{"id":209280,"date":"2025-04-29T04:10:34","date_gmt":"2025-04-29T04:10:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=209280"},"modified":"2025-04-29T04:10:36","modified_gmt":"2025-04-29T04:10:36","slug":"braums-icecream-store","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/29\/braums-icecream-store\/","title":{"rendered":"Braum’s Icecream Store"},"content":{"rendered":"\n

Braum’s Icecream Store. Braums is a popular ice cream store that sells frozen yogurt cones in 3 sizes: small, medium, and large. Let us consider a Braum’s store on West Campbell Rd, every day this store, maintains the following inventory of waffle cones:<\/p>\n\n\n\n

Small cones – 500 units,<\/p>\n\n\n\n

Medium cones – 700 units,<\/p>\n\n\n\n

Large cones – 600 units.<\/p>\n\n\n\n

Now, suppose you are a store manager, and you happen to know from past sales data that the demands for frozen yogurt cones are as follows:<\/p>\n\n\n\n

Small cones – Normally distributed with a mean of 400 units and deviation of 50 units,<\/p>\n\n\n\n

Medium cones – Normally distributed with a mean of 600 units and deviation of 100 units,<\/p>\n\n\n\n

Large cones – Normally distributed with a mean of 450 units and deviation of 100 units.<\/p>\n\n\n\n

Assume that sales of one type of cone does not affect the sales of other cone, in words what this means is that each cone has set of customers who always buy the respective cone. Use this information to answer the questions 5 to 10.<\/p>\n\n\n\n

Suppose you have a protocol from the heirarchy that you have to maintain a service level of 95%, what this means is that 5% of the time you can go complete stockout on all three cones combined. Now, the question is as follows: What is the total inventory Braums should maintain ? [A] (round up to nearest integer)<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the total inventory Braum’s should maintain for frozen yogurt cones, we need to account for the service level of 95%, meaning that we want to ensure that there is enough stock to meet customer demand 95% of the time. This involves calculating the safety stock<\/strong> for each type of cone and adding it to the regular inventory. The safety stock accounts for variations in demand, and the total inventory is the sum of regular stock and safety stock for each cone.<\/p>\n\n\n\n

Step-by-Step Calculation:<\/h3>\n\n\n\n
    \n
  1. Define the z-score for 95% service level<\/strong>:\n
      \n
    • A service level of 95% corresponds to a z-score of approximately 1.645<\/strong>, which is found from standard normal distribution tables.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Calculate the safety stock for each cone<\/strong>: The formula for safety stock is: Safety\u00a0Stock=z\u00d7\u03c3\\text{Safety Stock} = z \\times \\sigma Where:
      • zz is the z-score corresponding to the service level,<\/li>
      • \u03c3\\sigma is the standard deviation of demand.<\/li><\/ul>Small Cones<\/strong>:
        • Mean demand = 400 units,<\/li>
        • Standard deviation (\u03c3\\sigma) = 50 units,<\/li><\/ul>Safety\u00a0Stock\u00a0(Small)=1.645\u00d750=82.25\u224883\u00a0units.\\text{Safety Stock (Small)} = 1.645 \\times 50 = 82.25 \\approx 83 \\text{ units}. Medium Cones<\/strong>:
          • Mean demand = 600 units,<\/li>
          • Standard deviation (\u03c3\\sigma) = 100 units,<\/li><\/ul>Safety\u00a0Stock\u00a0(Medium)=1.645\u00d7100=164.5\u2248165\u00a0units.\\text{Safety Stock (Medium)} = 1.645 \\times 100 = 164.5 \\approx 165 \\text{ units}. Large Cones<\/strong>:
            • Mean demand = 450 units,<\/li>
            • Standard deviation (\u03c3\\sigma) = 100 units,<\/li><\/ul>Safety\u00a0Stock\u00a0(Large)=1.645\u00d7100=164.5\u2248165\u00a0units.\\text{Safety Stock (Large)} = 1.645 \\times 100 = 164.5 \\approx 165 \\text{ units}.<\/li>\n\n\n\n
            • Determine total inventory for each cone<\/strong>: Now, we add the safety stock to the regular inventory:\n
                \n
              • Small Cones<\/strong>: Total\u00a0Inventory\u00a0(Small)=500+83=583\u00a0units.\\text{Total Inventory (Small)} = 500 + 83 = 583 \\text{ units}.<\/li>\n\n\n\n
              • Medium Cones<\/strong>: Total\u00a0Inventory\u00a0(Medium)=700+165=865\u00a0units.\\text{Total Inventory (Medium)} = 700 + 165 = 865 \\text{ units}.<\/li>\n\n\n\n
              • Large Cones<\/strong>: Total\u00a0Inventory\u00a0(Large)=600+165=765\u00a0units.\\text{Total Inventory (Large)} = 600 + 165 = 765 \\text{ units}.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Calculate the total inventory<\/strong>: Total\u00a0Inventory=583+865+765=2213\u00a0units.\\text{Total Inventory} = 583 + 865 + 765 = 2213 \\text{ units}.<\/li>\n<\/ol>\n\n\n\n

                Conclusion:<\/h3>\n\n\n\n

                To maintain a 95% service level, Braum’s should maintain a total inventory of 2213 units<\/strong>. This total ensures that even with variability in demand, the store will have sufficient stock to meet customer needs 95% of the time.<\/p>\n","protected":false},"excerpt":{"rendered":"

                Braum’s Icecream Store. Braums is a popular ice cream store that sells frozen yogurt cones in 3 sizes: small, medium, and large. Let us consider a Braum’s store on West Campbell Rd, every day this store, maintains the following inventory of waffle cones: Small cones – 500 units, Medium cones – 700 units, Large cones […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","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":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","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-opacity":"","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-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-209280","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=209280"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209280\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=209280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=209280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=209280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}