Abstract Knapsack problem (KP) is a representative combinatorial optimization that aims to maximize the total profit by selecting subset of items under given constraints on weights. In this study, we analyze generalized version KP, which termed multidimensional knapsack (GMDKP). As opposed basic GMDKP allows multiple choices per item type weight constraints. Although several efficient algorithm...

We formulate the NP-hard n-dimensional knapsack feasibility problem as an equivalent absolute value equation (AVE) in an n-dimensional noninteger real variable space and propose a finite succession of linear programs for solving the AVE. Exact solutions are obtained for 1880 out of 2000 randomly generated consecutive knapsack feasibility problems with dimensions between 500 and one million. For...

In this note we study packing or covering integer programs with at most k constraints, which are also known as k-dimensional knapsack problems. For integer k > 0 and real ǫ > 0, we observe there is a polynomial-sized LP for the k-dimensional knapsack problem with integrality gap at most 1+ ǫ. The variables may be unbounded or have arbitrary upper bounds. In the (classical) packing case, we can ...

An employee transporting problem is described and a set partitioning model is developed. An investigation of the model leads to a knapsack problem as a surrogate problem. Finding a partition corresponding to the knapsack problem provides a solution to the problem. An exact algorithm is proposed to obtain a partition (subset-vehicle combination) corresponding to the knapsack solution. It require...

The online knapsack problem is a classic resource allocation in networking and operations research. Its basic version studies how to pack arriving items of different sizes values into capacity-limited knapsack. In this paper, we study general that includes item departures, while also considering multiple knapsacks multi-dimensional sizes. We design threshold-based algorithm prove the can achiev...

In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We first observe there is a Polynomial Time Approximation Scheme (PTAS) for the problem of packing weighted squares into rectangular bins with large resources, then...

We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request possesses an adversarial value and an adversarial size. The online algorithm must make an irrevocable accept/reject decision as soon as it sees each request. The ...

In this paper, we study shelf space allocation optimization which is important to retail operations management. Our approach is to formulate a model that is applicable to operational realities and to seek solutions with realistic test data. This model is linked to the multi-dimensional knapsack problem. We first solve a simplified version of the problem to achieve maximum profit by transforming...