Production optimization by agents of differing work rates

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Bibliographic Details
Main Author:	Higgins, Peter M.
Format:	Preprint
Published:	2023
Subjects:	Combinatorics Optimization and Control 90C27
Online Access:	Acceder al recurso
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_version_	1866916202042884096
author	Higgins, Peter M.
author_facet	Higgins, Peter M.
contents	We devise a scheme for producing, in the least possible time, $n$ identical objects with $p$ agents that work at differing speeds. This involves halting the process in order to transfer production across agent types. For the case of two types of agent, we construct a scheme based on the Euclidean algorithm that seeks to minimise the number of pauses in production.
format	Preprint
id	arxiv_https___arxiv_org_abs_2310_09208
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Production optimization by agents of differing work rates Higgins, Peter M. Combinatorics Optimization and Control 90C27 We devise a scheme for producing, in the least possible time, $n$ identical objects with $p$ agents that work at differing speeds. This involves halting the process in order to transfer production across agent types. For the case of two types of agent, we construct a scheme based on the Euclidean algorithm that seeks to minimise the number of pauses in production.
title	Production optimization by agents of differing work rates
topic	Combinatorics Optimization and Control 90C27
url	https://arxiv.org/abs/2310.09208

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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