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Inventory Mgt and Control 08_Practice_Problems_1, Exercises of Accounting

STI Colleges and Education Centers (STICEC)Accounting

PRACTICE PROBLEMS FOR STOCHASTIC INVENTORY MODELS

Typology: Exercises

2021/2022

Available from 07/05/2022

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bg1
BM2020
Darrenel M. Buenaobra
BSBA601
PRACTICE PROBLEMS FOR STOCHASTIC INVENTORY MODELS
1.
The daily demand for an item is 20 units. The procurement lead time for the item is ten (10) days, and the standard
deviation of the demand during the lead time is 12 units. Determine the cycle service level if the reorder level is 213
units.
Reorder point = (daily demand * lead time in days) + Safety stock
= 213 = (20*10) + Safety stock
= Safety stock = 213 - 200 = 13 units
Safety stock = Z * Standard deviation of demand during lead time
= 13 = Z * 12
= Z = 13/12 = 1.08
Z = 1.08 for service level of 86% as per stock coverage table.
2.
The daily demand for an item is 20 units. The procurement lead time for the item is ten (10) days. The standard
deviation of the lead time demand is 12 units. Determine the fill rate if an order for 300 units is placed each time the
inventory falls to 213 units.
Orders is placed when stock level falls to 213, which means reorder point is 213.
Reorder point = (daily demand * lead time in days) + Safety stock
= 213 = (20*10) + Safety stock
=Safety stock = 213 - 200 = 13 units
Safety stock = Z * Standard deviation of demand during lead time
=13 = Z * 12
=Z = 13/12 = 1.08
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BM

Darrenel M. Buenaobra

BSBA

PRACTICE PROBLEMS FOR STOCHASTIC INVENTORY MODELS

  1. The daily demand for an item is 20 units. The procurement lead time for the item is ten (10) days, and the standard deviation of the demand during the lead time is 12 units. Determine the cycle service level if the reorder level is 213 units.

Reorder point = (daily demand * lead time in days) + Safety stock

= 213 = (20*10) + Safety stock

= Safety stock = 213 - 200 = 13 units

Safety stock = Z * Standard deviation of demand during lead time

= 13 = Z * 12

= Z = 13/12 = 1.

Z = 1.08 for service level of 86% as per stock coverage table.

  1. The daily demand for an item is 20 units. The procurement lead time for the item is ten (10) days. The standard deviation of the lead time demand is 12 units. Determine the fill rate if an order for 300 units is placed each time the inventory falls to 213 units.

Orders is placed when stock level falls to 213, which means reorder point is 213.

Reorder point = (daily demand * lead time in days) + Safety stock

= 213 = (20*10) + Safety stock

=Safety stock = 213 - 200 = 13 units

Safety stock = Z * Standard deviation of demand during lead time

=13 = Z * 12

=Z = 13/12 = 1.

Z = 1.08 for service level of 86% as per stock coverage table.

  1. Weekly demand for a certain item at a firm follows a normal distribution with a mean of 50 units and a standard deviation of five (5) units. The optimal review period is three (3) weeks, while the lead time is constant at two (2) weeks. The firm wants to ensure there is no stockout 95% of the time during the lead time. Compute the safety stock, target inventory, and the order quantity if at the time of review there are 58 units in store.

Average Weekly Demand = 50 units

Standard deviation of Weekly demand = 5 units

Lead time = 2 weeks

Review time = 3 weeks

Protection period = Review time + Lead time = 2+3 = 5 weeks

Standard deviation of demand during Protection period

= SQRT (Protection period) * Standard deviation in weekly demand

= SQRT (5) *5 = 11.

Service level required = 95%

Z of 95% = 1.

Safety stock = Z * Standard deviation of demand during lead time

= 1.645 * 11.18 = 18.391 = 18 units

Target inventory = (Weekly demand * Protection Period) + Safety stock

= (50*5) + 18 = 268 unit

Order Quantity = Target inventory - In stock quantity = 268 - 58 = 210 units

  1. Weekly demand for a certain item at a firm follows a normal distribution with a mean of 200 units and a standard deviation of 50 units. The optimal review period is four (4) weeks, while the lead time is constant at three (3) weeks. If the firm wants to ensure a cycle service level of 98%, compute the safety stock, maximum inventory, and the order quantity if at the time of review there are 100 units in store.

Average Weekly Demand = 200 units

Standard deviation of Weekly demand = 50 units

Lead time = 3 weeks

Review time = 4 weeks

Protection period = Review time + Lead time = 4+3 = 7 weeks

Standard deviation of demand during Protection period

= SQRT (Protection period) * Standard deviation in weekly demand

= SQRT (7) *50 = 132.

Service level required = 98%

08 Practice Problems 1 _Property of STI_* Page 1 of 1