{"id":9822,"date":"2023-10-24T17:24:24","date_gmt":"2023-10-24T17:24:24","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=9822"},"modified":"2024-10-18T21:00:55","modified_gmt":"2024-10-18T21:00:55","slug":"operations-and-supply-chain-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/operations-and-supply-chain-learn-it-1\/","title":{"raw":"Operations and Supply Chain: Learn It 1","rendered":"Operations and Supply Chain: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Describe concepts like inventory management, production scheduling, and optimization\u00a0<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Operations and supply chain management are the backbone of any business, ensuring that products are produced and delivered efficiently. This section will delve into key topics like inventory management, production scheduling, and optimization techniques.<\/p>\r\n<h2>Inventory Management<\/h2>\r\n<p>Inventory management is a crucial part of any business that deals with physical goods. The objective is to maintain an optimal level of inventory to meet customer demand while minimizing costs.<\/p>\r\n<section class=\"textbox proTip\">\r\n<p><strong>Inventory versus Stock<\/strong><\/p>\r\n<p>You have probably heard the terms \"inventory\" and \"stock\" when it comes to describing the products a business has. In retail settings, the term \"stock\" is commonly used to describe inventory. The phrase \"stock on hand\" is often used by managers to refer to items like clothing and home goods. In a wider industrial context, \"inventory\" encompasses not just finished products for sale, but also the raw materials and components used in manufacturing.<\/p>\r\n<\/section>\r\n<p>Different businesses have different needs when it comes to managing inventory. Some rely on mathematical formulas and data analysis, while others depend on procedural methods. Regardless of the approach, the ultimate goal is to improve accuracy and efficiency. Here's a brief overview of some commonly used techniques and terms:<\/p>\r\n<ul>\r\n\t<li>\r\n<p><strong>ABC Analysis<\/strong>: Helps businesses prioritize items that are critical for their operations by classifying stock into categories based on its importance or popularity.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Demand Forecasting<\/strong>: Utilizes predictive analytics to estimate future customer demand, aiding in better stock planning.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Economic Order Quantity (EOQ)<\/strong>: A mathematical formula that calculates the most cost-effective quantity of items to order, balancing holding and ordering costs.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>FIFO and LIFO<\/strong>: These are inventory valuation methods. FIFO (First-In, First-Out) moves the oldest stock first, while LIFO (Last-In, First-Out) moves the newest stock first.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Just-In-Time (JIT)<\/strong>: Focuses on timing, aiming to maintain the lowest possible stock levels to reduce storage costs.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Materials Requirements Planning (MRP)<\/strong>: Used in manufacturing to manage planning, scheduling, and inventory control.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Reorder Point Formula<\/strong>: Helps businesses determine when it's time to reorder stock to avoid stockouts.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Safety Stock<\/strong>: An extra amount of stock kept as a buffer against unforeseen circumstances like delayed shipments or sudden spikes in demand.<\/p>\r\n<\/li>\r\n<\/ul>\r\n<p>Let's explore two of the most popular inventory systems: Economic Order Quantity (EOQ) and Just-In-Time (JIT).<\/p>\r\n<h3>Economic Order Quantity (EOQ)<\/h3>\r\n<p>EOQ is a formula used to calculate the most cost-effective quantity of items to order. The EOQ model aims to minimize the total holding and ordering costs. It considers factors like the cost to place an order ([latex]S[\/latex]), the cost to hold one unit in inventory for a year ([latex]H[\/latex]), and the annual demand for the product ([latex]D[\/latex]).<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>economic order quantity (EOQ)<\/h3>\r\n<p>EOQ is a mathematical model used to determine the most cost-effective quantity of items to order. The EOQ formula is:<\/p>\r\n<p>&nbsp;<\/p>\r\n<p style=\"text-align: center;\">[latex]EOQ = \\sqrt{\\frac{2DS}{H}}[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Where:<\/p>\r\n<p>&nbsp;<\/p>\r\n<ul>\r\n\t<li>[latex]D[\/latex] is the annual demand for the product<\/li>\r\n\t<li>[latex]S[\/latex] is the setup or ordering cost per order<\/li>\r\n\t<li>[latex]H[\/latex] is the holding or carrying cost per unit per year<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>The EOQ model aims to minimize the total holding and ordering costs, providing a balanced approach to inventory management.