Design and control of warehouse order picking: A literature review

The versatile Markovian point process was introduced by M. F. Neuts in 1979. This is a rich class of point processes whichcontains many familiar arrival process as very special cases. Recently, the Batch Markovian Arrival Process, a class of point processes which was subsequently shown to be equivalent to Neuts’ point process, has been studied using a more transparent notation. Recent results in the matrix-analytic approach to queueing theory have substantially reduced the computational complexity of the algorithmic solution of single server queues with a general Markovian arrival process. We generalize these results to the single server queue with the batch arrival process and emphasize the resulting simplifications. Algorithms for the special cases of the PH/G/l and MMPP/G/1 queues are highlighted as these models are receiving renewed attention in the literature and the new algorithms proposed here are simpler than existing ones. In particular, the PH/G/1 queue has additional structure which further enh...

New results on the single server queue with a batch markovian arrival process

https://isiarticles.com/bundles/Article/pre/pdf/12093.pdf

Research on warehouse operation: A comprehensive review

The purpose of this paper is to briefly trace the evolution of DEA from the initial publication by Charnes et al. (1978b) to the current state of the art (SOA). The state of development of DEA is characterized at four points in time to provide a perspective in both directions—past and future. An evolution map is provided which illustrates DEA growth during the 17-year period, the timing of the major events, and the interconnections and influences between topics. An extensive DEA bibliography is provided.

Data envelopment analysis: The evolution of the state of the art (1978–1995)

Several schemes for the linear mapping of a multidimensional space have been proposed for various applications, such as access methods for spatio-temporal databases and image compression. In these applications, one of the most desired properties from such linear mappings is clustering, which means the locality between objects in the multidimensional space being preserved in the linear space. It is widely believed that the Hilbert space-filling curve achieves the best clustering (Abel and Mark, 1990; Jagadish, 1990). We analyze the clustering property of the Hilbert space-filling curve by deriving closed-form formulas for the number of clusters in a given query region of an arbitrary shape (e.g., polygons and polyhedra). Both the asymptotic solution for the general case and the exact solution for a special case generalize previous work. They agree with the empirical results that the number of clusters depends on the hypersurface area of the query region and not on its hypervolume. We also show that the Hilbert curve achieves better clustering than the z curve. From a practical point of view, the formulas given provide a simple measure that can be used to predict the required disk access behaviors and, hence, the total access time.

/pdf/analysis-of-the-clustering-properties-of-the-hilbert-space-ryd2yctc2g.pdf

Analysis of the clustering properties of the Hilbert space-filling curve

To construct a short tour through points in the plane, the points are sequenced as they appear along a spacefilling curve. This heuristic consists essentially of sorting, so it is easily coded and requires only O(N) memory and O(N log N) operations. Its performance is competitive with that of other fast methods.

Spacefilling curves and the planar travelling salesman problem

We describe a family of heuristics to solve combinatorial problems such as routing and partitioning. These heuristics exploit geometry but ignore specific distance measures. Consequently they are simple and fast, but nonetheless fairly accurate, and so seem well-suited to operational problems where time or computing resources are limited. We survey promising new application areas, and show how procedures may be customized to reflect the structure of particular applications.

Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space

A highly decentralized greedy heuristic will enable a fleet of automated guided vehicles to deliver unit loads quickly on a simple loop track.

Decentralized Control of Automated Guided Vehicles on a Simple Loop

A novel routing system based on a new travelling salesman heuristic was successfully implemented to handle the efficient daily routing of a varying number of vehicles to more than 200 delivery points whose locations change daily. The system had to be easily mantained by one person and require no resources for example, no computer. Our system achieved these objectives, cost less than $50, and, moreover, shortened average travel times by 13% compared to previous performance.

Loren K. Platzman

Papers

Spacefilling curves and the planar travelling salesman problem

Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space

Decentralized Control of Automated Guided Vehicles on a Simple Loop

A Minimal Technology Routing System for Meals on Wheels

An O(N log N) planar travelling salesman heuristic based on spacefilling curves