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Safety Stock Models in Inventory Management: A Comprehensive Guide with Solved Problems, Summaries of Management of Financial Institutions

Universitas Airlangga (UA)Management of Financial Institutions

EOQ adalah titik pemesanan kembali. digunakan untuk mengetahui kapan perusahaan melakukan pemesanan ulang agar tidak terjadi stock out.

Typology: Summaries

2018/2019

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Module 6 – Safety stock models

1. Define reorder level?

Reorder level is the amount of inventory on hand at which an order is placed.

2. Define safety stock? Why is it necessary to have safety stock?

Safety stock is the buffer and is defined as the difference between the reorder level

and the lead time demand. It is the buffer that we have to make sure that demand

that exceeds the lead time demand is met during lead time

3. What is the relationship between service level and safety stock?

As safety stock increases, service level increases

4. What is the annual cost associated with holding a safety stock of k units?

kCc where Cc is the inventory holding cost per unit per year

5. How do we compute safety stock using the standard normal distribution for a given

service level?

For the given service level, we calculate z from the standard normal tables. zσ is the

safety stock, where σ is the standard deviation of the lead time demand.

6. How is the order quantity and reorder level related?

We have three equations – first relates order quantity Q to the expected shortage𝑆.

The next relates 𝑆 to r (reorder level) and the third relates Q to r. We can use the

three equations to compute Q, r and 𝑆.

7. Write the expression for total cost in a probabilistic setting?

The total cost in a probabilistic setting (in the usual notation) is given by

𝑇𝐶 = 𝐷𝐶0

𝑄+(𝑄

2+𝑟−𝐸(𝑥))𝐶𝑐+𝐷

𝑄𝑆𝑥



𝐶𝑠

8. If the lead time demand has a standard deviation of 25/week, what is the standard

deviation if the lead time is 3 weeks?

For three weeks σLT = √3 X 25 = 43.3

9. If there are two items having the same mean and standard deviation, what is the

advantage if they can be substituted for each other?

When they are not substitutable, σLT = 2σ. If they are substitutable, σLT = √2 σ. The

safety stock is less.

10. How does the variation in the lead time influence the safety stock?

When there is variation in lead time, the safety stock increases significantly.

Partial preview of the text

Download Safety Stock Models in Inventory Management: A Comprehensive Guide with Solved Problems and more Summaries Management of Financial Institutions in PDF only on Docsity!

Module 6 – Safety stock models

Define reorder level? Reorder level is the amount of inventory on hand at which an order is placed.
Define safety stock? Why is it necessary to have safety stock? Safety stock is the buffer and is defined as the difference between the reorder level and the lead time demand. It is the buffer that we have to make sure that demand that exceeds the lead time demand is met during lead time
What is the relationship between service level and safety stock? As safety stock increases, service level increases
What is the annual cost associated with holding a safety stock of k units? kCc where Cc is the inventory holding cost per unit per year
How do we compute safety stock using the standard normal distribution for a given service level? For the given service level, we calculate z from the standard normal tables. zσ is the safety stock, where σ is the standard deviation of the lead time demand.
How is the order quantity and reorder level related? We have three equations – first relates order quantity Q to the expected shortage𝑆̅. The next relates 𝑆̅ to r (reorder level) and the third relates Q to r. We can use the three equations to compute Q, r and 𝑆̅.
Write the expression for total cost in a probabilistic setting? The total cost in a probabilistic setting (in the usual notation) is given by 𝑇𝐶 = 𝐷𝐶 𝑄^0 + (𝑄 2 + 𝑟 − 𝐸(𝑥)) 𝐶𝑐 + 𝐷𝑄 𝑆̅̅𝑥̅ 𝐶𝑠
If the lead time demand has a standard deviation of 25/week, what is the standard deviation if the lead time is 3 weeks? For three weeks σLT = √3 X 25 = 43.
If there are two items having the same mean and standard deviation, what is the advantage if they can be substituted for each other? When they are not substitutable, σLT = 2σ. If they are substitutable, σLT = √2 σ. The safety stock is less.
How does the variation in the lead time influence the safety stock? When there is variation in lead time, the safety stock increases significantly.

