J. Gromicho

Buffering locations in retail deliveries

Procedia Computer Science, 2019

This research helps a European retailer with its daily goods delivery operations. The challenge i... more This research helps a European retailer with its daily goods delivery operations. The challenge is the limited capacity of the transportation network in the Amsterdam area. This leads to very strict requirements for the delivery routing plans. In order to respond to this challenge both an analytical model and a numerical method are proposed. This method is capable of generating routing plans given all the necessary constraints including the cost structure. The model takes into account all incurred costs such as mileage, unsatisfied demand and waiting times; they all are weighted according to their relative importance. Furthermore, in order to reduce waiting times, buffering locations within the Amsterdam area are considered where a truck can park and wait until the loading zone at a store becomes available. The numerical method is approximate in nature and is based on the Column Generation technique. This technique allows iterative explorations of the search space by adding new promising one-truck routes (columns). The Regret construction heuristic is applied to generate an initial solution. New promising columns are generated by means of solving the Pricing Sub-problem which takes into account the duals of the Master problem relaxation. The analysis demonstrates that the buffers help to reduce the waiting times incurred by early arrivals without any drop in the total solution costs. Furthermore, a method is proposed to verify the usefulness of different buffering locations in the model.

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New branch and bound approaches for truss topology design with discrete areas

An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm

Recent Advances in Nonsmooth Optimization, 1995

A deep cut ellipsoid algorithm and quasiconvex programming

Lecture Notes in Economics and Mathematical Systems, 1994

ABSTRACT We describe a deep cut version of the ellipsoid algorithm and introduce a class of funct... more ABSTRACT We describe a deep cut version of the ellipsoid algorithm and introduce a class of functions and their corresponding finite dimensional optimization problems to which it can be applied. Moreover, we show that an important subset of the quasiconvex functions belong to the above mentioned class.

Duality theory for convex/quasiconvex functions and its application to optimization

Lecture Notes in Economics and Mathematical Systems, 1994

In this paper an intuitive and geometric approach is presented explaining the basic ideas of conv... more In this paper an intuitive and geometric approach is presented explaining the basic ideas of convex/quasiconvex analysis and its relation to duality theory. As such, this paper does not contain new results but serves as a hopefully easy introduction to the most important results in duality theory for convex/quasiconvex functions on locally convex real topological vector spaces. Moreover, its connection to optimization is also discussed.

Fractional location problems

Location Science, 1997

In this paper we analyze some variants of the classical uncapacitated facility location problem w... more In this paper we analyze some variants of the classical uncapacitated facility location problem with a ratio as an objective function. Using basic concepts and results of fractional programming, we identify a class of one-level fractional location problems which can be solved in polynomial time in terms of the size of the problem. We also consider the fractional two-echelon location problem, which is a special case of the general two-level fractional location problem. For this two-level fractional location problem we identify cases for which its solution involves decomposing the problem into several one-level fractional location problems.

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Exponentially better than brute force: solving the jobshop scheduling problem optimally by dynamic programming

Scheduling problems received substantial attention during the last decennia. The job-shop problem... more Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on job-shop scheduling problem includes several approximation and optimal algorithms. So far, no algorithm is known which solves the job-shop scheduling problem optimally with a lower complexity than the exhaustive enumeration of all feasible solutions. We propose such an algorithm, based on the well-known Bellman equation designed by Held and Karp to find optimal sequences and which offers the best complexity to solve the Traveling Salesman Problem known to this date. For the TSP this means O(n 2 2 n) which is exponentially better than O(n!) required to evaluate all feasible solutions. We reach similar results by first recovering the principle of optimality, which is not obtained for free in the case of the job-shop scheduling problem, and by performing a complexity analysis of the resulting algorithm. Our analysis is conservative but nevertheless exponentially better than brute force. We also show very promising results obtained from our implementation of this algorithm, which seem to indicate two things: firstly that there is room for improvement in the complexity analysis (we observe the generation of a number of solutions per state for the benchmark instances considered which is orders of magnitude lower than the bound we could devise) and secondly that the potential practical implications of this approach are at least as exciting as the theoretical ones, since we manage to solve some celebrated benchmark instances in processing times ranging from seconds to minutes.

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Visual and interactive meeting planning (Planificação Visual e Interactiva de Reuniões PLAVIR)

ABSTRACT : In schools where the classes are given by several teachers the scheduling of regular t... more ABSTRACT : In schools where the classes are given by several teachers the scheduling of regular teachers&#39; meetings without overlapping can be a difficult task. Therefore a Decision Support System was developed to help this planning. The system is very flexible and user-friendly. Starting with an efficient and fast graph colouring heuristic solution it allows the user to make all the local adjustments that he wishes. The system also suggests to the user good ways of changing the current solution according to his own criteria but leaving the final decision to him. The system has been tested in several Portuguese high schools with success due mainly to the fast and absolutely error free way of finding good schedules.

A Network Airline Revenue Management Framework Based on Decomposition by Origins and Destinations

Transportation Science, 2014

We propose a framework for solving airline revenue management problems on large networks, where t... more We propose a framework for solving airline revenue management problems on large networks, where the main concern is to allocate the flight leg capacities to customer requests under fixed class fares. This framework is based on a mathematical programming model that decomposes the network into origin-destination pairs so that each pair can be treated as a single flight-leg problem. We first discuss that the proposed framework is quite generic in the sense that not only several well-known models from the literature fit into this framework, but also many single flight-leg models can be easily extended to a network setting through the prescribed construction. Then, we analyze the structure of the overall mathematical programming model and establish its relationship with other models frequently used in practice. The application of the proposed framework is illustrated through two examples based on static and dynamic single-leg models, respectively. These illustrative examples are then ben...

