Discrete time and continuous time formulations for a short sea inventory routing problem

Abstract

We consider a fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The production/consumption rates are given and assumed to be constant. We provide two alternative mixed integer formulations: a discrete time model adapted from the case where the production/consumption rates are varying and a classical continuous time formulation. We discuss different extended formulations and valid inequalities that allow us to reduce the linear gap of the two initial formulations. A computational study comparing the various models accordingly to their size, linear gap and running time, was conducted based on real small-size instances, using a commercial software.

Combined ship routing and inventory management in the salmon farming industry

“…The Arc-Flow formulation presented in Section 3 is the one that has provided better computational results for related problems, see Agra et al [3]. Nevertheless this formulation still provides large integrality gaps which is common for continuous time models.…”

“…Nevertheless this formulation still provides large integrality gaps which is common for continuous time models. Agra et al [3] compared continuous and discrete time models for a maritime inventory routing problem and found that the discrete time models tended to provide better bounds, but the running times using the discrete time models were in general worse than the running times using the continuous time model. They concluded that, for the constant consumption rate case, a continuous time model with valid inequalities was the best option among all the tested ones to solve small real sized instances.…”

A New Formulation for the Combined Maritime Fleet Deployment and Inventory Management Problem

“…There are a few examples in the literature for maritime inventory routing problems, though mostly in the industrial and tramp shipping (see for example [1,6,9,11,[14][15][16][17]). These literature suggest substantial financial savings by combining ship routing and scheduling planning with inventory management in industrial and tramp shipping.…”

An MILP model for optimization of a small-scale LNG supply chain along a coastline

“…Small-scale distribution of multiple oil products between islands has been studied by Agra and colleagues. Both a discrete time and a continuous time mixed integer formulation of the problem are presented in [12] and heuristic approaches for making real life problem sizes solvable are discussed in [12]. Small-scale LNG distribution differs somewhat from large-scale distribution and large-scale models are rarely adequate directly for small-scale purposes.…”