Full-shipload tramp ship routing and scheduling with variable speeds

Abstract

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A multiple ship routing and speed optimization problem under time, cost and environmental objectives

“…The SP model in the H-B&P is solved by CPLEX 12.6. The parameters γ and µ in strong branching were set to 3 4 and 15, as in [27] and [21]. The computational time is limited to 30 minutes.…”

“…Solving model (23)- (26) directly by an IP solver requires the enumeration of all feasible ship routes, which seems impossible given the huge size of feasible routes. Instead, we solve the model by a heuristic branch-and-price algorithm similar to [21]. Branch-and-Price (B&P) is a version of branch-and-bound, where the linear programming (LP) relaxation at each node of the branch-and-bound tree is obtained by using the Column Generation (CG) method ( [22]).…”

Robust and sustainable full-shipload routing and scheduling problem considering variable speed: A real case study

“…In popular methods decision maker (DM) should determine the priority or weight for the objective functions before or after the solution process or interactively. It is important to choose a method that be capable to choose efficient solutions rather that weakly efficient solutions [50]. {Please insert Figure 4 about here} One of the most used methods to achieve efficient Pareto-optimal solutions in MOP is the ɛ -constraint method.…”

Optimization in liner shipping

“…In the context of tramp shipping, Wen et al (2016) solve the simultaneous optimization of routing and sailing speed using a branch-and-price algorithm with heuristic column generation. The real-life test instances are solved to (near) optimality.…”