Economic Order Economic Order QuantityQuantity EOQ ModelEOQ Model Equations (part - 1)Equations (part - 1) Equations (part – 2)Equations (part – 2)

EOQ ModelEOQ Model

Total Inventory cost is the Total Inventory cost is the minimum.minimum.

Annual demand of the item is Annual demand of the item is constant and known.constant and known.

Annual demand of the item is Annual demand of the item is uniformly distributed through uniformly distributed through out the year.out the year.

Lead time is zero.Lead time is zero. Total OC (P) = Total CC (R)Total OC (P) = Total CC (R)

EquationsEquations

For EOQ, Total OC (P) = Total CC For EOQ, Total OC (P) = Total CC (R) Total OC (p) = AO/Q (R) Total OC (p) = AO/Q

Total CC (R) = QC/2Total CC (R) = QC/2

AO/Q = QC/2AO/Q = QC/2

Where, A = Annual DemandWhere, A = Annual Demand

O = Ordering Cost ( Rs)O = Ordering Cost ( Rs) / Order/ Order

Q = EOQQ = EOQ

C = Carrying Cost ( Rs )/ YearC = Carrying Cost ( Rs )/ Year

Equations (part - 1)Equations (part - 1)

1.1. Average Inventory = Average Inventory =

(Max. Inventory + Min. Inventory) / (Max. Inventory + Min. Inventory) / 22

Also, Average Inventory = Q / 2Also, Average Inventory = Q / 2

2.2. Total Inventory Cost (T) = P + RTotal Inventory Cost (T) = P + R

3.3. Number of Orders per year = A/QNumber of Orders per year = A/Q

4.4. Duration of one inventory cycle = Duration of one inventory cycle = Q/AQ/A

Problem SolutionProblem Solution

Zen Bicycles Ltd sources 3,000 seat covers Zen Bicycles Ltd sources 3,000 seat covers for its bicycles from an outside supplier. The for its bicycles from an outside supplier. The OC is Rs 10 per order and the CC is Rs 6 per OC is Rs 10 per order and the CC is Rs 6 per unit per year. The company has 300 unit per year. The company has 300 working days per year. Findworking days per year. Find

1.1. EOQEOQ

2.2. Number of orders/yearNumber of orders/year

3.3. Total Inventory CostTotal Inventory Cost

4.4. Number of Inventory Cycles in a YearNumber of Inventory Cycles in a Year

5.5. Duration of an Inventory CycleDuration of an Inventory Cycle

Problem SolutionProblem Solution

The demand of small electric motor used in The demand of small electric motor used in a fan is 20,000 per year. The price of the a fan is 20,000 per year. The price of the motor is Rs.100 per motor. The carrying motor is Rs.100 per motor. The carrying cost is 8 percent of the purchase price. The cost is 8 percent of the purchase price. The ordering cost is Rs.200 per order. The ordering cost is Rs.200 per order. The number of working days is 320.number of working days is 320.

1.1. EOQEOQ

2.2. Number of orders/yearNumber of orders/year

3.3. Total Inventory CostTotal Inventory Cost

4.4. Number of Inventory Cycles in a YearNumber of Inventory Cycles in a Year

5.5. Duration of an Inventory CycleDuration of an Inventory Cycle

Equation (Part – 2)Equation (Part – 2)

EOQ model with shortagesEOQ model with shortages 22

Q = (2AO/C)(C+K)/KQ = (2AO/C)(C+K)/KWhere Q = EOQWhere Q = EOQ

A = Annual DemandA = Annual Demand O = Order CostO = Order Cost

C = Carrying CostC = Carrying Cost K = Cost of K = Cost of

ShortageShortage

Equation (Part – 2)Equation (Part – 2)

Maximum inventory with shortagesMaximum inventory with shortages 22

QQ11 = (2AO/C)(K/(C+K) ) or = (2AO/C)(K/(C+K) ) or = Q - S= Q - S

Where Q = EOQWhere Q = EOQ A = Annual DemandA = Annual Demand O = Order CostO = Order Cost C = Carrying CostC = Carrying Cost K = Cost of ShortageK = Cost of Shortage S = Maximum ShortageS = Maximum Shortage

Equation (Part – 2)Equation (Part – 2)

Shortage,Shortage,

S = CQ/(C+K)S = CQ/(C+K)Where S = Maximum shortageWhere S = Maximum shortage

Q = EOQQ = EOQ

C = Carrying CostC = Carrying Cost

K = Cost of K = Cost of ShortageShortage

Equation (Part – 2)Equation (Part – 2)

Maximum inventory = Q – SMaximum inventory = Q – S

Reorder level = DDLT - SReorder level = DDLT - S

Where S = Maximum shortageWhere S = Maximum shortage

Q = EOQQ = EOQ

DDLT = Demand During lead DDLT = Demand During lead timetime

ProblemProblem

Vishal Computer sales (P) Ltd is a leading dealer Vishal Computer sales (P) Ltd is a leading dealer of computer servers and net working devices at of computer servers and net working devices at Raipur. Servers are expensive machines and Raipur. Servers are expensive machines and therefore, Vishal follows a back ordering policy. therefore, Vishal follows a back ordering policy. The CC is Rs. 50,000 per servers per year and the The CC is Rs. 50,000 per servers per year and the OC is Rs 1,200 per order. The cost of shortage OC is Rs 1,200 per order. The cost of shortage per server is estimated at Rs. 20,000. The annual per server is estimated at Rs. 20,000. The annual demand of servers is 300 units. Find demand of servers is 300 units. Find

1.1. The optimal order quantity (EOQ with intentional The optimal order quantity (EOQ with intentional shortages)shortages)

2.2. Maximum shortage levelMaximum shortage level

3.3. Maximum Inventory levelMaximum Inventory level

4.4. Reorder level, considering lead time 7 days and Reorder level, considering lead time 7 days and DDLT is 3 units.DDLT is 3 units.

ProblemProblem

The annual demand for an automobile The annual demand for an automobile component is 24,000 units. The carrying cost is component is 24,000 units. The carrying cost is Rs 0.40/unit/year, the ordering cost is Rs.20,00 Rs 0.40/unit/year, the ordering cost is Rs.20,00 per order and the shortage cost is per order and the shortage cost is Rs.10./unit/year. Find Rs.10./unit/year. Find

1.1. The optimal order quantity (EOQ with intentional The optimal order quantity (EOQ with intentional shortages)shortages)

2.2. Maximum shortage levelMaximum shortage level

3.3. Cycle TimeCycle Time

4.4. Maximum Inventory levelMaximum Inventory level

5.5. Reorder level, considering lead time 7 days and Reorder level, considering lead time 7 days and DDLT is 5 units.DDLT is 5 units.