2D-Packing with an Application to Stowage in Roll-On Roll-Off Liner Shipping

Abstract

Abstract. Roll-on/Roll-off (RoRo) ships represent the primary source for transporting vehicles and other types of rolling material over long distances. In this paper we focus on operational decisions related to stowage of cargoes for a RoRo ship voyage visiting a given set of loading and unloading ports. By focusing on stowage on one deck on board the ship, this can be viewed as a special version of a 2-dimensional packing problem with a number of additional considerations, such as one wants to place vehicles that belong to the same shipment close to each other to ease the loading and unloading. Another important aspect of this problem is shifting, which means temporarily moving some vehicles to make an entry/exit route for the vehicles that are to be loaded/unloaded at the given port. We present several versions of a new mixed integer programming (MIP) formulation for the problem. Computational results show that the model provides good solutions on small sized problem instances.

Optimal stowage on Ro-Ro decks for efficiency and safety

“…In Ro-Ro applications the work is represented by Øvstebø et al and Wathne [2][3][4], and Hansen et al [6]. The proposed approaches provide a solid basis for solving the Ro-Ro ship stowage problem, given its peculiarities compared to stowage problems on other ships (e.g., container ships).…”

“…If a stowage plan is suboptimal, precious revenues will be lost and safety jeopardised. And as the maritime industry is undergoing digitalisation with various onboard decision support systems becoming standard, the optimal stowage problem has attracted attention in the area of operational research (OR) [2][3][4][5][6][7][8].…”

A Shortest Path Heuristic for Evaluating the Quality of Stowage Plans in Roll-On Roll-Off Liner Shipping

“…Building on the previous work in [3], the SPEP is based on a grid representation of the given deck, where I is the set of rows and J the set of columns over a deck, indexed by i and j, respectively. A square (i, j) represents a physical area on the deck where the vehicles may be placed, where square (1,1) is defined as the square located at the stern of the ship's port side.…”

“…The SUFs used are 0.8 and >0.9. When creating an instance, the vehicles are either randomly placed on the deck (R) or placed in a logical manner (L) according to objective function (3) in [3]. Finally, the cargo list contains information about the number of cargoes, loading and unloading port of each cargo, and each vehicle's size and weight.…”

“…Recently, Hansen et al [3] presented a mathematical model for the twodimensional RSSP, a simplification of the RSSP which arises if only one deck is considered. They argue that dividing the decks into lanes, as done in [4], may be too restricting, especially when the cargoes stowed are heterogeneous, i.e.…”