
{"id":100568,"date":"2025-05-25T06:54:46","date_gmt":"2025-05-25T06:54:46","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a8%d8%b1%d9%86%d8%a7%d9%85%d9%87%d8%b1%db%8c%d8%b2%db%8c-%d8%ae%d8%b7%db%8c-%d8%a2%d9%86%d9%84\/"},"modified":"2025-05-25T06:54:46","modified_gmt":"2025-05-25T06:54:46","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a8%d8%b1%d9%86%d8%a7%d9%85%d9%87%d8%b1%db%8c%d8%b2%db%8c-%d8%ae%d8%b7%db%8c-%d8%a2%d9%86%d9%84-100568","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a8%d8%b1%d9%86%d8%a7%d9%85%d9%87%d8%b1%db%8c%d8%b2%db%8c-%d8%ae%d8%b7%db%8c-%d8%a2%d9%86%d9%84-100568\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0631\u06cc\u0632\u06cc \u062e\u0637\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc"},"content":{"rendered":"<table class=\"table table-striped table-hover\">\n<tbody>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n<td>Online Linear Programming with Batching<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n<td>\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0631\u06cc\u0632\u06cc \u062e\u0637\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\n<td>Haoran Xu, Peter W. Glynn, Yinyu Ye<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n<td>PDF<\/td>\n<\/tr>\n<tr>\n<td>\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n<td>\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n<td>\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n<td>\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n<td>78<\/td>\n<\/tr>\n<tr>\n<td>\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a  <\/td>\n<td>Machine Learning,Optimization and Control,\u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 , \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u0648 \u06a9\u0646\u062a\u0631\u0644 ,<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a    <\/td>\n<td>Submitted 1 August, 2024; originally announced August 2024.<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc    <\/td>\n<td>\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 1 \u0627\u0648\u062a 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0648\u062a 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"option-descriptions\" style=\"margin: 30px 0; padding: 15px; border: 1px solid #eee; border-radius: 5px; background-color: #f9f9f9;\">\n<h3>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u06af\u0632\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u062e\u0631\u06cc\u062f<\/h3>\n<div style=\"margin-bottom: 20px;\">\n<h4>\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/h4>\n<p>\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0641\u0627\u06cc\u0644 PDF \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc \u0631\u0627 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u062f\u0627\u0646\u0644\u0648\u062f \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0642\u06cc\u0645\u062a: 19,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n<\/p><\/div>\n<div style=\"margin-bottom: 20px;\">\n<h4>\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc + \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647 \u0627\u06cc \u0645\u0642\u0627\u0644\u0647 + \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647<\/h4>\n<p>\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc\u060c \u06cc\u06a9 \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647\u200c\u0627\u06cc \u0641\u0627\u0631\u0633\u06cc \u0648 \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u062f\u0631\u06cc\u0627\u0641\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f.<\/p>\n<p>\u0642\u06cc\u0645\u062a: 99,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n<\/p><\/div>\n<div>\n<h4>\u0633\u0641\u0627\u0631\u0634 \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 + \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647 \u0627\u06cc \u0645\u0642\u0627\u0644\u0647 + \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647<\/h4>\n<p>\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc \u0648 \u062a\u0631\u062c\u0645\u0647 \u06a9\u0627\u0645\u0644 \u0622\u0646\u060c \u06cc\u06a9 \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647\u200c\u0627\u06cc \u0641\u0627\u0631\u0633\u06cc \u0648 \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u062f\u0631\u06cc\u0627\u0641\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f.<\/p>\n<p>\u0642\u06cc\u0645\u062a: 3,120,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n<p>\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644: 2 \u062a\u0627 3 \u0631\u0648\u0632 \u06a9\u0627\u0631\u06cc<\/p>\n<\/p><\/div>\n<\/p><\/div>\n\r\n<table class=\"table table-striped table-hover table-primary\">\r\n    <tr>\r\n        <td>\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647  <\/td>\r\n        <td>\u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n    <\/tr>\r\n    <tr>\r\n        <td>\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647  <\/td>\r\n        <td>\u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n    <\/tr>\r\n\t<tr>\r\n        <td>\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647  <\/td>\r\n        <td>\u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n    <\/tr>\r\n\t\t<tr>\r\n        <td>\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627  <\/td>\r\n        <td>\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n    <\/tr>\r\n<\/table>\r\n\r\n\n<h2>\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n<p style=\"direction:ltr;\">We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without batching, the ability to delay decisions brings better operational performance, as measured by regret. Two research questions of interest are: (1) What is a lower bound of the regret as a function of $K$? (2) What algorithms can achieve the regret lower bound? These questions have been analyzed in the literature when the distribution of the reward and the resource consumption of the customers have finite support. By contrast, this paper analyzes these questions when the conditional distribution of the reward given the resource consumption is continuous, and we show the answers are different under this setting. When there is only a single type of resource and the decision maker knows the total number of customers, we propose an algorithm with a $O(log K)$ regret upper bound and provide a $\u03a9(log K)$ regret lower bound. We also propose algorithms with $O(log K)$ regret upper bound for the setting in which there are multiple types of resource and the setting in which customers arrive following a Poisson process. All these regret upper and lower bounds are independent of the length of the planning horizon, and all the proposed algorithms delay decisions on customers arriving in only the first and the last batch. We also take customer impatience into consideration and establish a way of selecting an appropriate batch size.