Abstract
In the dynamic vehicle routing problem with mixed backhauls (DVRPMB) both pick up orders and delivery orders, not related to each other, are served. The requests of the former arrive dynamically while the latter are known a priori. In this study, we focus on the case of limited fleet, which fulfills all delivery orders, but may not have enough capacity to serve all pick up orders within the available working horizon. The problem’s dynamic nature and the attention to customer service raise interesting considerations, especially related to the problem’s objectives. The problem is solved through periodic re-optimization, acknowledging the fact that this pseudo-dynamic approach may lead to some limitations. For the underlying (static) optimization problem we propose appropriate objective functions, which account for vehicle productivity and propose a branch-and-price (BP) approach to solve it to optimality. The results indicate how the performance of the various objectives is impacted by different re-optimization frequencies and policies in this practically relevant environment of dynamic demand served by a limited fleet. Specifically, extensive experimentation indicates that accounting for vehicle productivity within a typical periodic re-optimization solution framework may result to higher customer service under a range of operational settings, in comparison to conventional objectives.
Highlights
In the dynamic vehicle routing problem with mixed backhauls (DVRPMB) a fleet of vehicles originating from a depot is tasked to serve two types of orders: (i) static orders known prior to the start of operations; and (ii) dynamic pickup orders, which are received in real time and should be collected and returned to the depot for further processing
The master problem (MP) for the re-optimization problem of m-DVRPMB is formulated as a set partitioning problem (SPP), in which each column corresponds to a feasible route and each constraint corresponds to a customer been served
Assuming coefficient yr equal to 1 if route r ∈ Ω is used in the solution and zero otherwise, the set partitioning problem related to the master problem of m-DVRPMB may be formulated as follows: X
Summary
In the dynamic vehicle routing problem with mixed backhauls (DVRPMB) a fleet of vehicles originating from a depot is tasked to serve two types of orders: (i) static orders known prior to the start of operations (typically deliveries); and (ii) dynamic pickup orders, which are received in real time and should be collected and returned to the depot for further processing. In the former: (a) there is no revenue associated with pick-up orders; and (b) there are vehicles stationed at the depot that may be used to serve (some of) the increased load caused by the newly arrived requests This re-optimization problem is being solved by extending the heuristic branch-and-price (BP) approach proposed in [1], to address the fleet constraint;. Vehicle productivity is a newly introduced term that encourages the available fleet to complete as much of the known work as early as possible The performance of those proposed objective functions is compared to a conventional objective function that accounts only for service maximization, by deploying a series of experiments that consider various operating scenarios and parameters; The second research question is concerned with how the limited fleet constraint affects the trends related to the performance of the various re-optimization strategies, i.e., a combination of when to re-optimize and which part of the plan is released for implementation.
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