{"id":7324,"date":"2016-01-18T09:52:38","date_gmt":"2016-01-18T04:22:38","guid":{"rendered":"http:\/\/ucanalytics.com\/blogs\/?p=7324"},"modified":"2016-09-11T11:10:27","modified_gmt":"2016-09-11T05:40:27","slug":"business-process-optimization-call-center-case-study-example-part-2","status":"publish","type":"post","link":"https:\/\/ucanalytics.com\/blogs\/business-process-optimization-call-center-case-study-example-part-2\/","title":{"rendered":"Process Optimization &#038; Real Time Analytics  &#8211; Case Study Example (Part 2)"},"content":{"rendered":"<div id=\"attachment_7323\" style=\"width: 298px\" class=\"wp-caption alignright\"><a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg\" rel=\"attachment wp-att-7323\"><img aria-describedby=\"caption-attachment-7323\" data-attachment-id=\"7323\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/business-process-optimization-call-center-case-study-example-part-2\/ying-yang-jigsaw\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?fit=768%2C956&amp;ssl=1\" data-orig-size=\"768,956\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Ying Yang Jigsaw\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?fit=241%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?fit=640%2C797&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-7323\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?resize=288%2C359\" alt=\"Ying Yang Jigsaw\" width=\"288\" height=\"359\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?w=768&amp;ssl=1 768w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?resize=201%2C250&amp;ssl=1 201w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Ying-Yang-Jigsaw.jpg?resize=241%2C300&amp;ssl=1 241w\" sizes=\"(max-width: 288px) 100vw, 288px\" data-recalc-dims=\"1\" \/><\/a><p id=\"caption-attachment-7323\" class=\"wp-caption-text\">Yin Yang Jigsaw &#8211; Real Time Analytics Case Study Example &#8211; by Roopam<\/p><\/div>\n<hr \/>\n<p>This is a continuation of the case study example for\u00a0optimization of a business process. You can find the previous part at\u00a0<a href=\"http:\/\/ucanalytics.com\/blogs\/process-optimization-call-center-case-study-example-part-1\/\">this link<\/a>. In this case study example, you are helping a company reduce their process turn-around-time through advanced analytics and data science. You will use\u00a0some of the key data science activities including business\u00a0process optimization, customer &amp;\u00a0agent profiling, linear programming, and real-time analytics.\u00a0But before we do that, let&#8217;s decipher some similarities between this problem and jigsaw puzzles. As you will notice later, on some metaphysical level, the solution to this problem is about solving a jigsaw puzzle of yin yang to produce harmony.<\/p>\n<h2><span style=\"color: #3366ff;\">Optimization of Jigsaw Puzzles<\/span><\/h2>\n<p>For over 250 years jigsaw puzzles are among the most popular past times for youngsters and adults alike. The origins of\u00a0jigsaw puzzles, traced back to the 18th century, were\u00a0about putting together pieces of maps to help children\u00a0learn geography.\u00a0Solving a jigsaw puzzle requires the player to connect the right pieces together to complete the picture. Among the many strategies to\u00a0solve the game, a commonly used strategy is to classify and group the pieces with similar colors before connecting the pieces.<\/p>\n<p>The objective of the solution for this case study example is to solve a jigsaw puzzle between callers and agents. The purpose of this solution is to patch the callers to the right agents so that the overall call duration can be minimized. The underlining assumption is that certain agents are better suited to solve a certain kind of problems. Moreover, personality and demographic profile of certain agents\u00a0enable them\u00a0to have harmonious and purposeful communication with the\u00a0callers of a certain profile.<\/p>\n<div id=\"attachment_6961\" style=\"width: 930px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg\" rel=\"attachment wp-att-6961\"><img aria-describedby=\"caption-attachment-6961\" data-attachment-id=\"6961\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/process-optimization-call-center-case-study-example-part-1\/caller-agent-connector\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=1136%2C630&amp;ssl=1\" data-orig-size=\"1136,630\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Caller Agent Connector\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=300%2C166&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=640%2C355&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-6961\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=640%2C355\" alt=\"Caller Agent Connector\" width=\"640\" height=\"355\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?w=1136&amp;ssl=1 1136w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=250%2C139&amp;ssl=1 250w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=300%2C166&amp;ssl=1 