Problems

The following information about LTD is given. The values are 200, 250, 300 350 with probabilities 0.2, 0.3, 0.3 and 0.2. Find the reorder level if Cc = Rs 4/unit/year and Cs = Rs 10/unit/year? Since Cs is given in Rs/unit/year, we minimize the sum of inventory and shortage costs. We compute for r = 200, 250, 300 and 350. When r = 200, E(inv) = 0, E (s) = 75, TC = 75 x 10 = 750 When r = 250, E (I) = 10, E (s) = 35, TC = 4x10 + 35x10 = 390 When r = 300, E (I) = 45, E (s) = 10, TC = 45x4 + 10x10 = 280 When r = 350, E(I) = 75, E (s) = 0, TC = 75x4 = 300. The best decision is r = 300.
The following information about LTD is given. The values are 300, 350, 400 450 and 500 with probabilities 0.2, 0.25, 0.3 and 0.2 and 0.05. Find the reorder level if Cc = Rs 4/unit/year and Cs = Rs 10/unit/year? Since Cs is given in Rs/unit/year, we minimize the sum of inventory and shortage costs. We compute for r = 300, 350, 400, 450 and 500. When r = 300, E(inv) = 0, E (s) = 82.5, TC = 82.5 x 10 = 825 When r = 350, E (I) = 10, E (s) = 42.5, TC = 4x10 + 42.5x10 = 465 When r = 400, E (I) = 32.5, E (s) = 15, TC = 32.5x4 + 15x10 = 280 When r = 450, E(I) = 70, E (s) = 2.5, TC = 70x4 + 2.5x10= 305. When r = 500, E(I) = 117.5, E (s) = 0, TC = 117.5 x 4 = 470 The best decision is r = 400.
LTD follows a uniform distribution 200 ± 80. Find the reorder level for a service level of 75% The values are between 120 and 280. The range is 160. 75% of 160 is 120. ROL = 120+120 = 240
LTD follows a normal distribution with μ =200 and σ = 40. Find the reorder level for a service level of 95% (z = 1.645)? z = 1.645. zσ = 1.645 x 40 = 65. 8. ROL = 200 + 65.8 = 265.
LTD follows a normal distribution with μ =200 and σ = 40. Find the reorder level when Q = 1250, D = 10000, Cs = 10, Cc = 4? QCc/DCs = 1250x4/10000x10 = 5000/100000 = 0.005. From standard normal tables, we get z = 1.645, reorder level = 200 + 1.645 x 40 = 265.
Consider a single item with D = 12000/year, C 0 = 400, Cc = 12/unit/year, i = 20% and Cs = 400. Write the expression for TC in the usual notation for a probabilistic inventory model considering Q and r as decision variables? Find Q and r. The total cost in a probabilistic setting (in the usual notation) is given by 𝑇𝐶 = 𝐷𝐶 𝑄^0 + (𝑄 2 + 𝑟 − 𝐸(𝑥)) 𝐶𝑐 + 𝐷𝑄 𝑆̅̅𝑥̅ 𝐶𝑠. Using the EOQ model, we get Q = 894.43.

Q = 1600, OC = 300, CC = 1400x0.1666 = 233.32; Q = 2400, OC = 300, CC = 3300x0.1666 = 549.75. First order is at Q = 1600 because CC is closest to OC. For the second order, we start with Q = 800, CC = 66.66, For Q = 2000, CC = 2200 x 0.1666 = 366.65 and for Q = 3000, CC = 4700x0.1666 = 783.3. The second lot is for Q = 2000 because OC is close to CC.

We compute for Silver Meal heuristic. Q = 1000 TC = 300 + 83.33 = 383.33; Q = 1600, TC = 300 + 233.24 = 523.24; TC/period = 266.62; Q = 2400, TC = 300 + 549.75 = 849.75. TC/period = 283.25. Since TC/period increases here, best lot size is Q = 1600 where TC/period is minimum. For the second lot, Q = 800, TC = 300 + 66.66 = 366.66, Q = 2000, TC = 300 + 366.66 = 666.66. TC/period = 333.33. Q = 3000, TC = 300 + 783.33 = 1083.33. TC/period = 361.11. Since TC/period increases here, best lot size is Q = 2000 where TC/period is minimum

The demand for 8 months is 1000, 600, 800, 1200, 1000, 1200, 900 and 1000. Find the EOQ Use C 0 = 300 and Cc = 2/unit/year. Find the ordering and inventory costs for 8 months using the EOQ and the monthly data? ΣD = 7770 for 8 months, Cc = 4/3 for 8 months, Q = 1861.45 and TC = 2481.93. N = 4.13. We assume 4 orders and order quantity of 1925 per order. The calculations are shown month wise. Month Demand order B I E I Avg 1 2 3 4 5 6 7 8 1000 600 800 1200 1000 1200 900 1000

Total 7700 8963

(The EI at period 6 is negative. Average inventory is calculated as (1175+0)/2 = 588. TC = 300x4 + 8963x0.1666 = 2693.

Consider two items with LTD = 300 and 500 respectively. The variance of LTD is 400 and 900 for the two items. Assume normal distribution and 95% service level. What is the gain in the safety stock if these can be substituted? The standard deviations are 20 and 30. At 95% SL, z = 1.645. The safety stock values are zσ which are 1.645x20 = 32.9 (≈ 33) and 1.645x30 = 49.35 (≈ 49). Total SS = 82. When the products are substitutable, variance of LTD = 400 + 900 = 1300. σLT = √ = 36. SS = 1.645x36 = 59 (approx.). The gain is the reduction of SS by 23 units

Consider two items with D = 150 and 200 respectively. The variance of weekly demand is 400 and 900 for the two items. Assume normal distribution, 95% service level and LT = 2 weeks. What is the gain in the safety stock if these can be substituted? Considering that LT = 2 weeks, the SS for the two items are 32.9x√2 ≈ 47 and 49.35x√2 ≈ 70. Total SS = 117. When the products are substitutable, new SS = 59.31x√2 ≈ 84. There is a saving of 33 units

Safety Stock Models in Inventory Management: A Comprehensive Guide with Solved Problems, Summaries of Management of Financial Institutions

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Module 6 – Safety stock models