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Efficiently solving path planning problems for a large number of robots is critical to the successful operation of modern warehouses. The existing approaches adopt classical shortest path algorithms to plan in environments whose cells are…

We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We…

We study a wholesale supply chain ordering problem. In this problem, the supplier has an initial stock, and faces an unpredictable stream of incoming orders, making real-time decisions on whether to accept or reject each order. What makes…

We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…

Autonomous mobile robots (AMRs) are increasingly used to automate operations in intralogistics. One crucial feature of AMRs is their availability, allowing them to operate 24/7. This work addresses the multibay unit load pre-marshalling…

A linear algorithm is described for solving the n-Queens Completion problem for an arbitrary composition of k queens, consistently distributed on a chessboard of size n x n. Two important rules are used in the algorithm: a) the rule of…

We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…

We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover…

This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…

A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…

The well-known problem stated by A. Meir and L. Moser consists in tiling the unit square with rectangles (details), whose side lengths equal $1/n\times 1/(n+1)$, where indices~$n$ range from 1 to infinity. Recently, Terence Tao has proved…

We study the fabric spreading and cutting problem in apparel factories. For the sake of saving the material costs, the cutting requirement should be met exactly without producing additional garment components. For reducing the production…

In this paper, we provide details of a robotic system that can automate the task of picking and stowing objects from and to a rack in an e-commerce fulfillment warehouse. The system primarily comprises of four main modules: (1) Perception…

In this paper, we study the one-shot and lifelong versions of the Target Assignment and Path Finding problem in automated sortation centers, where each agent needs to constantly assign itself a sorting station, move to its assigned station…

The rail freight flow assignment (RFFA) is a key point of network design and operations management. Unlike a road network, the freight flow assignment pattern in a rail system has unique characteristics, and the most significant one is the…

Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…

Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment…

Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…

Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given $O(1/\epsilon)$ advice bits for each input item allows approximating the dual bin packing problem…