300w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=1024%2C568&amp;ssl=1 1024w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><p id=\"caption-attachment-6961\" class=\"wp-caption-text\">Real Time Analytics &#8211; Automated Intelligence to connect callers with agents to minimize call duration<\/p><\/div>\n<h2><span style=\"color: #3366ff;\">Call Center Case Study Example<\/span><\/h2>\n<p>Back to the case study example where you are helping\u00a0Cut-to-the-Chase, an inbound call center for a digital television network, to swiftly resolve customer complaint and grievance calls. As discussed in the <a href=\"http:\/\/ucanalytics.com\/blogs\/process-optimization-call-center-case-study-example-part-1\/\">previous part<\/a>, Cut-to-the-Chase has an average call handle time of 12\u00a0minutes with close to\u00a04 minutes of wait time for a customer call. The objective here is to reduce\u00a0the average call handle time (without hold time) to 5 and a half minutes from 8 minutes. This will be quite an elaborate solution with the following steps<\/p>\n<ol>\n<li><strong>Unsupervised learning<\/strong> to segment callers\u00a0into different profiles based on their demographic, usage and complaints log\u00a0information<\/li>\n<li><strong>Supervised learning<\/strong> to identify the propensity of an\u00a0agent to resolve a query for different\u00a0caller profiles within desired query resolution time<\/li>\n<li><strong>Linear\u00a0programming<\/strong> for real-time analytics\u00a0to patch the right caller\u00a0profile with the agent\u00a0profile based on propensity scores derived in step 3<\/li>\n<\/ol>\n<p>I will primarily focus on step 3 of real-time analytics and optimization through integer programming in this case study example. I will briefly discuss steps 1, and 2 in the next few segments. We have discussed both <a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/telecom-case-study-example\/\">unsupervised<\/a> and <a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/retail-case-study-example\/\">supervised<\/a> learning algorithms in a great detail in two different case study examples on YOU CANalytics. Please read those case studies to gain an intuitive and practical understanding of these learning algorithms.<\/p>\n<h2><span style=\"color: #3366ff;\">Step 1: Caller Profiling &#8211;\u00a0Unsupervised Learning<\/span><\/h2>\n<div id=\"attachment_7233\" style=\"width: 246px\" class=\"wp-caption alignright\"><a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/telecom-case-study-example\/\" rel=\"attachment wp-att-7233\"><img aria-describedby=\"caption-attachment-7233\" data-attachment-id=\"7233\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/?attachment_id=7233\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?fit=290%2C210&amp;ssl=1\" data-orig-size=\"290,210\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Slide3\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?fit=290%2C210&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?fit=290%2C210&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-7233\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?resize=236%2C171\" alt=\"Slide3\" width=\"236\" height=\"171\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?w=290&amp;ssl=1 290w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide3.jpg?resize=250%2C181&amp;ssl=1 250w\" sizes=\"(max-width: 236px) 100vw, 236px\" data-recalc-dims=\"1\" \/><\/a><p id=\"caption-attachment-7233\" class=\"wp-caption-text\"><span style=\"font-size: 13.3333px; line-height: 20px;\">Unsupervised learning &#8211; Case Study Example<\/span><\/p><\/div>\n<p>The first step for this solution is to segment the customer base into groups based on the similarity between them. The customer base is segmented based the following broad classes of variables.<\/p>\n<ul>\n<li>Demographic profile of callers<\/li>\n<li>Channel usage based on day and time<\/li>\n<li>Complaints log<\/li>\n<\/ul>\n<p>Cluster analysis of customer base is a highly creative exercise which requires a good understanding of customer demographics and sociology. From the machine learning point of view, the\u00a0methods used for customers profiling and segmentation are part of unsupervised learning. Some of the common unsupervised learning methods are K-mean clustering, hierarchy clustering, and self-organizing maps (SOM). Unsupervised learning and cluster analysis is discussed in greater details in an <a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/telecom-case-study-example\/\">earlier case study example<\/a> on YOU CANalytics. I recommend you read the telecom case study to learn more about unsupervised learning.