The document discusses inventory management and control techniques. It covers topics like setting stock levels, inventory budgeting, perpetual inventory systems, ABC analysis, economic order quantity (EOQ) modeling, and quantity discounts. ABC analysis involves categorizing inventory items into A, B, and C categories based on their value and accounting for 80%, 15-20%, and 5-10% of total spending, respectively. EOQ modeling determines the optimal order quantity to minimize total inventory costs based on factors like demand, ordering costs, and holding costs. Quantity discounts provide pricing incentives for purchasing higher volumes.
The document discusses deterministic inventory models, including the basic economic order quantity (EOQ) model and continuous rate EOQ model. It provides the assumptions and formulas for calculating the optimal order quantity in the basic EOQ model. An example is shown to illustrate how to determine the EOQ. The document also discusses how to compute the optimal order quantity when quantity discounts are allowed, using breakpoints. Finally, it describes the assumptions of the continuous rate EOQ model for producing goods internally.
This document provides information on inventory management and control. It discusses economic order quantity (EOQ) models, which aim to determine the optimal order size and timing to minimize total inventory costs. EOQ models balance ordering/setup costs with carrying costs. The document also covers dependent vs independent demand and compares fixed-order quantity (Q) models with fixed-time period (P) models. Q models specify a reorder point and fixed order quantity, while P models use a fixed time between orders and target inventory level.
This document provides an overview of inventory management concepts. It defines inventory and inventory systems, discusses the objectives and costs of holding inventory, and describes several inventory models for determining optimal order quantities and reorder points. These include single-period and multi-period models like the economic order quantity and fixed-time period models. It also covers miscellaneous inventory systems, classification techniques, and the importance of inventory accuracy.
This document discusses inventory control systems. It defines inventory and inventory systems, and describes the purposes of inventory. It covers inventory costs and the differences between independent and dependent demand. The document then explains single-period and multi-period inventory models, including the economic order quantity model and fixed-time period model. It provides examples of how to calculate optimal order quantities using these models. Finally, it briefly discusses miscellaneous inventory systems like optional replenishment, bin systems, and ABC classification.
The document discusses inventory management using analytics for better decision making. It covers key topics like why organizations want to hold inventories like to improve customer service but also don't want to hold too much inventory due to carrying costs. It discusses the tradeoff between inventory and transportation costs. Effective inventory management requires tracking inventory levels, demand forecasting, and estimating costs of holding, ordering and shortages. The nature of inventory can be independent or dependent demand and different systems are used. Key decisions involve how much to order and when to place orders to minimize total costs.
The document discusses the economic order quantity (EOQ) model and its assumptions. It defines key terms like replenishment quantity, fixed ordering costs, unit variable costs, carrying costs, total relevant costs, and EOQ. It also discusses extensions to the basic EOQ model, like quantity discounts, finite replenishment rates, and opportunities to procure items at special prices before a price increase.
This document discusses inventory management concepts and models. It begins by outlining learning objectives related to ABC analysis, cycle counting, economic order quantity (EOQ) models, reorder points, and other topics. It then provides details on Amazon's inventory management practices and types of inventory. The bulk of the document explains ABC analysis for classifying inventory, techniques for maintaining accurate records, factors that influence holding and ordering costs, and the EOQ model for determining optimal order quantities. It concludes by noting the robustness of the EOQ model and introducing the concept of reorder points.
The document discusses inventory management and control techniques. It covers topics like setting stock levels, inventory budgeting, perpetual inventory systems, ABC analysis, economic order quantity (EOQ) modeling, and quantity discounts. ABC analysis involves categorizing inventory items into A, B, and C categories based on their value and accounting for 80%, 15-20%, and 5-10% of total spending, respectively. EOQ modeling determines the optimal order quantity to minimize total inventory costs based on factors like demand, ordering costs, and holding costs. Quantity discounts provide pricing incentives for purchasing higher volumes.
The document discusses deterministic inventory models, including the basic economic order quantity (EOQ) model and continuous rate EOQ model. It provides the assumptions and formulas for calculating the optimal order quantity in the basic EOQ model. An example is shown to illustrate how to determine the EOQ. The document also discusses how to compute the optimal order quantity when quantity discounts are allowed, using breakpoints. Finally, it describes the assumptions of the continuous rate EOQ model for producing goods internally.
