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{r|r = 1, 2,…, M + N} Set of depots and customers nodes.
Also, the potential locations for depots and treatment facilities are given (i.e., the set of depots and treatment facilities must be chosen from these potential locations).
In this network, the set of depots (e.g., P depots) are considered as central zones that provide the neighboring zones (current customers or trains) with locomotives.
The problem includes a set of homogeneous locomotives, a set of depots where locomotives are initially located, and a set of pre-scheduled trains with different degrees of priority (e.g., normal passenger trains, high speed trains, freight trains, etc).
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The FSMVRPTW seeks to design a set of depot returning vehicle routes to service a set of customers with known demands, for a heterogeneous fleet of vehicles with different capacities and fixed costs.
The two-echelon location-routing problem (LRP-2E) is raised by the design of transportation networks with two types of trips: first-level trips serving from one main depot a set of satellite depots, to be located, and second-level trips supplying customers from these satellites.
The problem is to determine a set of candidate depots to open, the quantities to ship from suppliers to depots and from depots to retailers per period, and the sequence in which retailers are replenished by an homogeneous fleet of vehicles.
The set of all depots for coalition S m ; The set of all customers for coalition S m ; The set of all vehicles for coalition S m. i The depot index; j The customer index; k The route index; m The coalition index.
(I_{{left[ {S_{m} } right]}}) The set of all depots for coalition S m ; (J_{{left[ {S_{m} } right]}}) The set of all customers for coalition S m ; (K_{{left[ {S_{m} } right]}}) The set of all vehicles for coalition S m.
A two-phase approach is used which, in the first phase, the multi-depot locomotive assignment is converted to a set of single depot problems, and after that, each single depot problem is solved heuristically by a hybrid genetic algorithm.
A two-phase approach was used in which, in the first phase, the multi-depot locomotive assignment was converted to a set of single depot problems, and after that, each single depot problem was solved heuristically by a hybrid genetic algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com