<\/p>\n<h2><span style=\"color: #3366ff;\">Step 2: Query Resolution Score &#8211; Supervised Learning<\/span><\/h2>\n<div id=\"attachment_7247\" style=\"width: 247px\" class=\"wp-caption alignright\"><a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/retail-case-study-example\/\" rel=\"attachment wp-att-7247\"><img aria-describedby=\"caption-attachment-7247\" data-attachment-id=\"7247\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/?attachment_id=7247\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?fit=290%2C210&amp;ssl=1\" data-orig-size=\"290,210\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Slide1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?fit=290%2C210&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?fit=290%2C210&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-7247\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?resize=237%2C171\" alt=\"Slide1\" width=\"237\" height=\"171\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?w=290&amp;ssl=1 290w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/12\/Slide1.jpg?resize=250%2C181&amp;ssl=1 250w\" sizes=\"(max-width: 237px) 100vw, 237px\" data-recalc-dims=\"1\" \/><\/a><p id=\"caption-attachment-7247\" class=\"wp-caption-text\"><span style=\"font-size: 12pt;\"><span style=\"font-size: 10pt;\">Supervised Learning &#8211; Case Study Example<\/span><\/span><\/p><\/div>\n<p>The second\u00a0step is to profile agents based on their likelihood to\u00a0resolution queries of each caller\u00a0segment derived in step 1. These agent profiles and likelihood\u00a0scores for query resolution\u00a0are derived using supervised learning methods. Supervised learning methods are\u00a0discussed in greater details in an <a href=\"http:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/retail-case-study-example\/\">earlier case study example<\/a> on YOU CANalytics.\u00a0I recommend you read the telecom case study to learn more about supervised learning.<\/p>\n<p>Steps 1, and 2 are iterative in nature to arrive at optimal segments of callers and agents. Moreover, there will be as many propensity or estimation models for step 2 as the number of caller profiles in step 1.<\/p>\n<h2><span style=\"color: #3366ff;\">Step 3: Real Time Analytics &#8211; Optimization<\/span><\/h2>\n<p>The final step in the solution is to connect the dots between callers and agents based on their profiles and <a href=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg\" rel=\"attachment wp-att-6961\"><img data-attachment-id=\"6961\" data-permalink=\"https:\/\/ucanalytics.com\/blogs\/process-optimization-call-center-case-study-example-part-1\/caller-agent-connector\/\" data-orig-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=1136%2C630&amp;ssl=1\" data-orig-size=\"1136,630\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Caller Agent Connector\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=300%2C166&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?fit=640%2C355&amp;ssl=1\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-6961 alignright\" src=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=321%2C178\" alt=\"Caller Agent Connector\" width=\"321\" height=\"178\" srcset=\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?w=1136&amp;ssl=1 1136w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=250%2C139&amp;ssl=1 250w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=300%2C166&amp;ssl=1 300w, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/11\/Caller-Agent-Connector-e1447998513795.jpg?resize=1024%2C568&amp;ssl=1 1024w\" sizes=\"(max-width: 321px) 100vw, 321px\" data-recalc-dims=\"1\" \/><\/a>propensity to have a harmonious conversation to resolve callers&#8217; query. This optimization process is part of real-time analytics. Think of this step as a telephone operator connecting the callers to agents in real time with the objective of fast query resolution time. \u00a0To get a grip of this method we will use a simpler case of connecting 4 waiting-callers with 4 available agents as displayed in the adjacent schematic. We will use linear\u00a0programming to optimize these connections and solve our jigsaw puzzle of callers and agents.We have discussed in the previous part that\u00a0linear programming problem has the following 3 key components:<\/p>\n<ol>\n<li class=\"first-child\">Objective \/ Goal<\/li>\n<li>Decision Variables<\/li>\n<li class=\"last-child\">Constraints<\/li>\n<\/ol>\n<p><strong>Objective or Goal<\/strong>, in this case, is to minimize the average call time between callers and agents. In the previous 2 steps, we have derived the average time each agent takes to resolve the queries for the caller profiles. This table displayed the average time in seconds.