Approximate Dynamic Programming for a Class of Long-Horizon Maritime Inventory Routing Problems

Abstract

We study a deterministic maritime inventory routing problem with a long planning horizon. For instances with many ports and many vessels, mixed-integer linear programming (MIP) solvers often require hours to produce good solutions even when the planning horizon is 90 or 120 periods. Building on the recent successes of approximate dynamic programming (ADP) for road-based applications within the transportation community, we develop an ADP procedure to generate good solutions to these problems within minutes. Our algorithm operates by solving many small subproblems (one for each time period) and by collecting information about how to produce better solutions. Our main contribution to the ADP community is an algorithm that solves MIP subproblems and uses separable piecewise linear continuous, but not necessarily concave or convex, value function approximations and requires no off-line training. Our algorithm is one of the first of its kind for maritime transportation problems and represents a significant departure from the traditional methods used. In particular, whereas virtually all existing methods are "MIP-centric," i.e., they rely heavily on a solver to tackle a nontrivial MIP to generate a good or improving solution in a couple of minutes, our framework puts the effort on finding suitable value function approximations and places much less responsibility on the solver. Computational results illustrate that with a relatively simple framework, our ADP approach is able to generate good solutions to instances with many ports and vessels much faster than a commercial solver emphasizing feasibility and a popular local search procedure.

Adaptive railway traffic control using approximate dynamic programming

“…One promising method in the field of optimisation and control that has attracted much attention in the recent decades is Approximate Dynamic Programming (ADP) due to its effectiveness in tackling stochastic applications where the state and action spaces are large (Li and Womer, 2015;Medury and Madanat, 2013;Papadaki and Powell, 2002;Papageorgiou et al, 2014;Simão et al, 2009;Van Roy et al, 1997;Zhang and Dietterich, 1995). ADP is a variant of DP which uses approximation in the evaluation of candidate control decisions.…”

Sustainable maritime inventory routing problem with time window constraints

“…Travel time is considered as a parameter in both the model, although in practicality voyage time keeps changing depending upon the speed of the vessel. Other researchers such as Agra et al 2013a andPapageorgiou et al 2014a extensively studied ship routing and scheduling problem for a planning horizon and integrated inventory management within the problem for addressing varying supply and demand rates at ports. Each of the respective problem deals with routing of a heterogeneous fleet of ships between multiple ports with limited storage capacity and carrying out loading/unloading operations at ports.…”

Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

“…In a shipment planning problem of bitumen, Persson and Göthe-Lundgren [23] allow for a vessel to discharge at no more than two ports per voyage. In liquefied natural gas (LNG) transportation, the most common practice is to have full load and full discharge where a vessel travels between only one loading port and discharging port in a trip [4,14,22,25]. In the LNG setting studied by [15], multiple port visits in discharging regions are possible, but the number of ports visits are limited to two due to tank restrictions.…”

“…Although it can be applied to any solution (feasible or infeasible) at any time in the search procedure, we apply it immediately following the construction phase described in Section 3 and to each solution stored in a solution pool of SystemModel-2Port (6). Several authors have shown how local search can be used to find highquality solutions and improve existing solutions [14,19,22,28,29,30]. Note that in [29], one loading region, one discharging region, and voyage-chartered vessels are considered so that a vessel path involves a single inter-regional trip.…”