<\/p>\r\n<section class=\"textbox connectIt\">\r\n<p>\u00a0If you run a grocery store, using EOQ can help you determine the optimal amount of perishable items to order, thus minimizing waste and storage costs.<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<p>Your store sells an average of [latex]100[\/latex] units of a product per week. The cost to hold one unit in inventory for a year is [latex]$2.50[\/latex]. The fixed cost per order is [latex]$75[\/latex]. Calculate the economic order quantity.<\/p>\r\n\r\n\r\n[reveal-answer q=\"4331\"]Show Solution[\/reveal-answer] [hidden-answer a=\"4331\"] First, we need to convert the average sales of [latex]100[\/latex] units per week to an annual figure. There are [latex]52[\/latex] weeks in a year, so:\r\n<p style=\"text-align: center;\">[latex]D=100 \\text{ units\/week}\u00d752 \\text{ weeks\/year}=5200 \\text{ units\/year}[\/latex]<\/p>\r\nThe fixed cost per order [latex]S[\/latex] is given as [latex]$75[\/latex]. The holding cost per unit per year [latex]H[\/latex] is given as [latex]$2.50[\/latex]. Now we can plug these values into the EOQ formula:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{lcl} EOQ &amp; = &amp; \\sqrt{\\frac{2 \\times 5200 \\times 75}{2.5}} \\\\ EOQ &amp; = &amp; \\sqrt{\\frac{780000}{2.5}}\u00a0 \\\\ EOQ &amp; = &amp; \\sqrt{312000} \\\\ EOQ &amp; \\approx &amp; 558.5 \\\\ \\end{array}[\/latex]<\/p>\r\nSince we can't order a fraction of a unit, we'll round to the nearest whole number. In this case, that would be [latex]559[\/latex] units. [\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13789[\/ohm2_question]<\/p>\r\n<\/section>\r\n<h3>Just-In-Time (JIT) Inventory<\/h3>\r\n<p>The Just-In-Time (JIT) inventory system is a management strategy that aligns raw-material orders from suppliers directly with production schedules. It aims to increase efficiency and decrease waste by receiving goods only as they are needed in the production process, thereby reducing inventory costs. Unlike EOQ, which focuses on order quantity, JIT focuses on order timing.<\/p>\r\n<p>JIT operates on a few key principles:<\/p>\r\n<ul>\r\n\t<li><strong>Pull Method<\/strong>: Unlike traditional methods that forecast demand and produce accordingly, JIT uses a pull method where products are made to meet actual demand, not projected estimates.<\/li>\r\n\t<li><strong>Quality Over Quantity<\/strong>: JIT emphasizes quality control to reduce defects and waste. This is crucial because there's little room for error when inventory levels are kept low.<\/li>\r\n<\/ul>\r\n<p>Let's look at some advantages and disadvantages of using a just-in-time inventory system.<\/p>\r\n<table border=\"1\">\r\n<thead>\r\n<tr>\r\n<th style=\"text-align: center;\">Advantages<\/th>\r\n<th style=\"text-align: center;\">Disadvantages<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\">Reduced storage and holding costs<\/td>\r\n<td style=\"text-align: center;\">Vulnerability to supply chain disruptions<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">Improved cash flow<\/td>\r\n<td style=\"text-align: center;\">Requires strong supplier relationships<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">Less waste due to overproduction<\/td>\r\n<td style=\"text-align: center;\">Not suitable for all types of businesses<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section class=\"textbox connectIt\">\r\n<p>A fast-food restaurant might use JIT to ensure that fresh ingredients arrive just before the weekend rush. This approach allows the restaurant to keep minimal stock during the weekdays, thereby reducing the need for extensive storage space and minimizing waste.<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<p>Consider a small bakery that bakes fresh bread daily. What are two advantages and two disadvantages of using a JIT inventory system for this bakery.<\/p>\r\n\r\n\r\n[reveal-answer q=\"43312\"]Show Solution[\/reveal-answer] [hidden-answer a=\"43312\"]\r\n\r\n\r\n<p><strong>Advantages<\/strong>: Reduced storage costs, fresher ingredients<\/p>\r\n<p><strong>Disadvantages<\/strong>: Vulnerability to supply chain disruptions, requires precise timing<\/p>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<p>Managing inventory effectively is a balancing act. Overstocking can lead to high holding costs, including storage, insurance, and the risk of obsolescence. Understocking, on the other hand, can result in stockouts, lost sales, and potentially lost customers.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13790[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Describe concepts like inventory management, production scheduling, and optimization\u00a0<\/li>\n<\/ul>\n<\/section>\n<p>Operations and supply chain management are the backbone of any business, ensuring that products are produced and delivered efficiently. This section will delve into key topics like inventory management, production scheduling, and optimization techniques.