This document provides information on inventory management and control. It discusses economic order quantity (EOQ) models, which aim to determine the optimal order size and timing to minimize total inventory costs. EOQ models balance ordering/setup costs with carrying costs. The document also covers dependent vs independent demand and compares fixed-order quantity (Q) models with fixed-time period (P) models. Q models specify a reorder point and fixed order quantity, while P models use a fixed time between orders and target inventory level.
This document provides an overview of inventory management concepts. It defines inventory and inventory systems, discusses the objectives and costs of holding inventory, and describes several inventory models for determining optimal order quantities and reorder points. These include single-period and multi-period models like the economic order quantity and fixed-time period models. It also covers miscellaneous inventory systems, classification techniques, and the importance of inventory accuracy.
This document discusses inventory control systems. It defines inventory and inventory systems, and describes the purposes of inventory. It covers inventory costs and the differences between independent and dependent demand. The document then explains single-period and multi-period inventory models, including the economic order quantity model and fixed-time period model. It provides examples of how to calculate optimal order quantities using these models. Finally, it briefly discusses miscellaneous inventory systems like optional replenishment, bin systems, and ABC classification.
The document discusses inventory management using analytics for better decision making. It covers key topics like why organizations want to hold inventories like to improve customer service but also don't want to hold too much inventory due to carrying costs. It discusses the tradeoff between inventory and transportation costs. Effective inventory management requires tracking inventory levels, demand forecasting, and estimating costs of holding, ordering and shortages. The nature of inventory can be independent or dependent demand and different systems are used. Key decisions involve how much to order and when to place orders to minimize total costs.
The document discusses the economic order quantity (EOQ) model and its assumptions. It defines key terms like replenishment quantity, fixed ordering costs, unit variable costs, carrying costs, total relevant costs, and EOQ. It also discusses extensions to the basic EOQ model, like quantity discounts, finite replenishment rates, and opportunities to procure items at special prices before a price increase.
This document discusses inventory management concepts and models. It begins by outlining learning objectives related to ABC analysis, cycle counting, economic order quantity (EOQ) models, reorder points, and other topics. It then provides details on Amazon's inventory management practices and types of inventory. The bulk of the document explains ABC analysis for classifying inventory, techniques for maintaining accurate records, factors that influence holding and ordering costs, and the EOQ model for determining optimal order quantities. It concludes by noting the robustness of the EOQ model and introducing the concept of reorder points.
The document discusses various inventory management techniques. It begins by explaining ABC analysis, which classifies inventory into A, B, and C categories based on annual dollar value. It then discusses the economic order quantity (EOQ) model and how to calculate optimal order size to minimize total costs. Finally, it covers reorder points, production order quantities, and using quantity discounts to reduce product costs.
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This chapter discusses inventory management concepts including opposing views of holding inventories, the nature of inventories, fixed order quantity systems, and determining order points. It describes why companies want and don't want to hold inventories. Fixed order quantity systems use economic order quantity models to determine optimal order sizes based on costs. Order points are set based on expected demand during lead time plus a safety stock to achieve a desired customer service level.
This document provides an overview of inventory management concepts. It discusses the meaning and types of inventory, related costs like ordering, carrying, and shortage costs. It introduces the basic Economic Order Quantity (EOQ) model, which aims to minimize total inventory costs by balancing ordering and carrying costs. The EOQ model formulas and assumptions are explained. It is noted that total costs are not very sensitive around the optimal order quantity. The document also discusses decoupling inventory, quantity discounts, and ABC classification of inventory items.
This document discusses the economic order quantity (EOQ) model. The EOQ model determines the optimal order quantity that minimizes total inventory costs by balancing order processing costs and inventory holding costs. It assumes known demand, lead times, and costs. The formula for economic order quantity is derived and explained. An example application to a coffee maker order at SaveMart is provided to illustrate calculating optimal order quantity and reorder point using EOQ equations. Factors that could impact the EOQ are also listed.
