Related papers: Online General Knapsack with Reservation Costs
Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…
The "0-1 knapsack problem" stands as a classical combinatorial optimization conundrum, necessitating the selection of a subset of items from a given set. Each item possesses inherent values and weights, and the primary objective is to…
We consider the problem of online resource allocation with average budget constraints. At each time point the decision maker makes an irrevocable decision of whether to accept or reject a request before the next request arrives with the…
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…
We study the knapsack problem with group fairness constraints. The input of the problem consists of a knapsack of bounded capacity and a set of items, each item belongs to a particular category and has and associated weight and value. The…
In retail warehouses, returned products are typically placed in an intermediate storage until a decision regarding further shipment to stores is made. The longer products are held in storage, the higher the inefficiency and costs of the…
In many online advertisement (ad) exchanges, ad slots are each sold via a separate second-price auction. This paper considers the bidder's problem of maximizing the value of ads they purchase in these auctions, subject to budget…
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
Imagine yourself moving to another place, and therefore, you need to pack all of your belongings into moving boxes with some capacity. In the classical bin packing model, you would try to minimize the number of boxes, knowing the exact size…
We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary…
Two related online problems: knapsack and truthful bipartite matching are considered. For these two problems, the common theme is how to `match' an arriving left vertex in an online fashion with any of the available right vertices, if at…
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some…
We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource requirements to physical…
In this paper we propose primal-dual algorithms for different variants of the online resource allocation problem with departures. In the basic variant, requests (items) arrive over time to a set of resources (knapsacks) and upon arrival,…
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for…
We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not…
A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…