The Minimum Step Linkage Algorithm and Cumulative Cost Model for Time-Dependent Shortest Paths

2016 ◽  
Vol 20 (6) ◽  
pp. 962-975 ◽  
Author(s):  
Vini Indriasari ◽  
Denis Dean
Keyword(s):  
Cost Model ◽  
Shortest Paths ◽  
Time Dependent ◽  
Linkage Algorithm ◽  
Cumulative Cost ◽  
Cumulative Cost Model

scholarly journals Estimating the economic life of forest machinery using the cumulative cost model and cost minimization model in Iranian Caspian forests

2018 ◽  
Vol 64 (No. 5) ◽  
pp. 216-223 ◽  
Author(s):  
Hejazian Mohammad ◽  
Lotfalian Majid ◽  
Limaei Soleiman Mohammadi
Keyword(s):  
Life Cycle ◽  
Cost Minimization ◽  
Cost Model ◽  
Life Cycle Costing ◽  
Economic Life ◽  
Cumulative Cost ◽  
Cumulative Cost Model ◽  
The Cost ◽  
Costing Analysis

This study was conducted in order to estimate the economic life of two models of rubber-tired skidders, namely Timberjack 450C and HSM 904, in Iranian Caspian forests. The total annual costs and average cumulative cost of skidders were calculated by life-cycle costing analysis. The economic life of the machines was estimated by both the cumulative cost model and cost minimization model. The results indicated that the economic life of Timberjack 450C and HSM 904 is 7,700 h (at the end of the 11<sup>th</sup> year) and 15,300 h (at the end of the 17<sup>th</sup> year), respectively, using the cost minimization model. Furthermore, the results indicated that the economic life of Timberjack 450C and HSM 904 is 9,100 h (at the end of the 13<sup>th</sup> year) and 11,900 h (at the end of the 21<sup>st</sup> year), respectively, using the cumulative cost model. The cumulative cost model estimated the economic life of skidders longer than the cost minimization model.

scholarly journals Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Christoph Hansknecht ◽  
Imke Joormann ◽  
Sebastian Stiller
Keyword(s):  
Column Generation ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Valid Inequalities ◽  
Shortest Paths ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Full Generality ◽  
Branching Rule ◽  
The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

Shortest paths in piecewise continuous time-dependent networks

2008 ◽  
Vol 36 (6) ◽  
pp. 688-691 ◽  
Author(s):  
M. Dell’Amico ◽  
M. Iori ◽  
D. Pretolani
Keyword(s):  
Continuous Time ◽  
Shortest Paths ◽  
Time Dependent ◽  
Piecewise Continuous

The Constrained Reliable Shortest Path Problem in Stochastic Time-Dependent Networks

2021 ◽  
Author(s):  
Matthias Ruß ◽  
Gunther Gust ◽  
Dirk Neumann
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Stochastic Time

Finding Shortest Paths That Are Reliable and Satisfy Constraints on Time-Dependent Weights

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