Salvatore Ricciardelli

Scheduling tasks with sequence-dependent processing times

In this article we consider the problem of minimizing the maximum completion time of a sequence of n jobs on a single machine. Nonzero ready times and sequence-dependent processing times are allowed. Upper bounds, lower bounds, and dominance criteria are proposed and exploited in a branch-and-bound algorithm. Computational results are given.

Dynamic Programming Strategies for the Traveling Salesman Problem with Time Window and Precedence Constraints

The Traveling Salesman Problem with Time Window and Precedence Constraints (TSP-TWPC) is to find an Hamiltonian tour of minimum cost in a graph G = (X, A) of n vertices, starting at vertex 1, visiting each vertex i ∈ X during its time window and after having visited every vertex that must precede i, and returning to vertex 1. The TSP-TWPC is known to be NP-hard and has applications in many sequencing and distribution problems. In this paper we describe an exact algorithm to solve the problem that is based on dynamic programming and makes use of bounding functions to reduce the state space graph. These functions are obtained by means of a new technique that is a generalization of the “State Space Relaxation” for dynamic programming introduced by Christofides et al. (Christofides, N., A. Mingozzi, P. Toth. 1981b. State space relaxation for the computation of bounds to routing problems. Networks 11 145–164.). Computational results are given for randomly generated test problems.

The traveling salesman problem with cumulative costs

In this paper, we consider a special case of the time-dependent traveling salesman problem where the objective is to minimize the sum of all distances traveled from the origin to all other cities. Two exact algorithms, incorporating lower bounds provided by a Lagrangean relaxation of the problem, are presented. We also investigate a heuristic procedure derived from dynamic programming that is able to evaluate the distance from optimality of the produced solution. Computational results for a number of problems ranging from 15 to 60 cities are given. They show that problems up to 35 cities can be solved exactly and problems up to 60 cities can be solved within 3% from optimality.

A heuristic procedure for the crew rostering problem

Abstract This paper deals with the problem of planning work schedules in a given time horizon so as to evenly distribute the workload among the drivers in a mass transit system. An integer programming formulation of this problem is given. An iterative heuristic algorithm is described which makes use of a lower bound derived from the mathematical formulation. Furthermore, the algorithm at each iteration solves a multilevel bottleneck assignment problem for which a new procedure that gives asymptotically optimal solutions is proposed. Computational results for both the rostering problem and the multilevel bottleneck assignment problem are given.

EXACT AND HEURISTIC PROCEDURES FOR THE TRAVELING SALESMAN PROBLEM WITH PRECEDENCE CONSTRAINTS, BASED ON DYNAMIC-PROGRAMMING

AbstractThe Traveling Salesman Problem with Precedence Constraints is to find an hamiltonian tour of minimum cost in a graph G = (X,A) of n vertices, starting from vertex 1, visiting every vertex t...

A set partitioning approach to the multiple depot vehicle scheduling problem

We address the problem of scheduling a fleet of vehicles, stationed in different depots, in such a way to perform a set of time-tabled trips and to minimize a given objective function. We consider the consti that requires each vehicle to return to the starting depot. This problem, known as Multiple Depot V& Scheduling (MD-VSP), is NP-hard. In this paper we formulate the MD-VSP as a Set Partitioning Prot with side constraints (SP). We describe a procedure that, without using the SP matrix, computes a lower bound to the MD-VSP by finding a heuristic solution to the dual of the continuous relaxation of SP. dual solution obtained is used to reduce the number of variables in the SP in such a way that the resu SP problem can be solved by usual branch and bound techniques. The computational results show effectiveness of the proposed method.

A dual ascent procedure for the set partitioning problem

The set partitioning problem is a fundamental model for many important real-life transportation problems, including airline crew and bus driver scheduling and vehicle routing. In this paper we propose a new dual ascent heuristic and an exact method for the set partitioning problem. The dual ascent heuristic finds an effective dual solution of the linear relaxation of the set partitioning problem and it is faster than traditional simplex based methods. Moreover, we show that the lower bound achieved dominates the one achieved by the classic Lagrangean relaxation of the set partitioning constraints. We describe a simple exact method that uses the dual solution to define a sequence of reduced set partitioning problems that are solved by a general purpose integer programming solver. Our computational results indicate that the new bounding procedure is fast and produces very good dual solutions. Moreover, the exact method proposed is easy to implement and it is competitive with the best branch and cut algorithms published in the literature so far.

A simulation model for aircraft sequencing in the near terminal area

Abstract The objective of this study is the development of a simulation model to assist in aircraft sequencing operations in the terminal area. After the definition of the main characteristics of the model, a general structure of a terminal area is considered with a variable number of feeder fixes and alternative paths from the fixes to the runways. The model is designed so as to evaluate different operating policies. A discrete events simulation philosophy, using Fortran as simulation language, is employed. Finally a model application to the Rome terminal area is illustrated. The results obtained show that the model, here presented, is general enough to simulate the terminal area behaviour of any airport.

An Exact Algorithm for Combining Vehicle Trips

We consider a vehicle scheduling problem arising in freight transport systems where a vehicle fleet of different classes, split among different depots, must be used to perform a set of trips over a time period horizon minimizing a given cost function. The set of trips must be partitioned in a number of disjoint sequences (called duties) and each duty must be assigned to a vehicle satisfying time window and vehicle-trip objection constraints. Moreover, a vehicle can perform only one duty and must return to the starting depot. This problem is an extension of a simpler problem known as Multiple Depot Vehicle Scheduling Problem (MD-VSP) that is NP hard.

Partitioning a matrix to minimize the maximum cost

Abstract A matrix A = [ a ij ] of nonnegative integers must be partitioned into p blocks (submatrices) corresponding to a set of vertical cuts parallel to the columns and a set of horizontal cuts parallel to the rows. With each block is associated a cost equal to the sum of its elements. We consider the problem of finding a matrix partitioning that minimizes the cost of the block of maximum cost. In this paper a mathematical formulation of the problem is given and used to derive both exact and heuristic algorithms. Lower bounds and dominance criteria are exploited in a tree search algorithm for finding the optimal solution of the problem. Computational results of the proposed algorithm are given on a number of randomly generated test problems.