Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.Comment: 11 pages, 2 tables; v3: minor revisions, to appear in Journal of Global Optimizatio

Preemptive scheduling on identical parallel machines subject to deadlines

We consider the problem of scheduling n preemptive jobs with deadlines on in identical parallel machines so as to minimize total completion time. We show that the problem is polynomially solvable when the processing times and deadlines are agreeable

Parallel machine scheduling to minimize total cost functions

Ph.D. - Doctoral Progra

An airport gate reassignment problem with gate closures

In this study, we consider an airport gate reassignment problem where an airport has assigned gates to aircraft, but then a disruption occurs at some of the gates. After the disruption, we need to reassign the aircraft to the gates while taking into account both efficiency and stability measures. For efficiency, we want to use the gates as much as possible, considering both the number of aircraft and the number of passengers in these aircraft. For stability, we want to stick as closely as possible to the initial plan. We suggest solution procedures for finding two extreme ends of the nondominated objective vectors, all extreme supported nondominated objective vectors, and all nondominated objective vectors with respect to our efficiency and stability measures. An optimal decomposition rule is presented to simplify the complexity of the solution. Our extensive experiments have shown that our optimization procedures can handle the instances with up to 150 aircraft and 40 gates, and approximation algorithms can handle the instances with up to 200 aircraft and 40 gates.</p

A resource investment problem with time/resource trade-offs

In this study, we consider a Resource Investment Problem with time/resource trade-offs in project networks. We assume that there is a single renewable resource and the processing requirement of an activity can be reduced by investing extra resources. Our aim is to minimize the maximum resource usage, hence, the total amount invested for the single resource, while meeting the pre-specified deadline. We formulate the problem as a mixed integer linear model and find optimal solutions for small-sized problem instances. For large-sized problem instances, we propose a heuristic solution procedure. We develop several lower bounds and use them to evaluate the performance of our heuristic procedure. The results of our computational experiments have revealed the satisfactory behaviour of our optimality properties, lower bounds and heuristic procedure

Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponential-time algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions. Journal of the Operational Research Society (2011) 62, 152-164. doi:10.1057/jors.2009.157 Published online 3 February 201

A Lagrangean relaxation based approach for the capacity allocation problem in flexible manufacturing systems

This study considers the operation assignment and capacity allocation problem in flexible manufacturing systems. A set of operations is selected to be processed and assigned to the machines together with their required tools. The purchase or usage of the required tools incurs a cost. The machines have scarce time and tool magazine capacities. The objective is to maximize the total weight of the assigned operations minus the total tooling costs. We use Lagrangean relaxation approach to obtain upper and lower bounds on the optimal objective function values. The computational experiments show that our approach provides near optimal bounds in reasonable solution times. Journal of the Operational Research Society (2010) 61, 872-877. doi:10.1057/jors.2009.1

Multi-objective integer programming: A general approach for generating all non-dominated solutions

In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical epsilon-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical epsilon-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided

Dynamic programming algorithms for scheduling parallel machines with family setup times

We address the problem of scheduling jobs with family setup times on identical parallel machines to minimize total weighted flowtime. We present two dynamic programming algorithms - a backward algorithm and a forward algorithm - and we identify characteristics of problems where each algorithm is best suited. We also derive two properties that improve the computational efficiency of the algorithms. Scope and purpose While most production schedulers must balance conflicting goals of high system efficiency and timely completion of individual jobs, consideration of this conflict is underdeveloped in the scheduling literature. This paper examines a model that incorporates a fundamental cause of the efficiency/timeliness conflict in practice. We propose solution methodologies and properties of an optimal solution for the purpose of exposing insights that may ultimately be useful in research on more complex models. (C) 2000 Elsevier Science Ltd. All rights reserved. We address the problem of scheduling jobs with family setup times on identical parallel machines to minimize total weighted flowtime. We present two dynamic programming algorithms - a backward algorithm and a forward algorithm - and we identify characteristics of problems where each algorithm is best suited. We also derive two properties that improve the computational efficiency of the algorithms