<\/p>\n<h2>Inventory Management<\/h2>\n<p>Inventory management is a crucial part of any business that deals with physical goods. The objective is to maintain an optimal level of inventory to meet customer demand while minimizing costs.<\/p>\n<section class=\"textbox proTip\">\n<p><strong>Inventory versus Stock<\/strong><\/p>\n<p>You have probably heard the terms &#8220;inventory&#8221; and &#8220;stock&#8221; when it comes to describing the products a business has. In retail settings, the term &#8220;stock&#8221; is commonly used to describe inventory. The phrase &#8220;stock on hand&#8221; is often used by managers to refer to items like clothing and home goods. In a wider industrial context, &#8220;inventory&#8221; encompasses not just finished products for sale, but also the raw materials and components used in manufacturing.<\/p>\n<\/section>\n<p>Different businesses have different needs when it comes to managing inventory. Some rely on mathematical formulas and data analysis, while others depend on procedural methods. Regardless of the approach, the ultimate goal is to improve accuracy and efficiency. Here&#8217;s a brief overview of some commonly used techniques and terms:<\/p>\n<ul>\n<li>\n<p><strong>ABC Analysis<\/strong>: Helps businesses prioritize items that are critical for their operations by classifying stock into categories based on its importance or popularity.<\/p>\n<\/li>\n<li>\n<p><strong>Demand Forecasting<\/strong>: Utilizes predictive analytics to estimate future customer demand, aiding in better stock planning.<\/p>\n<\/li>\n<li>\n<p><strong>Economic Order Quantity (EOQ)<\/strong>: A mathematical formula that calculates the most cost-effective quantity of items to order, balancing holding and ordering costs.<\/p>\n<\/li>\n<li>\n<p><strong>FIFO and LIFO<\/strong>: These are inventory valuation methods. FIFO (First-In, First-Out) moves the oldest stock first, while LIFO (Last-In, First-Out) moves the newest stock first.<\/p>\n<\/li>\n<li>\n<p><strong>Just-In-Time (JIT)<\/strong>: Focuses on timing, aiming to maintain the lowest possible stock levels to reduce storage costs.<\/p>\n<\/li>\n<li>\n<p><strong>Materials Requirements Planning (MRP)<\/strong>: Used in manufacturing to manage planning, scheduling, and inventory control.<\/p>\n<\/li>\n<li>\n<p><strong>Reorder Point Formula<\/strong>: Helps businesses determine when it&#8217;s time to reorder stock to avoid stockouts.<\/p>\n<\/li>\n<li>\n<p><strong>Safety Stock<\/strong>: An extra amount of stock kept as a buffer against unforeseen circumstances like delayed shipments or sudden spikes in demand.<\/p>\n<\/li>\n<\/ul>\n<p>Let&#8217;s explore two of the most popular inventory systems: Economic Order Quantity (EOQ) and Just-In-Time (JIT).<\/p>\n<h3>Economic Order Quantity (EOQ)<\/h3>\n<p>EOQ is a formula used to calculate the most cost-effective quantity of items to order. The EOQ model aims to minimize the total holding and ordering costs. It considers factors like the cost to place an order ([latex]S[\/latex]), the cost to hold one unit in inventory for a year ([latex]H[\/latex]), and the annual demand for the product ([latex]D[\/latex]).<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>economic order quantity (EOQ)<\/h3>\n<p>EOQ is a mathematical model used to determine the most cost-effective quantity of items to order. The EOQ formula is:<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]EOQ = \\sqrt{\\frac{2DS}{H}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Where:<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>[latex]D[\/latex] is the annual demand for the product<\/li>\n<li>[latex]S[\/latex] is the setup or ordering cost per order<\/li>\n<li>[latex]H[\/latex] is the holding or carrying cost per unit per year<\/li>\n<\/ul>\n<\/section>\n<p>The EOQ model aims to minimize the total holding and ordering costs, providing a balanced approach to inventory management.<\/p>\n<section class=\"textbox connectIt\">\n<p>\u00a0If you run a grocery store, using EOQ can help you determine the optimal amount of perishable items to order, thus minimizing waste and storage costs.<\/p>\n<\/section>\n<section class=\"textbox example\">\n<p>Your store sells an average of [latex]100[\/latex] units of a product per week. The cost to hold one unit in inventory for a year is [latex]$2.50[\/latex]. The fixed cost per order is [latex]$75[\/latex]. Calculate the economic order quantity.