Single machine batch scheduling with release times

Motivated by a high-throughput logging system, we investigate the single machine scheduling problem with batching, where jobs have release times and processing times, and batches require a setup time. Our objective is to minimize the total flow time, in the online setting. For the online problem where all jobs have identical processing times, we propose a 2-competitive algorithm and we prove acorresponding lower bound. Moreover, we show that if jobs with arbitrary processing times can be processed in any order, any online algorithm has a linear competitive ratio in the worst cas

Determining Number of Zones in a Pick-and-pack Orderpicking System

In this study we consider a pick-to-pack orderpicking system, in which batches of orders are picked simultaneously from different(work) zones by a group of order pickers. After picking, the orders are transported by a conveyor to the next station for packing. Our aim is to determine the optimal number of zones such that the overall (picking and packing) time to finish a batch is minimized. We solve this problem by optimally assigning items to pick routes in each zone. We illustrate the method with data taken from a distribution center of one of the largest online retailers in the Netherlands

High-Level Object Oriented Genetic Programming in Logistic Warehouse Optimization

Disertační práce je zaměřena na optimalizaci průběhu pracovních operací v logistických skladech a distribučních centrech. Hlavním cílem je optimalizovat procesy plánování, rozvrhování a odbavování. Jelikož jde o problém patřící do třídy složitosti NP-težký, je výpočetně velmi náročné nalézt optimální řešení. Motivací pro řešení této práce je vyplnění pomyslné mezery mezi metodami zkoumanými na vědecké a akademické půdě a metodami používanými v produkčních komerčních prostředích. Jádro optimalizačního algoritmu je založeno na základě genetického programování řízeného bezkontextovou gramatikou. Hlavním přínosem této práce je a) navrhnout nový optimalizační algoritmus, který respektuje následující optimalizační podmínky: celkový čas zpracování, využití zdrojů, a zahlcení skladových uliček, které může nastat během zpracování úkolů, b) analyzovat historická data z provozu skladu a vyvinout sadu testovacích příkladů, které mohou sloužit jako referenční výsledky pro další výzkum, a dále c) pokusit se předčit stanovené referenční výsledky dosažené kvalifikovaným a trénovaným operačním manažerem jednoho z největších skladů ve střední Evropě.This work is focused on the work-flow optimization in logistic warehouses and distribution centers. The main aim is to optimize process planning, scheduling, and dispatching. The problem is quite accented in recent years. The problem is of NP hard class of problems and where is very computationally demanding to find an optimal solution. The main motivation for solving this problem is to fill the gap between the new optimization methods developed by researchers in academic world and the methods used in business world. The core of the optimization algorithm is built on the genetic programming driven by the context-free grammar. The main contribution of the thesis is a) to propose a new optimization algorithm which respects the makespan, the utilization, and the congestions of aisles which may occur, b) to analyze historical operational data from warehouse and to develop the set of benchmarks which could serve as the reference baseline results for further research, and c) to try outperform the baseline results set by the skilled and trained operational manager of the one of the biggest warehouses in the middle Europe.

Atari games and Intel processors

The asynchronous nature of the state-of-the-art reinforcement learning algorithms such as the Asynchronous Advantage Actor-Critic algorithm, makes them exceptionally suitable for CPU computations. However, given the fact that deep reinforcement learning often deals with interpreting visual information, a large part of the train and inference time is spent performing convolutions. In this work we present our results on learning strategies in Atari games using a Convolutional Neural Network, the Math Kernel Library and TensorFlow 0.11rc0 machine learning framework. We also analyze effects of asynchronous computations on the convergence of reinforcement learning algorithms

Batching Problems with Constraints

There is an increasing demand for a phenomenon that can manifest benefits gained from grouping similar jobs together and then scheduling these groups efficiently. Batching is the decision of whether or not to put the jobs into same group based on certain criteria. Batching plays a major role in job scheduling in Information Technology, traffic controlling systems, and goods-flow management. A list batching problem refers to batching a list of jobs in the same order or priority as given in the problem. In this thesis we consider a one-machine list batching problem under weighted average completion. Given sequence of jobs are scheduled on single machine into distinct batches. Constraint is to batch these jobs into a fixed but arbitrary number ‘k’ of batches. Each batch can have any number of jobs (within the given list) grouped without changing the order of jobs. We call it a k-Batch problem. This is offline form of the batching problems, and is solved by reducing to a shortest path problem. We give an improved and faster version of the algorithm to solve k-Batch problem in O(n2) time

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Compatibility graphs in scheduling on batch processing machines

We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are modeled by an undirected graph $G$, in which compatible jobs are represented by adjacent vertices. We show that several subproblems are polynomial. We propose some exact polynomial algorithms to solve these subproblems. To solve the general case, we propose a mixed-integer linear programming (MILP) formulation alongside with heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods.Comment: 25 pages, 11 figure

Constraint Programming Approach to Steelmaking-making Process Scheduling

This paper presents a constraint programming (CP) approach to optimal steelmaking process scheduling with constraints of processing time, limited waiting time between adjacent stages, serial batching, sequence independent setup time, release/due time, and with the objective of minimizing maximal total waiting time between adjacent charges in the same casts. The model and search strategies are proposed. Numerical experiments with the steel making process show that CP approach, under appropriate formulation and search strategies, can not only describe the problem exactly, but also can solve the problem more effectively and efficiently compared with classical exact algorithms and heuristic rule

Approximation for Batching via Priorities

We consider here the one-machine serial batching problem under weighted average completion. This problem is known to be $cal Ncal P$-hard and no good approximation algorithms are known. Batching has wide application in manufacturing, decision management, and scheduling in information technology. We give an approximation algorithm with approximation ratio of $2$; the algorithm is a priority algorithm, which batches jobs in decreasing order of priority. We also give a lower bound of $frac{2 +sqrt{6}}{4} approx 1.1124$ on the approximation ratio of any priority algorithm and conjecture that there is a priority algorithm which matches this bound. Adaptive algorithm experiments are used to support the conjecture. An easier problem is the list version of the problem where the order of the jobs is given. We give a new linear time algorithm for the list batching problem