Economic Order Quantity (EOQ) MCQ Quiz in मल्याळम - Objective Question with Answer for Economic Order Quantity (EOQ) - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

The ordering quantity Q* at which holding cost becomes equal to ordering cost and the total inventory cost is minimum is known as Economic order Quantity (EOQ).

At EOQ:

Ordering cost = Holding cost

\(\frac{D}{{{Q^*}}}{C_o} = \frac{{{Q^*}}}{2}{C_h} \Rightarrow {Q^*} = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}} \)

D = Annual or yearly demand of inventory (unit/year)

Q = Quantity to be ordered at each order point (unit/order)

C_o = Cost of placing one order [Rs/order]

C_h = Cost of holding one unit in inventory for one complete year [Rs/unit/year]

Calculation:

D = 6000 units, C_o = Rs. 1000, C_h = 48

\({{\rm{Q}}^{\rm{*}}} = \sqrt {\frac{{2{\rm{D}}{{\rm{C}}_{\rm{o}}}}}{{{{\rm{C}}_{\rm{h}}}}}} = \sqrt {\frac{{2 \times 6000 \times 1000}}{{48}}} = 500{\rm{\;units}}\)

Concept:

In a back order model every time after stock out period when quantity Q is received the inventory level reaches its maximum level.

Economic order quantity \( = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}\left( {\frac{{{C_b} + {C_h}}}{{{C_b}}}} \right)}\) 

Maximum inventory \(= \sqrt {\frac{{2D{C_o}}}{{{C_h}}} \times \left( {\frac{{{C_b}}}{{{C_b} + {C_h}}}} \right)}\) 

Where, D is the demand per year, C_b is the backordering cost per unit per year and C_h is the carrying cost per unit per year

C_o is the ordering cost per order

Calculation:

Given, D = 10000/year, C_h = 4 /unit/year, C_o = 300/order, C_b = 25 /unit/year

\({Q_{max}} = \sqrt {\frac{{2 \times 10,000 \times 300}}{4} \times \frac{{25}}{{25 + 4}}}\)

Q_max = 1137.147 units

Explanation:

Curve P₂: Holding cost

Holding cost = \(\rm \frac{Order\ quantity}{2}× \frac{Carrying\ cost}{\frac{unit}{unit\ time}}\)

\(\rm =\frac{Q}{2}× C_c\)

⇒ Holding cos t ∝ Q

Curve P3: Setup cost

Setup cost (or) ordering cost

= No. of setups × setup cost / setup

\(\rm=\frac{Annual\ demand}{Order\ quantity}× \frac{setup\ cos\ t}{setup}\)

\(\rm =\frac{D}{Q}× C_0\)

⇒ Ordering (or setup cost ∝ \(\rm \frac{1}{Q}\)

Curve P₄: Production (or) Material cost

Curve P1: Total cost

Annual production cost = Annual demand × unit cost

= D × C_u

⇒ Production cost is independent of order quantity.

TC = holding cost + setup cost + production cost

Explanation:

Economic order quantity (EOQ):

• Economic order quantity is the size of the order which helps in minimizing the total annual cost of inventory in the organization.
• When the size of the order increases, the ordering costs (cost of purchasing, inspection, etc.) will decrease whereas the inventory carrying costs (costs of storage, insurance, etc.) will increase.
• Economic Order Quantity (EOQ) is the size of an order which minimizes total annual costs of carrying and cost of ordering.

• It is evident from above that the minimum total costs occur at a point where the ordering costs and inventory carrying costs are equal.

At EOQ:

Ordering cost = Holding cost

\(\frac{D}{{{Q^*}}}{C_o} = \frac{{{Q^*}}}{2}{C_h} \Rightarrow {Q^*} = \sqrt {\frac{{2A{P}}}{{{C}}}} =\sqrt {\frac{2(Annual\:Usage\:in\:units)\times (Order\:cost)}{(Annual\:carrying\:cost\:per\:unit)}}\)

A = Annual or yearly demand for inventory (unit/year)

Q = Quantity to be ordered at each order point (unit/order)

P = Cost of placing one order [Rs/order]

C = Cost of holding one unit in inventory for one complete year [Rs/unit/year]

Concept:

For production model

\(EOQ = \sqrt {\frac{{2D{C_0}}}{{{C_h}}}\left\{ {\frac{p}{{p - d}}} \right\}} \)