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4331\">Show Solution<\/button> <\/p>\n<div id=\"q4331\" class=\"hidden-answer\" style=\"display: none\"> First, we need to convert the average sales of [latex]100[\/latex] units per week to an annual figure. There are [latex]52[\/latex] weeks in a year, so:<\/p>\n<p style=\"text-align: center;\">[latex]D=100 \\text{ units\/week}\u00d752 \\text{ weeks\/year}=5200 \\text{ units\/year}[\/latex]<\/p>\n<p>The fixed cost per order [latex]S[\/latex] is given as [latex]$75[\/latex]. The holding cost per unit per year [latex]H[\/latex] is given as [latex]$2.50[\/latex]. Now we can plug these values into the EOQ formula:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{lcl} EOQ & = & \\sqrt{\\frac{2 \\times 5200 \\times 75}{2.5}} \\\\ EOQ & = & \\sqrt{\\frac{780000}{2.5}}\u00a0 \\\\ EOQ & = & \\sqrt{312000} \\\\ EOQ & \\approx & 558.5 \\\\ \\end{array}[\/latex]<\/p>\n<p>Since we can&#8217;t order a fraction of a unit, we&#8217;ll round to the nearest whole number. In this case, that would be [latex]559[\/latex] units. <\/p><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13789\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13789&theme=lumen&iframe_resize_id=ohm13789&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<h3>Just-In-Time (JIT) Inventory<\/h3>\n<p>The Just-In-Time (JIT) inventory system is a management strategy that aligns raw-material orders from suppliers directly with production schedules. It aims to increase efficiency and decrease waste by receiving goods only as they are needed in the production process, thereby reducing inventory costs. Unlike EOQ, which focuses on order quantity, JIT focuses on order timing.<\/p>\n<p>JIT operates on a few key principles:<\/p>\n<ul>\n<li><strong>Pull Method<\/strong>: Unlike traditional methods that forecast demand and produce accordingly, JIT uses a pull method where products are made to meet actual demand, not projected estimates.<\/li>\n<li><strong>Quality Over Quantity<\/strong>: JIT emphasizes quality control to reduce defects and waste. This is crucial because there&#8217;s little room for error when inventory levels are kept low.<\/li>\n<\/ul>\n<p>Let&#8217;s look at some advantages and disadvantages of using a just-in-time inventory system.<\/p>\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\">Advantages<\/th>\n<th style=\"text-align: center;\">Disadvantages<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Reduced storage and holding costs<\/td>\n<td style=\"text-align: center;\">Vulnerability to supply chain disruptions<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Improved cash flow<\/td>\n<td style=\"text-align: center;\">Requires strong supplier relationships<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Less waste due to overproduction<\/td>\n<td style=\"text-align: center;\">Not suitable for all types of businesses<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"textbox connectIt\">\n<p>A fast-food restaurant might use JIT to ensure that fresh ingredients arrive just before the weekend rush. This approach allows the restaurant to keep minimal stock during the weekdays, thereby reducing the need for extensive storage space and minimizing waste.<\/p>\n<\/section>\n<section class=\"textbox example\">\n<p>Consider a small bakery that bakes fresh bread daily. What are two advantages and two disadvantages of using a JIT inventory system for this bakery.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q43312\">Show Solution<\/button> <\/p>\n<div id=\"q43312\" class=\"hidden-answer\" style=\"display: none\">\n<p><strong>Advantages<\/strong>: Reduced storage costs, fresher ingredients<\/p>\n<p><strong>Disadvantages<\/strong>: Vulnerability to supply chain disruptions, requires precise timing<\/p>\n<\/div>\n<\/div>\n<\/section>\n<p>Managing inventory effectively is a balancing act. Overstocking can lead to high holding costs, including storage, insurance, and the risk of obsolescence. Understocking, on the other hand, can result in stockouts, lost sales, and potentially lost customers.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13790\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13790&theme=lumen&iframe_resize_id=ohm13790&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":23,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":92,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/9822"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":17,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/9822\/revisions"}],"predecessor-version":[{"id":12825,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/9822\/revisions\/12825"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/92"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/9822\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=9822"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=9822"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=9822"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=9822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}