In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem that requires an exponential number of variables, corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints. Different relaxations of the above formulation are used to derive new lower bounds, which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by Stinson et al. (1978). A tree search algorithm, based on the above formulation, that uses new lower bounds and dominance criteria is also presented. Computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature.Project Scheduling, Branch-and-Bound Methods, Networks/Graphs, Lower Bounds

In this paper, we define and solve the sensor location problem (SLP), that is, we look for the minimum number and location of counting points in order to infer all traffic flows in a transport network. We set up a couple of greedy heuristics that find lower and upper bounds on the number of sensors for a set of randomly generated networks. We prove that solving the SLP implies that the Origin/Destination (O/D) matrix estimation error be always bounded. With respect to alternative sensor location strategies, simulation experiments show that: (i) measurement costs being equal, the O/D estimation error is lower, and (ii) conversely, O/D estimation error being equal, the number of sensors is smaller.

We propose a job-shop scheduling model with sequence dependent set-up times and release dates to coordinate both inbound and outbound traffic flows on all the prefixed routes of an airport terminal area and all aircraft operations at the runway complex. The proposed model is suitable for representing several operational constraints (e.g., longitudinal and diagonal separations in specific airspace regions), and different runway configurations (e.g., crossing, parallel, with or without dependent approaches) in a uniform framework. The complexity and the highly dynamic nature of the problem call for heuristic approaches. We propose a fast dynamic local search heuristic algorithm for the job-shop model suitable for considering one of different performance criteria and embedding aircraft position shifting control technique to limit the controllers/pilots’ workload. Finally, we describe in detail the experimental analysis of the proposed model and algorithm applied to two real case studies of Milan-Malpensa and Rome-\ud Fiumicino airport terminal areas

No abstract

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.

In this paper the n/I/q 2 O / x wjCj problem under the assumptions of nonpreemptive sequencing and sequence independent processing times is investigated. After pointing out the fundamental properties, some dominance sufficient conditions among sequences are obtained and a branch and bound algorithm is proposed. Computational results are reported and discussed.i

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.

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.