• Author / Uploaded
• Prashant Kanaujia

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Problems on Inventory Control 1. A product is priced to sell at $ 100 per unit and its cost is constant at $70 per unit. Each unsold unit has a salvage value of $20. Demand is expected to range between 35 and 40 units for the period. 35 definitely can be sold and no units over 40 will be sold. The demand probabilities and the associated cumulative probability distribution (P) for this situation are shown below. Number of units demanded 35 36 37 38 39 40

Probability of this demand 0.10 0.15 0.25 0.25 0.15 0.10

Cumulative probability 0.10 0.25 0.50 0.75 0.90 1.00

How many units should be ordered? [Answer: 37 units] ANS:Cost of under stock (Cu) = $ 30. {100-70} Cost of Over Stock (Co) = $ 50 Demand Range For 35-36

{70-20} Profit

Vs

Loss

(1-0.10) x 30= 27

50 x 0.10 = 5

36-37

(1-0.25) x 30 =22.5

50 x 0.25 = 12.5

37-38

(1-0.5) x 30 = 15

50 x 0.5 = 25

Here you can see that Loss is more than profit when the range is beyond 37. Thus optimum product to sale is “37 Unit”.

2. Items purchased from a vendor cost $ 20 each and forecast for next year’s demand is 1000 units. If it costs $ 5 every time an order is placed for more units and the storage cost is $ 4 per unit per year, what quantity should be ordered each time? a. What is the total ordering cost for the year? b. What is the total storage cost for a year? [Answer: $ 100 each] ANS:- Annual Demand (D)= 1000 units Order or setup Cost (S)= $ 5 per order Annual holding cost (iC) = $ 4 per order Optimistic Quantity = √

=√ = 50 units. Total Order per year (T) = = = 20 order. (a) Ans. Total Ordering Cost for year = 20 x 5 =$100. (b) Ans. Total Holding Cost = 20 x 4 =$ 80.

3. Daily demand for a product is 120 units, with a standard deviation of 30 units. The review period is 14 days and the lead time is 7 days. At the time of review, 130 units are in stock. If only 1% risk of stocking out is acceptable, how many units should be ordered? [Answer: 2710 units] ANS:-

Demand of the product (µ)

= 120

Standard Deviation ( )

=30

Review Period (T)

=14days

Lead Time (L)

=7days

Unit in stock (I)

=130

Q = (T+L) x 120 + Z ( 2 (T+L)

= (T+L) x

(T+L))

-I

2

= (14+7) x 302 =18900 (T+L) =

30

“Z = 2.33”, according to the condition 1% risk of stocking out.

50% always use to be covered as the diagram has and rest is (Z+remaining) Here 1% risk thus 49% under cover. Remaining area = 0.49 – Z Z = 2.33  value from table.

Substitute these all equations in the main formula, Q = 21 x 120 + 2.33 x 30

-130

= 2710 units.

4. A company orders every two weeks when the salesperson visits the premises. Demand for the product averages 20 units per day with a standard deviation of 5 units. Lead time for the product to arrive is 7 days. Management has a goal of a 95 percent probability of not stocking out for this product. The salesperson is due to come in late this afternoon when 180 units are left in stock. How many units should be ordered?

[Answer: 278 units]

ANS:-

Demand of the product (µ)

= 20 units

Standard Deviation ( )

= 5 units

Review Period (T)

=14days (2 weeks given)

Lead Time (L)

=7days

Unit in stock (I)

=180

Q = (T+L) x 120 + Z ( 2 (T+L)

= (T+L) x

= (14+7) x 52 (T+L) =

5

2

(T+L))

-I

“Z = 1.65” as, according to the condition 95% risk of not stocking out.

50% always use to be covered as the diagram has and rest is (Z+remaining) thus 45% under cover. Remaining area = 0.45 – Z Z = 1.65  value from table.

Substitute these all equations in the main formula, Q = 21 x 20 + 1.65(5

) – 180

= 277.6 units.