Vehicle routing problem with stochastic travel times including soft time windows and service costs

Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach

“…In this paper, we focus on the mathematical formulation introduced in Taş et al [29]. We first summarize the notation used in this formulation in Table 1.…”

“…Parameter ρ is needed to obtain various combinations of the two main cost components by adjusting their values with scaling parameters C 1 and C 2 . The interested reader is referred to Taş et al [29] for the details about these parameters and their calculations.…”

“…In our study, we optimally solve this model which provides solutions by placing importance both on efficiency and on reliability. The interested reader is referred to Taş et al [29] for an in-depth discussion about the framework of the model.…”

“…The study conducted in [29] extends existing models, which are generated for stochastic routing problems, by proposing a one-stage formulation in which the objective function copes with time-window violations and expected over-time, and all constraints are linear (see Ando and Taniguchi [1], Russell and Urban [26], and Li et al [23] for existing models). In this formulation, the objective is to minimize the sum of transportation costs and service costs.…”

“…For our problem, we consider the formulation introduced in Taş et al [29] where the authors focus on modeling aspects and on solving the problem effectively with a new solution procedure based on metaheuristics. The study conducted in [29] extends existing models, which are generated for stochastic routing problems, by proposing a one-stage formulation in which the objective function copes with time-window violations and expected over-time, and all constraints are linear (see Ando and Taniguchi [1], Russell and Urban [26], and Li et al [23] for existing models).…”