The document discusses inventory management concepts including the reasons for holding inventory, types of inventory, costs of inventory, and inventory control systems. It describes the economic order quantity (EOQ) model which aims to minimize total inventory costs by balancing ordering and holding costs. The EOQ model assumes constant demand, lead times, and avoids stockouts. ABC analysis prioritizes inventory items based on their value to focus management efforts on the most important items. Cycle counting helps maintain accurate inventory records by regularly counting samples of inventory.
This document discusses inventory problems and the economic order quantity (EOQ) model. It covers:
- Types of inventory costs and notations used in EOQ models.
- The basic EOQ model which assumes constant demand rate and minimizes total inventory costs. This model is used to determine the optimal order quantity.
- Extensions of the basic EOQ model which relax some assumptions, such as models allowing for finite replenishment rates, shortages, quantity discounts, etc.
- Examples demonstrating how to apply the EOQ model to determine optimal order quantity and total costs for different inventory situations.
1. The document discusses quantity discount models, where the price per unit decreases as the order quantity increases. It presents the total cost curve approach to determine the optimal order quantity under different discount levels.
2. A two-step solution procedure is outlined: (1) calculate the EOQ for each price level to find the first feasible one, (2) compare the total cost of the feasible EOQ to the total costs at higher discount price break points to determine the lowest cost option.
3. An example application demonstrates finding the optimal order quantity for a hospital item given price discounts at 300, 500, and over 500 units that minimizes total purchase and holding costs.
This document discusses inventory management concepts including types of inventory, ABC analysis for inventory classification, and inventory control models. It provides examples of deterministic and probabilistic inventory control problems involving determining economic order quantity, reorder levels, and dominant sequences for dynamic demand. The key tradeoffs considered are between inventory carrying costs and ordering/shortage costs.
The document discusses cycle inventory and economies of scale in supply chains. Cycle inventory is the average inventory that builds up due to purchasing or producing goods in batches larger than customer demand. This allows companies to benefit from economies of scale by reducing production and transportation costs. While cycle inventory lowers costs, it also increases the average time goods spend in the supply chain before being sold. The optimal lot size balances order and holding costs to minimize total supply chain costs.
The document discusses the economic order quantity (EOQ) model, which is used to determine the optimal order quantity and time to place orders to minimize total inventory costs. The EOQ model balances ordering costs with carrying costs using formulas to calculate the economic order quantity, total annual inventory costs, reorder point, and other metrics. The document also provides examples of using the EOQ model formulas to analyze inventory management for different companies.
The document discusses the economic order quantity (EOQ) model, which aims to determine the optimal lot size that minimizes total annual inventory holding and ordering costs. It provides the assumptions of the EOQ model and guidelines for when to use, modify, or not use the EOQ. It also gives an example calculation of the EOQ, total costs, and time between orders for a bird feeder item carried by a museum gift shop. The optimal lot size, or EOQ, balances annual holding and ordering costs and results in lower total annual inventory costs compared to the shop's current large lot size policy.
This document discusses inventory management concepts including independent vs dependent demand, objectives of inventory management, relevant inventory costs, order quantity strategies, and mathematical models for determining order quantity. It provides examples and explanations of economic order quantity (EOQ), economic production quantity (EPQ), and quantity discount models. It also discusses how to determine safety stock and reorder points when demand is uncertain.
This document discusses inventory control models and techniques for determining optimal order quantities and reorder points. The Economic Order Quantity (EOQ) model is introduced as a method to determine how much of an item to order to minimize total inventory costs. The EOQ model balances ordering costs and carrying costs. It assumes demand is known and constant. The Economic Production Quantity (EPQ) model extends the EOQ model to situations where inventory is produced rather than ordered. Safety stock models account for uncertain demand by holding extra inventory to prevent stockouts. ABC analysis classifies inventory items into important and less important groups.
This document discusses inventory management models. It describes opposing views on holding inventory, including reasons for and against it. It also covers the nature of inventory, including independent and dependent demand systems. Different inventory models are explained, including fixed order quantity and period systems. Key factors in inventory like order quantities, order points, and costs are defined.
This document discusses inventory management concepts including:
- Defining inventory and providing examples of inventory levels in different industries.
- The costs of holding inventory and pressures to reduce inventory levels.
- The economic order quantity (EOQ) model for determining optimal order sizes to minimize total costs of ordering and holding inventory.
