Bin Packing Problem with Item Time Window Conflict Dependent Profits

The problem of packing with items with conflicting time-window dependence on profit considering departure time is studied in the context of consolidation of goods in transport, which is a practical problem in the logistics industry. The objective is to select the loading plan that is most profitable based on the volume and time windows of the items. The time windows of items in the same box must intersect, and the intersection of the items’ time windows affects the box’s departure time and hence the profit-dependent time. The problem is identified as an integer programming model for decision making, and two modeling strategies are proposed to address it by improving the GRASP heuristic. Multi-class examples are used in experiments to confirm that the improved algorithm can solve the problem efficiently, find the near-optimal solution in a shorter time, and enhance customer satisfaction.