scholarly journals Optimization of the task of forming a management system of hierarchical multilevel complex organizational systems

2021 ◽  
Vol 2094 (3) ◽  
pp. 032034
Author(s):  
A S Zuev ◽  
T E Smolentseva ◽  
R A Isaev
Keyword(s):  
Dynamic Programming ◽  
Initial Approximation ◽  
Organizational Structures ◽  
Traveling Salesman ◽  
Organizational Systems ◽  
Directed Search ◽  
Recursive Procedure ◽  
Combined Application ◽  
Discrete Programming ◽  
The Traveling Salesman Problem

Abstract A hierarchical configuration procedure in the process of analyzing the functioning of organizational structures using algorithms for solving problems using discrete programming methods is considered in detail in this paper. On the basis of the research, the authors propose a methodology for the combined application of an initial approximation algorithm with certain properties and an algorithm for a recursive procedure for a directed search for the optimal hierarchy, which, in the future, solving the traveling salesman problem in a minimum time much more efficient than using the methods of dynamic programming of branches and boundaries.

scholarly journals Dynamic programming approaches for the traveling salesman problem with drone

Networks ◽  
2018 ◽  
Vol 72 (4) ◽  
pp. 528-542 ◽  
Author(s):  
Paul Bouman ◽  
Niels Agatz ◽  
Marie Schmidt
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals Exact Methods for the Traveling Salesman Problem with Drone

2021 ◽  
Vol 55 (2) ◽  
pp. 315-335
Author(s):  
Roberto Roberti ◽  
Mario Ruthmair
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
The State ◽  
Set Partitioning ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Branch And Price ◽  
Last Mile ◽  
The Traveling Salesman Problem

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

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