colapop requires, an average, 2,700 tons of aluminum each week, with a standard deviation of 700 tons. The lead time to receive its orders is 8 weeks. The holding cost for one ton of aluminum for one week is $9. It operates with a 0.99 in-stock probability on average how many tons does it have on hand? if its average inventory was 9000 tons, what would be its average holding cost per week? Suppose its on-hand is 5375 tons, on average, what in stock probability does it offer to customers?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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colapop requires, an average, 2,700 tons of aluminum each week, with a standard deviation of 700 tons. The lead time to receive its orders is 8 weeks. The holding cost for one ton of aluminum for one week is $9. It operates with a 0.99 in-stock probability

on average how many tons does it have on hand?

if its average inventory was 9000 tons, what would be its average holding cost per week?

Suppose its on-hand is 5375 tons, on average, what in stock probability does it offer to customers?

**Table 11.5: In-Stock Probabilities and Matching Safety Factors, z**

This table provides data on the relationship between in-stock probabilities and their corresponding safety factors. It helps in determining how much safety stock is needed to achieve a desired service level in inventory management.

- **Left Column:**

  - **In-Stock Probability and Safety Factor, z:**
    - In-Stock Probability: 0.9000, Safety Factor, z: 1.28
    - In-Stock Probability: 0.9800, Safety Factor, z: 2.05
    - In-Stock Probability: 0.9900, Safety Factor, z: 2.33
    - In-Stock Probability: 0.9950, Safety Factor, z: 2.58
    - In-Stock Probability: 0.9999, Safety Factor, z: 3.72

- **Right Column:**

  - **Safety Factor and In-Stock Probability:**
    - Safety Factor, z: 1.25, In-Stock Probability: 0.8944
    - Safety Factor, z: 2.00, In-Stock Probability: 0.9773
    - Safety Factor, z: 2.25, In-Stock Probability: 0.9878
    - Safety Factor, z: 2.50, In-Stock Probability: 0.9938
    - Safety Factor, z: 3.00, In-Stock Probability: 0.9987

This data is pivotal for calculating the level of inventory required to meet specified service levels in supply chain management.
Transcribed Image Text:**Table 11.5: In-Stock Probabilities and Matching Safety Factors, z** This table provides data on the relationship between in-stock probabilities and their corresponding safety factors. It helps in determining how much safety stock is needed to achieve a desired service level in inventory management. - **Left Column:** - **In-Stock Probability and Safety Factor, z:** - In-Stock Probability: 0.9000, Safety Factor, z: 1.28 - In-Stock Probability: 0.9800, Safety Factor, z: 2.05 - In-Stock Probability: 0.9900, Safety Factor, z: 2.33 - In-Stock Probability: 0.9950, Safety Factor, z: 2.58 - In-Stock Probability: 0.9999, Safety Factor, z: 3.72 - **Right Column:** - **Safety Factor and In-Stock Probability:** - Safety Factor, z: 1.25, In-Stock Probability: 0.8944 - Safety Factor, z: 2.00, In-Stock Probability: 0.9773 - Safety Factor, z: 2.25, In-Stock Probability: 0.9878 - Safety Factor, z: 2.50, In-Stock Probability: 0.9938 - Safety Factor, z: 3.00, In-Stock Probability: 0.9987 This data is pivotal for calculating the level of inventory required to meet specified service levels in supply chain management.
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