On the Sequential Multiknapsack polytope

TL;DR

This paper characterizes the optimal solutions and describes the convex hull of integer solutions for the Sequential Multiple Knapsack Problem, introducing a new formulation and inequalities for the problem's polytope.

Contribution

It provides a new formulation and a decomposition approach to generate inequalities describing the Sequential Multiple Knapsack polytope, advancing understanding of its structure.

Findings

Characterization of optimal solutions for the problem

Description of the convex hull of integer solutions

Development of inequalities defining the polytope

Abstract

The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the integer solutions are presented. More precisely, it is shown that a new formulation of the problem allows to generate a decomposition approach for enumerating all optimal solutions of the problem. Such a decomposition approach is used for finding the inequalities (defined by an inductive scheme) describing the Sequential Multiple Knapsack polytope.