<\/p>\n<table style=\"height: 165px;\" border=\"2\" width=\"715\">\n<tbody>\n<tr>\n<td style=\"width: 77px; background-color: #bce4f7;\" width=\"77\"><\/td>\n<td style=\"width: 64px; text-align: center; background-color: #f7dfb5;\" width=\"64\"><strong>Agent 1<\/strong><\/td>\n<td style=\"width: 64px; text-align: center; background-color: #f7dfb5;\" width=\"64\"><strong>Agent 2<\/strong><\/td>\n<td style=\"width: 64px; text-align: center; background-color: #f7dfb5;\" width=\"64\"><strong>Agent 3<\/strong><\/td>\n<td style=\"width: 64px; text-align: center; background-color: #f7dfb5;\" width=\"64\"><strong>Agent 4<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 77px; background-color: #bce4f7;\" width=\"77\"><strong>Caller Profile 1<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"64\">215<\/td>\n<td style=\"text-align: center;\" width=\"64\">246<\/td>\n<td style=\"text-align: center;\" width=\"64\">540<\/td>\n<td style=\"text-align: center;\" width=\"64\">221<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 77px; background-color: #bce4f7;\" width=\"77\"><strong>Caller Profile 2<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"64\">436<\/td>\n<td style=\"text-align: center;\" width=\"64\">936<\/td>\n<td style=\"text-align: center;\" width=\"64\">848<\/td>\n<td style=\"text-align: center;\" width=\"64\">542<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 77px; background-color: #bce4f7;\" width=\"77\"><strong>Caller Profile\u00a03<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"64\">81<\/td>\n<td style=\"text-align: center;\" width=\"64\">328<\/td>\n<td style=\"text-align: center;\" width=\"64\">324<\/td>\n<td style=\"text-align: center;\" width=\"64\">288<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 77px; background-color: #bce4f7;\" width=\"77\"><strong>Caller Profile 4<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"64\">579<\/td>\n<td style=\"text-align: center;\" width=\"64\">263<\/td>\n<td style=\"text-align: center;\" width=\"64\">775<\/td>\n<td style=\"text-align: center;\" width=\"64\">157<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If caller profile 1 is connected with agent 3 then expected call\u00a0time will be 540 seconds. Similarly, Caller profile 2&#8217;s connection with agent 2 will result in 936 seconds of average call time. The maximum query resolution time for the above matrix is 540+936+288+576 = 2343 seconds. This is roughly 9 minutes 45 seconds average call time. Even the most likely average call time for this matrix is close to 7 minutes. The idea is to identify connections to achieve minimum average call.<\/p>\n<p><strong>Decision variables :\u00a0<\/strong>here the decision variables are the connection between callers and agents. There is a total of 16 possibilities of connections (i.e. 4 \u00d7 4) hence there are 16 decision variables. These variables can only take the value of either 0 or 1 which makes this a special case of linear\u00a0programming. Here, 0 means no connection and 1 means connection.<\/p>\n<p><strong>Constraints :\u00a0<\/strong>there are two main\u00a0constraints in this problem i.e.<\/p>\n<ul>\n<li>Each caller can be connected to just one agent<\/li>\n<li>Similarly, each agent needs to be connected to just one caller<\/li>\n<\/ul>\n<p>This is, of course, a special case where the number of callers is equal to the number of agents. However, in real life, this is not always the case hence constraints need to be modified for an unbalanced problem where callers \u2260 agents. Moreover, other business rules can also be added to the list of constraints such as preferential treatment for a certain set of customers etc.<\/p>\n<p><strong>Solution to linear programming<\/strong><\/p>\n<p>The solution to the above linear programming problem to\u00a0minimize total time is 246+436+324+157 = 1163 Seconds.\u00a0This makes the average call time equal to 4 minutes and 51 seconds. This is a significant improvement over 7 minutes\u00a0of average call time achieved through creating random connections between callers and agents. This is a strong case for\u00a0Cut-to-the-Chase to implement this real-time analytics solution in their existing process.<\/p>\n<p>Find the solution to the linear programming problem in the attached Excel<\/p>\n<table style=\"background-color: #ffebad; border-color: #000000;\" cellspacing=\"2\">\n<tbody>\n<tr>\n<td>Excel Solver Solution to\u00a0<a href=\"http:\/\/ucanalytics.com\/blogs\/wp-content\/uploads\/2016\/01\/Real-Time-Analytics-Linear-Programming-Solver.xlsx\" rel=\"\">Real Time Analytics &#8211; Linear Programming Solver<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><span style=\"color: #3366ff;\">Sign-off Note<\/span><\/h4>\n<p>Jigsaw puzzles have so many similarities with life. Our every act in life is to create connections with the next step. We get a good education in the hope of a good job. A good job is to provide for our loved ones. The goal of a jigsaw puzzle is to create a\u00a0complete picture through several parts. At times\u00a0working on one single part seems tedious and pointless, but when it adds to the wholesome\u00a0picture of life it all seems worthwhile.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a continuation of the case study example for\u00a0optimization of a business process. You can find the previous part at\u00a0this link. In this case study example, you are helping a company reduce their process turn-around-time through advanced analytics and data science. 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