Objective | Maximize the total value of items packed into a single knapsack. | Minimize the number of bins needed to pack all items. |
Number of Containers | Only one knapsack (container) is available. | Multiple bins (containers) are available. |
Capacity Constraint | The knapsack has a fixed capacity that cannot be exceeded. | Each bin has a fixed capacity, but you can use as many bins as needed. |
Item Selection | Not all items have to be packed; select a subset that maximizes value within the capacity. | All items must be packed into the bins. |
Focus | Choosing items with the highest value-to-weight ratio. | Efficiently packing all items to minimize the number of bins used. |
Item Value | Each item has an associated weight and value. | Items have only weight; no value is associated with them. |
Type of Problem | Optimization problem (maximization). | Combinatorial problem (minimization). |
Typical Approach | Use dynamic programming or greedy algorithms to maximize value. | Use greedy or heuristic algorithms to minimize bin usage. |
Example | Packing a backpack with the most valuable items without exceeding weight. | Packing boxes in a truck, minimizing the number of trips required. |
Common Variants | 0/1 Knapsack, Fractional Knapsack, Multi-dimensional Knapsack | One-dimensional Bin Packing, Two-dimensional Packing |
Complexity | NP-complete for 0/1 Knapsack and bin packing. | NP-complete, especially for the one-dimensional bin packing problem. |