Integer Linear Programming Models for the Containership Stowage Problem

Table 1

List of established containership stowage mathematical models.

Literature	Hatch cover	Ship-bay configuration	Container type			Container size		Container weight	Stability		Objective
			General	Refrigerated	Others	20′	40′		Tolerance	Accuracy
Avriel et al. [3]		Rectangular structure	√			√					To minimize the number of overstows
Ambrosino and Sciomachen [13]		Not mentioned	√			√	√	Groups	√		To minimize the stowage time
Ambrosino et al. [14]	√	Not mentioned	√			√	√	Groups	√		To minimize the stowage time
Li et al. [15]	√	Not mentioned	√			√	√	Groups	√		Multiobjectives: (1) to minimize the number of overstows; (2) to maximize the vessel utilization
Pacino et al. [18]	√	Not mentioned	√			√	√	Groups		√	To minimize the difference between ballast water and its initial value
Delgado et al. [16]		Rectangular structure	√	√	High cube	√	√	Individuals			Weighted goal
Azevedo et al. [5]		Rectangular structure	√			√		Same			Weighted goal
Ambrosino et al. [11]	√	Practical	√			√	√	Groups	√		Weighted goal
Ambrosino et al. [28]	√	Practical	√	√	Open top	√	√	Groups	√		Weighted goal
Christensen and Pacino [29]		Not mentioned	√	√	High cube	√	√	Groups			To maximize the loading capacity/revenue
Roberti and Pacino [30]		Rectangular structure	√			√					To minimize the number of unloading operations
Li et al. [31]		Not mentioned	√			√		Groups	√		To minimize the number of occupied ship stacks
Li et al. [32]		Rectangular structure	√			√	√	Groups	√		Two-stage objectives: (1) to minimize the ship-bay occupancy rate; (2) to minimize the heeling moment of each ship bay at each port
Fazi [33]		Not mentioned	√		High cube	√	√	Individuals		√	To maximize the loading capacity
Parreno-Torres et al. [34]		Rectangular structure	√			√					To minimize the number of overstows
Korach et al. [35]		Rectangular structure	√	√	High cube	√	√	Individuals	√		Weighted goal
This study	√	Practical	√	√		√	√	Individuals		√	To minimize the number of overstows