Optimizing Knapsack Allocation: The Preemptive Multiple Bounded Knapsack Problem

DOI

10.2991/978-94-6463-413-6_21How to use a DOI?

Keywords

multiple bounded knapsack problem; preemptive multiple bounded knapsack problem; priority; preemptive; bounded knapsack

Abstract

The Multiple Bounded Knapsack Problem (MBKP) involves the task of allocating a set of items, each with bounded availability, into different knapsacks with the goal of maximizing the overall profit from the selected items while ensuring that the capacity of each knapsack is not exceeded. Knapsacks in the MBKP can be prioritized based on their importance. Priority refers to the sequence or level of importance in a system. Preemptive priority is an approach where certain objectives are given higher priority than others, allowing for faster handling or higher service for higher-priority objectives. This enables designers or systems to focus on objectives assumed most important. The MBKP with prioritized knapsacks is referred to as the Preemptive Multiple Bounded Knapsack Problem (PMBKP). It involves a process in solving the problem. The PMBKP algorithm begins by establishing a canonical form of the problem. It initiates the solving process starting with the first priority. The result obtained in the first process is then substituted into the second process with constraints on the second-priority knapsack, and this process continues until solving the knapsack in the last priority order. The solutions from the first to last priority are consolidated to form the solution for the problem Solving the PMBKP will optimize the knapsacks based on priority.

Copyright

© 2024 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Aditya Ambarwati
AU  - Sobri Abusini
AU  - Vira Hari Krisnawati
PY  - 2024
DA  - 2024/05/13
TI  - Optimizing Knapsack Allocation: The Preemptive Multiple Bounded Knapsack Problem
BT  - Proceedings of the First International Conference on Applied Mathematics, Statistics, and Computing (ICAMSAC 2023)
PB  - Atlantis Press
SP  - 214
EP  - 220
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-413-6_21
DO  - 10.2991/978-94-6463-413-6_21
ID  - Ambarwati2024
ER  -