First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...

We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) ...

We consider a cement delivery problem with an heterogeneous fleet of vehicles and several depots. The demands of the customers are typically larger than the capacity of the vehicles which means that most customers are visited several times. This is a split delivery vehicle routing problem with additional constraints. We first propose a two phase solution method that assigns deliveries to the ve...

Examination Timetable Problem (ETP) is NP–Hard combinatorial optimization problem. It has received tremendous research attention during the past few years given its wide use in universities. ETP can be defined as assignment of courses to be examined, candidates to time periods and examination rooms while satisfying a set of constraints which may be either hard or soft. Several methods have been...

Bayesian networks are a commonly used method of representing conditional probability relationships between a set of variables in the form of a directed acyclic graph (DAG). Determination of the DAG which best explains observed data is an NP-hard problem [1]. This problem can be stated as a constrained optimisation problem using Integer Linear Programming (ILP). This paper explores how the perfo...

The Generalized Vehicle Routing Problem (GVRP) is an extension of the Vehicle Routing Problem (VRP) defined on a graph in which the nodes (customers, vertices) are grouped into a given number of mutually exclusive and exhaustive clusters (nodesets). In this paper, an integer linear programming formulation of the GVRP with O(n 2 ) binary variables and O(n 2 ) constraints is presented. It is show...

for installing a large number of sizes and types of items (e.g., machines) over time so as to optimize some measure (e.g., initial capital investment), subject to various resource constraints. Examples of this problem are scheduling the installation of point-of-sale terminals in supermarket and retail chains, and teller terminals in banks. We have formulated the installation scheduling problem ...

In this paper we consider a packing problem arising in inventory allocation applications, where the operational cost for packing the bins is comparable, or even higher, than the cost of the bins (and of the items) themselves. This is the case, for example, of warehouses that have to manage a large number of different customers (e.g., stores), each requiring a given set of items. For this proble...

bilevel linear programming  is a decision making problem with a two-level decentralized organization. the textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. making a decision at one level affects that at the other one. in this paper, bilevel linear programming  with inexact parameters has been studied and a method is...