Where,

p = production per week, d = demand per week

\(d = \frac{{24000}}{{50}} = 480/week\)

p = 1000/week

\(\therefore EOQ = \sqrt {\frac{{2 \times 24000 \times 20}}{{1.5}}\left\{ {\frac{{1000}}{{1000 - 480}}} \right\}} \)

∴ EOQ = 1109.4 units

\(\therefore {Q_{max}} = \frac{{\left( {p - d} \right)}}{p}EOQ\)

∴ Q_max = 576.88 = 577

Concept:

Total inventory cost is given by,

\(\left( {TIC} \right) = \sqrt {2D{C_o}{C_h}} .\sqrt {\frac{{{C_b}}}{{{C_b} + {C_h}}}} \)

where, D = annual demand, C0 = ordering cost, Ch = holding cost, C_b = Shortage cost 

Calculation:

Given:

Demand (D) = 200

Shortage cost (C_b) = 0.75 Rs. Per unit

Ordering cost (C_o) = 10 Rs. Per order

Item cost (C) = 8 per unit

Holding cost (C_h) = 15% = 0.15 × 8 = 1.20 Rs.

Now, Total inventory cost 

\(\left( {TIC} \right) = \sqrt {2D{C_o}{C_h}} .\sqrt {\frac{{{C_b}}}{{{C_b} + {C_h}}}} \)

\( = \sqrt {2 \times 200 \times 10 \times 1.2} \sqrt {\frac{{0.75}}{{0.75 + 1.2}}} \)

= Rs. 42.96.

Thus, The minimum inventory cost is Rs. 42.96

Annual demand = 10000 × 300 = 3000000

Holding cost C_h = 2

Set-up cost (C_o) = 1800

Production rate (p) = 25000 bearings per day

Consumption rate (d) = 10,000 bearings per day

Economic order quantity \({Q^*} = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}\left( {\frac{P}{{P - d}}} \right)} \)

\( = \sqrt {\frac{{2 \times 3000000 \times 1800}}{2}\left( {\frac{{25000}}{{25000 - 10,000}}} \right)} \)

Q^* = 94868 bearings

Calculation:

Given:
D = 50,000 units per year  C_O = Rs.25 per order, C_u = Rs. 40 per unit

C_c = 0.1 of C_u = 0.1 × 40 = 4 Rs per unit per year

\(EOQ = \sqrt {\frac{{2D{C_O}}}{{{C_c}}}} \)  

\(EOQ = \sqrt {\frac{{2 \times 50,000 \times 25}}{4}} \)
⇒ [EOQ = 790.569 units]

∵ EOQ > Maximum quantity that can be ordered at one

So, (TIC)_{Q = 600} \(= \frac{D}{Q} \times {C_O}\, + \,\frac{Q}{2} \times {C_N}\)

\((TIC)_{Q = 600 } = \frac{{50,000}}{{600}} \times 25 + \frac{{600}}{2} \times 4\)

⇒ (TIC)_{Q = 600} = Rs. 3283.33

Explanation:

Economic Order Quantity (EOQ): 

• A decision about how much to order has great significance in inventory management.
• The quantity to be purchased should neither be small nor big because the costs of buying and carrying materials are very high.
• Economic order quantity is the size of the lot to be purchased which is economically viable.
• This is the number of materials that can be purchased at minimum costs.
• Generally, economic order quantity is the point at which inventory carrying costs are equal to order costs.

Concept:

Economic order quantity

Economic order quantity is that size of the order which helps in minimizing the total annual cost of inventory in the organization.

When the size of the order increases, the ordering costs (cost of purchasing, inspection, etc.) will decrease whereas the inventory carrying costs (costs of storage, insurance, etc.) will increase. Economic Order Quantity (EOQ) is that size of order which minimizes total annual costs of carrying and cost of ordering.

The ordering quantity Q* at which holding cost becomes equal to ordering cost and the total inventory cost is minimum is known as Economic order Quantity (EOQ).

At EOQ:

Ordering cost = Holding cost

\(\frac{D}{{{Q^*}}}{C_o} = \frac{{{Q^*}}}{2}{C_h} \Rightarrow {Q^*} = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}} \)

D = Annual or yearly demand of inventory (unit/year)

Q = Quantity to be ordered at each order point (unit/order)

Co = Cost of placing one order [Rs/order]

Ch = Cost of holding one unit in inventory for one complete year [Rs/unit/year]

if the total ordering quantity is less than the EOQ quantity, then the holding cost is less than the ordering quantity.