by considering different scenarios which are reproduced based on real data. First-order Markov chain is used to generate monthly wind power time series. Numerical experiments are conducted to investigate the effect of the cost parameters on the system design

Linear and conic reformulations for the maximum capture location problem under multinomial logit choice

This paper presents three reformulations for the well-known maximum capture location problem under multinomial logit choice. The problem can be cast as an integer fractional program and it has been the subject of several linear reformulations in the past. Here we develop two linear and a conic reformulation based on alternative treatments of fractional programs. Numerical experiments conducted on established sets of instances have shown that conic reformulation has greatly improved the solution times as well as the size of the solvable problems as compared to the most successful reformulations to date

Solving a bi-objective unmanned aircraft system location-allocation problem

In this paper we introduce a bi-objective location-allocation problem for Unmanned Aircraft Systems (UASs) operating in a hostile environment. The objective is to find the locations to deploy UASs and assign Unmanned Aerial Vehicles to regions for surveillance. One of the objectives is to maximize search effectiveness, while the second is the minimization of the threats posed to the UASs. These two objectives are in conflict, because they are affected differently by the proximity between the UAS locations and the target regions. First, we have formulated this problem as a mixed integer nonlinear program. Next, we have developed its linearization which can be solved by a commercial optimizer for small-scale problem instances. To solve large-scale problems, we have adopted a well-known metaheuristic for multi-objective problems, namely the elitist non-dominated sorting genetic algorithm. We have also developed a hybrid approach, which has proven to be more effective than each approach alone