PPT 07 Inventory Management NewsVendor
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Transcript of PPT 07 Inventory Management NewsVendor
Inventory ManagementInventory Management
Single PeriodSingle PeriodSanjay Choudhari
Indian Institute of Management Indore
Single Period Inventory Single Period Inventory
Inventory planning is limited to single period
Inventory can not be used for the next period due to perishable nature of the item e.g. Newspaper, Airline
Uncertainty of demand only for a period and no sufficient time (lead time) for rush order to cover unexpectedly high demand
Similar problem exists for manufactures of fashion goods
Profit Function Profit Function
Revenue from sold items Revenue or costs associated with unsold
items. These may include revenue from salvage or cost associated with disposal.
Costs associated with not meeting customers’ demand. The lost sales cost can include lost of good will and actual penalties for low service.
The cost of buying the merchandise in the first place.
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
15 19 9 12 9 22 4 7 8 1114 11 6 11 9 18 10 0 14 128 9 5 4 4 17 18 14 15 86 7 12 15 15 19 9 10 9 168 11 11 18 15 17 19 14 14 1713 12
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Probability estimates of number of copies sold in any week is specific value e.g. Demand (D= 10) = 2/52 = 0.0385
Cumulative probability e.g. (D<= 9) = (1+0+0+0+3+1+2+2+4+6) = 19/52= 0.3654
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Empirical Probability Distribution
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Cumulative Probability Distribution
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
D= 11.73
s = 4.74
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Demand during any week is a random variable that is approximately normally distributed, with mean 11.73 and standard deviation 4.74
• Selling price is Rs 75
• Salvage OR scrap value is Rs 10
• Purchasing cost is Rs 25
Co = 25 – 10 = 15
Cost per unit of positive inventory remaining at the end of the period (Overage cost)
Cu = 75 – 25 = 50
Cost per unit of unsatisfied demand (Underage cost)
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Q = Optimal number of units to be stocked
D = Single period demand
Co = Cost of overstocking per unit when D < Q
Cu = Cost of Understocking per unit when D > Q
Critical ratio = Probability that the demand does not exceed Q*
𝑃(𝐷≤ 𝑄∗) = 𝐶𝑢𝐶𝑢 + 𝐶𝑜
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
𝑃(𝐷≤ 𝑄∗) = 𝐶𝑢𝐶𝑢 + 𝐶𝑜
𝑃ሺ𝐷≤ 𝑄∗ሻ∗𝐶𝑜= 𝑃ሺ𝐷> 𝑄∗ሻ∗𝐶𝑢
𝑃ሺ𝐷≤ 𝑄∗ሻ∗𝐶𝑜= (1− 𝑃ሺ𝐷≤ 𝑄∗ሻ) ∗𝐶𝑢
𝑃ሺ𝐷≤ 𝑄∗ሻ∗(𝐶𝑢 + 𝐶𝑜) = 𝐶𝑢
Area = 0.77 : Z = O.74
11.73 Q*
Example : Example : Computer Journal , Weekly Popular magazine Computer Journal , Weekly Popular magazine
Q* = Mean demand + Z = 11.73 + 4.74 * 0.74 = 15.24 15