Analytic solution for the nucleolus of a three-player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large-scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed-form) for a three-player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions

The retail space-exchange problem with pricing and space allocation decisions

We consider retail space-exchange problems where two retailers exchange shelf space to increase accessibility to more of their consumers in more locations without opening new stores. Using the Hotelling model, we find two retailers’ optimal prices, given their host and guest space in two stores under the space-exchange strategy. Next, using the optimal space-dependent prices, we analyze a non-cooperative game, where each retailer makes a space allocation decision for the retailer\u27s own store. We show that the two retailers will implement such a strategy in the game, if and only if their stores are large enough to serve more than one-half of their consumers. Nash equilibrium for the game exists, and its value depends on consumers’ utilities and trip costs as well as the total available space in each retailer\u27s store. Moreover, as a result of the space-exchange strategy, each retailer\u27s prices in two stores are both higher than the retailer\u27s price before the space exchange, but they may or may not be identical

Dynamic Allocation of Airline Check-in Counters: A Queueing Optimisation Approach

Published version made available in SMU repository with permission of INFORMS, 2014, February 28</p

Event-based allocation of airline check-in counters: A simple dynamic optimization method supported by empirical data

Ministry of Education, Singapore under its Academic Research Funding Tier

Interactive operations research with Maple: methods and models

Interactive Operations Research with Maple: Methods and Models has two ob­ jectives: to provide an accelerated introduction to the computer algebra system Maple and, more importantly, to demonstrate Maple's usefulness in modeling and solving a wide range of operations research (OR) problems. This book is written in a format that makes it suitable for a one-semester course in operations research, management science, or quantitative methods. A nwnber of students in the departments of operations research, management science, oper­ ations management, industrial and systems engineering, applied mathematics and advanced MBA students who are specializing in quantitative methods or opera­ tions management will find this text useful. Experienced researchers and practi­ tioners of operations research who wish to acquire a quick overview of how Maple can be useful in solving OR problems will find this an excellent reference. Maple's mathematical knowledge base now includes calculus, linear algebra, ordinary and partial differential equations, nwnber theory, logic, graph theory, combinatorics, statistics and transform methods. Although Maple's main strength lies in its ability to perform symbolic manipulations, it also has a substantial knowledge of a large nwnber of nwnerical methods and can plot many different types of attractive-looking two-dimensional and three-dimensional graphs. After almost two decades of continuous improvement of its mathematical capabilities, Maple can now boast a user base of more than 300,000 academics, researchers and students in different areas of mathematics, science and engineering