Stochastic Hierarchical Multimodal Hub Location Problem for Cargo Delivery Systems: Formulation and Algorithm

Abstract

This study aims at developing a stochastic hierarchical multimodal hub location modeling framework for cargo delivery systems to capture uncertainty in hub construction cost and travel time at the strategic level. From a ring-star-star type network design perspective, a stochastic model is established to formulate this problem formally via the expected value and chance-constrained programming techniques. In particular, three types of chance constraints are proposed to ensure that the on-time delivery with prespecified confidence levels in their respective layer networks. For normal distributions, the original stochastic model can be reformulated as a crisp equivalent mixed-integer linear programming (MILP) model by invoking the central limit theorem. Since the number of constraints and variables increases drastically with the size of cargo delivery distribution network, a memetic algorithm (MA) is designed. This algorithm incorporates genetic search and local intensification to obtain optimal/near-optimal solutions for realistic instance size within a reasonable time limit. For general distributions, it is difficult to convert the stochastic model into its deterministic counterpart. Hence, a hybrid methodology is further designed by combining the MA and Monte Carlo (MC) simulation to solve the proposed stochastic model. To demonstrate the properties of the proposed model and the performance of the designed algorithm, a series of numerical experiments are set up based on the Civil Aeronautics Board (CAB) and Turkish network data sets. Computational results indicate as the confidence level increases, the airport hubs are located further apart in the cargo delivery distribution network for gaining a greater time advantage. In addition, comparative results demonstrate that the MA algorithm proposed herein performs better than the genetic algorithm (GA) in terms of computing speed and quality of the solution. INDEX TERMS Hierarchical multimodal hub location, cargo delivery systems, stochastic programming, mixed-integer linear programming, memetic algorithm, Monte Carlo simulation.

Optimization of the Collaborative Hub Location Problem with Metaheuristics

“…At the same time, Özgün-Kibiro glu et al [42] suggested a mixed integer nonlinear programming (MINLP) formulation to solve an uncapacitated multiple allocation hub location problem (UMAHLP) using a PSO algorithm, which was applied to effectively solve the model. In addition, a HLP was studied by Shang et al [43] with a stochastic programming model formulated in MILP to minimize distribution and opening costs. Due to the complexity of the computation, a memetic algorithm (MA) was introduced to solve the considered problem.…”

“…The reviewed studies are summarized in Table 1. Single ACO [28] CSApHLP Single Hm 1 Single GA [27] USAp-HLP Single Hm 1 Single GVNS [29] CMAp-HLP Single Hm 1 Single GA [30] USAp-HLP Single Hm 1 Single GA-LS [31] USAp-HLP Single Hm Single SA [40] USAp-HLP Multiple Hm 1 Single GA, SA [41] USAp-HLP Single Hm 1 Single GA [42] UMAHLP Single Hm 1 Single PSO [43] USAp-HLP Single Hm 1 Single MA [45] USAp-HLP Single Hm 1 Single GA [44] SAp-HLP Multiple Hm From this table, we can see that, in most of the studies dealing with HLP, the objective function of the proposed metaheuristics was to minimize logistics costs (transportation, storage, opening, etc.). However, none of these research works considered the three sustainability levels when designing the distribution networks and not all introduced models were flexible in terms of the delivery time.…”

Uncertain Programming Models for Sustainable Hub Covering Location Problem Over Incomplete Network

“…airline planning [12], [13] and telecommunication network design [14]. For more details of the current progress, interested readers may refer to [15].…”

The Optimization of the Location of the Cargo in Three-Dimension Shelf: Employing the FP-Tree and the Artificial Fish Swarm Algorithms

“…Haoxiang et al [13] put forward an adaptive multiobjective genetic algorithm aiming at reaching the highest efficacy and shelf stability for the efficiency of warehousing. Shang et al [14] proposed a memetic algorithm incorporating both genetic search and local intensification to attain an optimal/near-optimal solution for realistic sizes within a reasonable period. It was observed that the distribution network size of cargo delivery amplifies when the number of constraints and variables increases drastically.…”