Economic Order Quantity (EOQ) MCQ Quiz - Objective Question with Answer for Economic Order Quantity (EOQ) - Download Free PDF

Concept:

The Economic Order Quantity (EOQ) model is a fundamental inventory management formula used to determine the optimal order quantity that minimizes total inventory costs, including ordering and holding costs.

Standard Assumptions of EOQ:

• Demand is known, constant, and continuous
• Lead time (the time between ordering and receiving) is constant
• Replenishment is instantaneous (all items are delivered at once)
• No stockouts or shortages are allowed
• Ordering and holding costs are constant and known

Analysis:

Option 1: "Material cannot be supplied in variable quantities" – This is not a part of EOQ assumptions. EOQ aims to determine the best (variable) quantity to order, making this statement invalid in the EOQ context.

Concept:

EOQ (Economic Order Quantity) is calculated using the formula:

\( EOQ = \sqrt{\frac{2AD}{H}} \)

Where:

• A = Annual demand = 400 units
• D = Ordering cost = ₹20
• H = Holding cost per unit per year = 10% of ₹100 = ₹10

Calculation:

\( EOQ = \sqrt{\frac{2 \times 400 \times 20}{10}} = \sqrt{\frac{16000}{10}} = \sqrt{1600} = 40 \)

Concept:

EOQ (Economic Order Quantity) is calculated by:

\( EOQ = \sqrt{\frac{2DS}{H}} \)

Given:

\( D = 12,50,000~\text{units/year},~S = ₹1500,~H = ₹150 \)

Calculation:

\( EOQ = \sqrt{\frac{2 \times 1250000 \times 1500}{150}} = \sqrt{25000000} = 5000 \)

Explanation:

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 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.

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

Concept:

The Economic Order Quantity (EOQ) is a formula used to determine the optimal order quantity that minimizes the total cost of inventory, including ordering and holding costs.

\( EOQ = \sqrt{\frac{2DS}{H}} \)

Where:

• D" id="MathJax-Element-14-Frame" role="presentation" style="position: relative;" tabindex="0">DD $D$ = Annual demand (units/year)
• S" id="MathJax-Element-15-Frame" role="presentation" style="position: relative;" tabindex="0">SS $S$ = Ordering cost per order
• H" id="MathJax-Element-16-Frame" role="presentation" style="position: relative;" tabindex="0">HH $H$ = Holding or carrying cost per unit per year

Given Data:

• Demand D" id="MathJax-Element-17-Frame" role="presentation" style="position: relative;" tabindex="0">DD $D$ = 800 units/year
• Ordering cost S" id="MathJax-Element-18-Frame" role="presentation" style="position: relative;" tabindex="0">SS $S$ = 150
• Carrying cost percentage = 1.5%
• Unit cost = 400

Calculate Carrying Cost per Unit:

\( H = 1.5\% \times 400 = \frac{1.5}{100} \times 400 = 6 \, \text{per unit per year} \)

Substitute into the EOQ Formula:

\( EOQ = \sqrt{\frac{2 \times 800 \times 150}{6}} = \sqrt{\frac{240000}{6}} = \sqrt{40000} = 200 \)

The Economic Order Quantity (EOQ) is 200 units.

Given:

The cost of 157 litre of oil is Rs.  29763.65

Calculation:

Cost price of 157 liters of oil = Rs. 29763.65

Cost price of 1 liter of oil = 29763.65/157

⇒ 189.577 ≈ 189.58

∴ The cost per liter is 189.58 (rounded off to two decimal places).

Concept:

This model is used when the replacement is instantaneous and no shortage is allowed. The Economic Order Quantity for this model is given by Wilson Formula.

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

where Q^* = Economic Order Quantity (Units), D = Demand rate (Units/month or Units/year), C_o = Ordering cost/order (Rs.), C_h = Handling cost (Rs./unit/year)

[Note: Time unit of Demand & Handling Cost must be same i.e. units/year or units/month]

Calculation:

Given:

D = 12000 units/year, C_o = Rs. 100, C_h = Rs. 0.80/unit/month ⇒ Rs. 0.80 × 12/unit/year

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

\( \Rightarrow {Q^*} = \sqrt {\frac{{2 \times 12000 \times 100}}{{0.80 \times 12}}} \)

⇒ Q^* = 500 units.

Explanation:

Lead Time:

• The time gap between the placing of an order and its actual arrival in the inventory is known as Lead Time.
• Lead Time can be greater, less, or equal to Order Cycle.

Order Cycle:

• The time period between two successive orders is called Order Cycle.

Re-order Level (ROL):

• The quantity in hand while placing the order.
• ROL = Lead Time × Demand.

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

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

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

D = Annual or yearly demand for inventory (unit/day)

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/day]

Cycle time:

Order cycle time refers to the time period between placing one order and the next order.

