# Output maximization container loading problem with time availability constraints

## TL;DR

This paper introduces a container loading optimization model that incorporates time constraints and arrival schedules, aiming to improve container utilization under logistical pressures and uncertainties.

## Contribution

It presents a novel framework that separates geometric and temporal factors, allowing effective handling of scheduling uncertainties in container loading problems.

## Key findings

- Framework effectively models time and geometric constraints.
- Handles schedule uncertainties and delays.
- Quantifies impact on capacity and departure times.

## Abstract

Research on container loading problems has been proved effective in increasing the filling rate of containers in different practical situations. However, the broader logistic context might pressure the loading process, leading to sub-optimal solutions. Some facilities like cross-docks have reduced storage space which might force early loading activities. We propose a container loading problem which accounts for this limited storage by explicitly considering the schedule of arrival for the boxes and the departure time of the trucks. Also, we design a framework which handles the geometric and temporal characteristics of the problem separately, enabling the use of methods found in the literature for solving the extended problem. Our framework can handle uncertainty in the schedule and be used to quantify the impact of delays on capacity utilization and departure time of trucks.