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


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


Empirical Probability Distribution


Cumulative Probability Distribution


D= 11.73

s = 4.74


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)


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


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*


Q* = Mean demand + Z = 11.73 + 4.74 * 0.74 = 15.24 15


Cumulative Probability Distribution

PPT 07 Inventory Management NewsVendor

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