<\/p>\n<h2>\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n<p>    \u0645\u0627 \u0628\u0631\u0646\u0627\u0645\u0647 \u0646\u0648\u06cc\u0633\u06cc \u062e\u0637\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 (OLP) \u0631\u0627 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0627\u0641\u0642 \u0628\u0631\u0646\u0627\u0645\u0647 \u0631\u06cc\u0632\u06cc \u0628\u0647 \u062f\u0633\u062a\u0647 \u0647\u0627\u06cc $ $ $ \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f \u060c \u0648 \u062a\u0635\u0645\u06cc\u0645\u0627\u062a \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0645\u0634\u062a\u0631\u06cc\u0627\u0646\u06cc \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u062f\u0633\u062a\u0647 \u0627\u0632 \u0622\u0646\u0647\u0627 \u0648\u0627\u0631\u062f \u0645\u06cc \u0634\u0648\u0646\u062f \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062a\u0627 \u067e\u0627\u06cc\u0627\u0646 \u062f\u0633\u062a\u0647 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0622\u0646\u0647\u0627 \u0628\u0647 \u062a\u0623\u062e\u06cc\u0631 \u0628\u06cc\u0641\u062a\u062f.\u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 OLP \u0628\u062f\u0648\u0646 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u060c \u062a\u0648\u0627\u0646\u0627\u06cc\u06cc \u062a\u0623\u062e\u06cc\u0631 \u062f\u0631 \u062a\u0635\u0645\u06cc\u0645 \u06af\u06cc\u0631\u06cc \u060c \u0639\u0645\u0644\u06a9\u0631\u062f \u0639\u0645\u0644\u06cc\u0627\u062a\u06cc \u0628\u0647\u062a\u0631\u06cc \u0631\u0627 \u0628\u0647 \u0647\u0645\u0631\u0627\u0647 \u062f\u0627\u0631\u062f \u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0628\u0627 \u067e\u0634\u06cc\u0645\u0627\u0646\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f.\u062f\u0648 \u0633\u0624\u0627\u0644 \u062a\u062d\u0642\u06cc\u0642 \u0645\u0648\u0631\u062f \u0639\u0644\u0627\u0642\u0647 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632: (1) \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0627\u0628\u0639\u06cc \u0627\u0632 $ $ $ \u060c \u067e\u0634\u06cc\u0645\u0627\u0646\u06cc \u06a9\u0645\u062a\u0631 \u0627\u0632 \u062d\u0633\u0631\u062a \u0686\u06cc\u0633\u062a\u061f(2) \u0686\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0647 \u067e\u0634\u06cc\u0645\u0627\u0646\u06cc \u06a9\u0645\u062a\u0631\u06cc \u0628\u0631\u0633\u0646\u062f\u061f\u0627\u06cc\u0646 \u0633\u0624\u0627\u0644\u0627\u062a \u062f\u0631 \u0627\u062f\u0628\u06cc\u0627\u062a \u0645\u0648\u0631\u062f \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 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\u067e\u0634\u06cc\u0645\u0627\u0646\u06cc \u0645\u0631\u0632\u0647\u0627\u06cc \u0628\u0627\u0644\u0627 \u0648 \u067e\u0627\u06cc\u06cc\u0646 \u0645\u0633\u062a\u0642\u0644 \u0627\u0632 \u0637\u0648\u0644 \u0627\u0641\u0642 \u0628\u0631\u0646\u0627\u0645\u0647 \u0631\u06cc\u0632\u06cc \u0647\u0633\u062a\u0646\u062f \u0648 \u062a\u0645\u0627\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc \u062a\u0635\u0645\u06cc\u0645\u0627\u062a \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u0634\u062a\u0631\u06cc\u0627\u0646\u06cc \u06a9\u0647 \u0641\u0642\u0637 \u0628\u0647 \u062f\u0633\u062a\u0647 \u0627\u0648\u0644 \u0648 \u0622\u062e\u0631 \u0645\u06cc \u0631\u0633\u0646\u062f \u062a\u0623\u062e\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f.\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u06cc \u062d\u0648\u0635\u0644\u06af\u06cc \u0645\u0634\u062a\u0631\u06cc \u0631\u0627 \u0645\u0648\u0631\u062f \u062a\u0648\u062c\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0648 \u0631\u0627\u0647\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0633\u062a\u0647 \u0645\u0646\u0627\u0633\u0628 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n\r\n<table class=\"table table-striped table-hover table-primary\">\r\n    <tr>\r\n        <td>\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647  <\/td>\r\n        <td>\u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n    <\/tr>\r\n    <tr>\r\n        <td>\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647  <\/td>\r\n        <td>\u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n    <\/tr>\r\n\t<tr>\r\n        <td>\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647  <\/td>\r\n        <td>\u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n    <\/tr>\r\n\t\t<tr>\r\n        <td>\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627  <\/td>\r\n        <td>\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n    <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"<p>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Online Linear Programming with Batching \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0631\u06cc\u0632\u06cc \u062e\u0637\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 \u0628\u0627 [&hellip;]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[511,1158],"product_tag":[],"class_list":{"0":"post-100568","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-511","7":"product_cat-1158","8":"pmpro-has-access","9":"desktop-align-left","10":"tablet-align-left","11":"mobile-align-left","13":"first","14":"instock","15":"shipping-taxable","16":"purchasable","17":"product-type-variable"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0631\u06cc\u0632\u06cc \u062e\u0637\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc - 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