Deterministic Inventory Control Model Formulas Rushabh

8/9/2019 Deterministic Inventory Control Model Formulas Rushabh

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Created By: Rushabh Shah

p=rate of receipt of inventory d=rate of usage of inventory

+. Model II(a) !" model #ith Constant Rate o$ Demand and ,ariable !rder

Cycle -ime

*

*

*

*

* * *

2

2

2

o h s

h s

o s

h h s

so h

h s

DC C CQ

C C

DC CM

C C C

Qt

D

CTVC DC C

C CR Q M

+=

= +

=

=

+ =

Where R=maximum Shortage nits

!=Optimal Stoc" #evel

$=%conomic Order $uantity

&s=&ost of shortage

. Model II(b) !" Model /ith Constant rate o$ Demand and Fi0ed Reorder

Cycle -ime

* *

** *

s

h s

h s

h s

CM D tC C

C CTVC D t

C C

= +

= +

*. Model II(c) !" Model #ith radual suly and shortae allo#ed

'ae % o$ *


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*

* *

2

'

* '

(

2

2

2

o h s

h s

h

h s

sh

h s

s

h h s

DC C C pQ

C C p d

Cp dQ Q

p C C

Cp dTVC DC C

p C C

C Cp dQ D

C p C C

+=

=

+

= +

= +

. Model III(a) !" model #ith /arehouse Sace Constraint

(

* 2

2

n

i i

i

i oi

i

hi i

f Q W

D CQ

C f

=

=+

2. Model III(b) !" model #ith Investment Constraint

(

* 2

2

*

n

i i

i

i oi

i

hi i

hi i

C Q F

D CQ

C C

where

C r C

=

=+

=

3. Model III(c) !" model #ith averae Inventory level Constraint

(

(

2

n

i

i

Q M=

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14. Model III(d) !" model #ith 5umber o$ orders Constraint

Number of Orders per year = *

)here

N= specified number of orders

&= emand in rupees

DCN

DC

11. Model I, !" model #ith all units discounts available

(i) Model #ith one rice brea6

(ii) Model #ith t#o rice brea6

Sums o$ Deterministic Inventory Control Model

1. I(a) +he production department for a company re,uires -.'' /0g of ra)material for manufacturing a particular item per year0 1t has been

estimated that the cost of placing an order is Rs0 -. and the cost of

carrying inventory is 2 percent of the investment in the inventories0 +heprice is Rs0 (' per /0g0 +he purchase manager )ishes to determine an

ordering policy for ra) material0

%. I(c) 3 contractor has to supply ('4''' bearings per day to an automobile

manufacturer0 He find that )hen he starts production run he can produce

24''' bearing per day0 +he cost of holding a bearing in stoc" for a yearis Rs 2 and the set up cost of a production run is Rs0 (5'0 Ho) fre,uently

should production run be made0

&. I(c) 3 product is sold at the rate of ' pieces per day and is manufactured at a

rate of 2' pieces per day0 +he set up cost of the machines is Rs0 ('''

and the storage cost is found to be Rs0 '0''( per piece per day0 Withlabour charges of Rs0 -02' per piece4 material cost at Rs 20(' per piece

and overhead cost of Rs0 60(' per piece4 find the minimum cost batch si7e

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if the interest charges are 5 percent 8assume -'' )or"ing days in a year90&ompute the optimal number of cycles re,uired in a year for the

manufacturing of this product0

+. II(a) 3 commodity is to be supplied at a constant rate of 2'' units per day0Supplies of any amount can be obtained at any re,uired time4 but each

ordering cost Rs '4 cost of holding the commodity in inventory is Rs

20'' per unit per day )hile the delay in the supply of the item induces a

penalty of Rs (' per unit per day0 :ind the optimal policy 8$4t9 )here t isthe reorder cycle period and $ is the inventory after reorder0

. II(c) +he demand for an item in a company is (54''' units per year and the

company can produce the item at a rate of -4''' per month0 +he cost ofone set up is Rs '' and the holding cost of one unit per month is (

paise0 +he shortage cost of one unit is Rs0 26' per year0 *etermine the

optimum manufacturing ,uantity and the number of shortages0 3lsodetermine the manufacturing time and the time bet)een set;ups0

*. III(a) A small shop produces three machine parts 1,2,3 in lots. The shophas only 650 sq. m of storage space. The appropriate data for the

three items are presented in the following tale.

!tem 1 2 3"emand#units per year$ 5000 2000 10000

%et up &ost #'s$ 100 200 (5

&ost per unit#'s$ 10 15 5

)loor space required #sq

ft*unit$

0.(0 0.+0 0.0

The shop uses an in-entory carrying charge of 20 percent of a-eragein-entory -aluation per annum. !f no stoc outs are allowed,

determine the optimal lot si/e of each item under gi-en storage

constraint.

. III(b) A shop produces three items in lots. The demand rate for each item isconstant and can e assumed to e deterministic. o ac orders areto e allowed. The pertinent data for the items is gi-en in the

following tale.

!tem 1 2 3

&arrying &ost#'s. er

unit per year$

20 20 20

%et up &ost #'s per

setup$

50 0 60

&ost per unit#'s$ 6 ( 5

early "emand #units$ 10,000 12,000 (,500

"etermine approimately the economic order quantities for threeitems su4ect to the condition that the total -alue of a-erage

in-entory le-els of these items does not eceed 's. 1,000.2. III(c) &onsider the data of ao-e eample no 6. with a constraint of limited

storage space sufficient only for 560 units of all types of items insteadof 650 sq. ft. of storage space. "etermine the optimal numer of

units of each item separately so as to satisfy the gi-en constraint.

3. III(d) A company has to purchase four items A,,& and " for the net year.The pro4ected demand and the unit price in 's are as follows

!tem "emand#units$ nit rice #'s$

A 60,000 3

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Created By: Rushabh Shah 0,000 2

& 1,200 2

" 5,000

!f the company wants to restrict the total numer of orders to 0 for

all the four items, how many orders should e placed for each item.

14. I,

(one

rice

brea6)

The annual demand of a product is 10,000 units. 7ach unit cost 's100 if orders placed in quantities elow 200 units ut for orders of

200 or ao-e the price is 's. 85. The annual in-entory holding cost is10 percent of the -alue of the item and the ordering cost is 's 5 per

order. )ind the economic lot si/e.

11. I,

(t#o

rice

brea6)

A shopeeper estimates annual requirement of an item as 2000 units.

9e uys from supplier at a cost of 's 10 per item and the cost ofordering is 's 50 each time. !f the stoc holding costs are 25 percent

per year of stoc -alue, how frequently should he replenish hisstocs: )urther suppose the supplier offers a 10 per cent discount on

orders etween 100 and 88 items, and a 20 percent discount onorders eceeding or equal to 500. &an the shop eeper reduce his

costs y taing ad-antage of either of these discounts.

'ae * o$ *

Deterministic Inventory Control Model Formulas Rushabh

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