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General models in min-max continous location: Theory and solution techniques

Journal of Optimization Theory and Applications, 1996

In this paper, a class of min-max continuous location problems is discussed. After giving a compl... more In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of the stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented. Key Words. Location theory, min-max programming, ellipsoid algorithm, quasiconvexity. ~The work of the second author was supported by JNICT (Portugal), under Contract BD/ 631/90-RM, during his stay at Erasmus University in Rotterdam. 2The authors would like to thank the anonymous referees for simplifying the proofs in the first part of Section 2 and for their constructive remarks improving the presentation.

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Solving the job-shop scheduling problem optimally by dynamic programming

Computers & Operations Research, 2012

Scheduling problems received substantial attention during the last decennia. The job-shop problem... more Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on job-shop scheduling problem includes several approximation and optimal algorithms. So far, no algorithm is known which solves the job-shop scheduling problem optimally with a lower complexity than the exhaustive enumeration of all feasible solutions. We propose such an algorithm, based on the well-known Bellman equation designed by Held and Karp to find optimal sequences and which offers the best complexity to solve the Traveling Salesman Problem known to this date. For the TSP this means O(n 2 2 n) which is exponentially better than O(n!) required to evaluate all feasible solutions. We reach similar results by first recovering the principle of optimality, which is not obtained for free in the case of the job-shop scheduling problem, and by performing a complexity analysis of the resulting algorithm. Our analysis is conservative but nevertheless exponentially better than brute force. We also show very promising results obtained from our implementation of this algorithm, which seem to indicate two things: firstly that there is room for improvement in the complexity analysis (we observe the generation of a number of solutions per state for the benchmark instances considered which is orders of magnitude lower than the bound we could devise) and secondly that the potential practical implications of this approach are at least as exciting as the theoretical ones, since we manage to solve some celebrated benchmark instances in processing times ranging from seconds to minutes.

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An integrated approach to single-leg airline revenue management: The role of robust optimization

Abstract: In this paper we introduce robust versions of the classical static and dynamic single l... more Abstract: In this paper we introduce robust versions of the classical static and dynamic single leg seat allocation models as analyzed by Wollmer, and Lautenbacher and Stidham, respectively. These robust models take into account the inaccurate estimates of the underlying probability distributions. As observed by simulation experiments it turns out that for these robust versions the variability compared to their classical counter parts is considerably reduced with a negligible decrease of average revenue.

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Application of selection hyper-heuristics to the simultaneous optimisation of turbines and cabling within an offshore windfarm

Renewable Energy

Fractional location problems

by Hans J B G Frenk and J. Gromicho

Location Science, 1997

In this paper we analyze some variants of the classical uncapacitated facility location problem w... more In this paper we analyze some variants of the classical uncapacitated facility location problem with a ratio as an objective function. Using basic concepts and results of fractional programming, we identify a class of one-level fractional location problems which can be solved in polynomial time in terms of the size of the problem. We also consider the fractional two-echelon location problem, which is a special case of the general two-level fractional location problem. For this two-level fractional location problem we identify cases for which its solution involves decomposing the problem into several one-level fractional location problems. 0 1997 Elsevier Science Ltd. All rigkts reserved

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A unified race algorithm for offline parameter tuning

Proceedings of the Winter Simulation Conference 2014, 2014

Exact Solution of Multiple Traveling Salesman Problems

Combinatorial Optimization, 1992

A Network Airline Revenue Management Framework Based on Decomposition by Origins and Destinations

by Hans J B G Frenk and J. Gromicho

Transportation Science, 2013

We propose a framework for solving airline revenue management problems on large networks. This fr... more We propose a framework for solving airline revenue management problems on large networks. This framework is based on a mathematical programming model that decomposes the network into origin-destination pairs so that each pair can be treated as a single flight leg problem. We first discuss that the proposed framework is quite generic in the sense that not only several well-known models from the literature fit into this framework but also many single flight leg models can be easily extended to a network setting through the prescribed construction. Then, we formally analyze the structure of the overall mathematical programming model and establish its relationship with other models frequently used in practice. The application of the proposed framework is illustrated through two examples based on static and dynamic single-leg models, respectively. These illustrative examples are then benchmarked against several existing methods on a set of real-life network problems acquired from a major European airline.

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A deep cut ellipsoid algorithm for convex programming: Theory and applications

Mathematical Programming, 1994

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of ... more This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algoritbm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min-max stochastic queue location problem are reported.

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General models in min-max continous location: Theory and solution techniques

by Hans J B G Frenk and J. Gromicho

Journal of Optimization Theory and Applications, 1996

In this paper, a class of min-max continuous location problems is discussed. After giving a compl... more In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of the stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented.

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General models in min-max planar location: Checking optimality conditions

Journal of Optimization Theory and Applications, 1996

This paper studies the problem of deciding whether the present iteration point of some algorithm ... more This paper studies the problem of deciding whether the present iteration point of some algorithm applied to a planar singlefacility min-max location problem, with distances measured by either an/:norm or a polyhedral gauge, is optimal or not. It turns out that this problem is equivalent to the decision problem of whether 0 belongs to the convex hull of either a finite number of points in the plane or a finite number of different/q-circles_ R 2. Although both membership problems are theoretically solvable in polynomial time, the last problem is more difficult to solve in practice than the first one. Moreover, the second problem is solvable only in the weak sense, i.e., up to a predetermined accuracy. Unfortunately, these polynomial-time algorithms are not practical. Although this is a negative result, it is possible to construct an efficient and extremely simple linear-time algorithm to solve the first problem. Moreover, this paper describes an implementable procedure to reduce the second decision problem to the first with any desired precision. Finally, in the last section, some computational results for these algorithms are reported.

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