\(T=\frac{Q}{D}\)

Re-order Level (ROL): 

The quantity in hand while placing the order.

Case - I

When lead time is lower than cycle time (T_L < T).

ROL = Lead Time (T_L) × Demand (D).

Case - II

When lead time TL is greater than cycle time T, then:

ROL = (TL - T) × Demand (D)

Calculation:

Given:

D = 100 unit/day, Co = 400 unit/order, Ch = 0.08 Rs./unit/day, Lead time T_L = 13 days

EOQ:

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

\({Q^*} = \sqrt {\frac{{2× 100×{400}}}{{{0.08}}}}=1000\;units \)

Cycle Time:

\(T=\frac{Q}{D}\)

\(T=\frac{1000}{100}=10\;days\)

T_L > T

ROL = (TL - T) × Demand (D)

ROL = (13 - 10) × 100 = 300 units.

Concept:

The total annual cost for the inventory system is given as:

 \(\mathbf{C~=~\frac{D}{Q}C_o~+~\frac{Q}{2}C_h}\)

where C is the total annual cost, D is the annual demand, Q is the order quantity, C_o is the ordering cost and C_h is the holding cost per unit per year.

In economic order quantity (EOQ), \(\mathbf{\frac{D}{Q}C_o~=~\frac{Q}{2}C_h}\)

Calculation:

Given:

In economic order quantity,  

\(\frac{D}{Q}C_o=\frac{Q}{2}C_h\) or C = \(\frac{Q}{2}C_h~+~\frac{Q}{2}C_h\)

⇒ C = QC_h

Now, the new order quantity is Q′ = 2Q, so the new total cost is

\(C^′~=~\frac{D}{Q^′ }C_o~+~\frac{Q^′}{2}C_h\) = \(C^′~=~\frac{D}{2Q }C_o~+~\frac{2Q}{2}C_h\)

⇒ \(\frac{1}{2}\left ( \frac{Q}{2}C_h \right)+QC_h\) = \( \frac{Q}{4}C_h~+~QC_h\) = \(\frac{5}{4}QC_h\)

∴ C′ = 1.25C  

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.
• First, EOQ policy is not optimal in MRP system because the assumptions of constant demand are not met.
• As compared with a lot-for-lot policy, the setup costs for an EOQ policy will generally be lower and holding costs will be higher.
• Second, in an EOQ policy, extra inventory is unnecessarily carried to the end of the planning horizon.

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 for 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]

Concept:

Reorder level is the inventory level at which a company should place a new order in order to maintain the stock for selling and running the business effectively.

Lead time represents the time gap between placing an order and when the order is received.

Reorder level (RoL) = Lead time × daily demand

Calculation:

Given:

The annual demand for item D = 2555 units, Lead time =  8 days

daily demand of item d = \(\frac{d}{365} = \frac{2555}{365}\)

= 7 units

Reorder level (RoL) = Lead time × daily demand

= 8 × 7 

= 56 units

Additional Information

• The Economic order quantity or optimum quantity is the order quantity that minimizes the total holding cost and ordering cost in an inventory. At this point Holding cast is equal to ordering cast.

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 that size of 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

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

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

D = Annual or yearly demand for 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]

Calculation:

Given: D =16,000 units, C_u = Rs. 2 per unit, C_o = Rs. 45 per order, C_h = 10% of C_u = 0.10 × 2 Rs/unit/year

\(\Rightarrow {Q^*} = \sqrt {\frac{2 \times 16,000\times 45}{0.10 \times 2}}\)

\(\Rightarrow {Q^*} = 2683.28 \ Units\)

So, the closest answer will be option 1.

Concept:

Economic order quantity is given by:

\({EOQ}= \sqrt {\frac{2DC_o}{C_h}} \)

where D =  demand (unit/time), C_o = ordering cost (Rs/order), C_h = cost of carrying inventory (Rs/unit/time)

Calculation:

Given:

D = 9000 \(\frac{{Units}}{{year}}\), Cost of one part (C) = Rs. 20, Co = Rs. 15/order

Ch = 15% of unit cost = \( \frac{{15}}{{100}} \times 20 = Rs.3/unit/year\)

Economic order quantity is:

\(\left( {EOQ} \right) = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}} = \sqrt {\frac{{2 \times 9000 \times 15}}{3}} = 300~units\)

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)

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

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

Calculation:

D = 800 units, Co = Rs. 200, Ch = 10% of value/year = Rs. 2

\({{\rm{Q}}^{\rm{*}}} = \sqrt {\frac{{2{\rm{D}}{{\rm{C}}_{\rm{o}}}}}{{{{\rm{C}}_{\rm{h}}}}}} = \sqrt {\frac{{2 \times 800 \times 200}}{{2}}} = 400{\rm{\;units}}\)