- Key factors that influence the EOQ like demand, ordering costs, holding costs.
- How the EOQ is applied in examples and the insights from sensitivity analysis.
- Extensions of the EOQ model when lead times are present.
- Different inventory control systems for handling demand uncertainty.
This document discusses inventory models, including the basic economic order quantity (EOQ) model and quantity discounts. It begins by defining inventory and explaining the importance of inventory control. It then covers the basic EOQ model assumptions and formulas for calculating optimal order quantity, expected number of orders per year, time between orders, total cost, and average inventory value. The document also discusses using a reorder point and provides an example calculation. Finally, it introduces quantity discount models, where purchasing larger quantities results in decreased unit costs.
This document discusses the economic order quantity (EOQ) model, which aims to minimize total inventory costs by balancing order processing costs and inventory holding costs. It provides the EOQ formula and assumptions, including known constant demand and lead times. An example is shown for a company ordering coffee makers with annual demand of 1000 units. The optimal order quantity is calculated as 80 coffee makers with an expected reorder point of 14 units. Factors that could impact the EOQ are also listed.
This document discusses managing inventory and cycle inventory in supply chains. It describes how cycle inventory is held to take advantage of economies of scale and reduce costs. Cycle inventory is the average inventory that builds up because supply chain stages purchase in lot sizes larger than customer demand. This adds to the average time products spend in the supply chain. The optimal lot size balances ordering, holding, and transportation costs to minimize total supply chain costs.
This document discusses inventory management in supply chains. It begins by defining inventory as materials awaiting future sale or use. It then describes the different types of inventory held at various stages of the supply chain, from raw materials to finished goods.
The document outlines the costs associated with holding inventory, including purchase, ordering, and holding costs. It introduces concepts like economic order quantity (EOQ) and economic production quantity (EPQ) models to determine optimal lot sizes that minimize total costs.
The role of cycle inventory is explained, which allows different supply chain stages to purchase in larger lots than customer demand to take advantage of economies of scale. However, this increases total inventory levels and costs across the supply chain. Finally, the
The document discusses various inventory management techniques. It begins by explaining ABC analysis, which classifies inventory into A, B, and C categories based on annual dollar value. It then discusses the economic order quantity (EOQ) model and how to calculate optimal order size to minimize total costs. Finally, it covers reorder points, production order quantities, and using quantity discounts to reduce product costs.
********************************************************************************************************************************************************
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and/or publication of this e-mail message,contents or ts attachment(s) other than by its intended recipient(s) is strictly prohibited. Any opinions expressed in this email are those of the individual and not necessarily of the organization. Before opening attachment(s), please scan for viruses."
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********************************************************************************************************************************************************
"This e-Mail may contain proprietary and confidential information and is sentfor the intended recipient(s) only. If, by an addressing or transmission error,this mail has been misdirected to you, you are requested to delete this mailimmediately. You are also hereby notified that any use, any form of reproduction, dissemination, copying, disclosure, modification, distribution
and/or publication of this e-mail message,contents or ts attachment(s) other than by its intended recipient(s) is strictly prohibited. Any opinions expressed in this email are those of the individual and not necessarily of the organization. Before opening attachment(s), please scan for viruses."
********************************************************************************************************************************************************
This chapter discusses inventory management concepts including opposing views of holding inventories, the nature of inventories, fixed order quantity systems, and determining order points. It describes why companies want and don't want to hold inventories. Fixed order quantity systems use economic order quantity models to determine optimal order sizes based on costs. Order points are set based on expected demand during lead time plus a safety stock to achieve a desired customer service level.
This document provides an overview of inventory management concepts. It discusses the meaning and types of inventory, related costs like ordering, carrying, and shortage costs. It introduces the basic Economic Order Quantity (EOQ) model, which aims to minimize total inventory costs by balancing ordering and carrying costs. The EOQ model formulas and assumptions are explained. It is noted that total costs are not very sensitive around the optimal order quantity. The document also discusses decoupling inventory, quantity discounts, and ABC classification of inventory items.
This document discusses the economic order quantity (EOQ) model. The EOQ model determines the optimal order quantity that minimizes total inventory costs by balancing order processing costs and inventory holding costs. It assumes known demand, lead times, and costs. The formula for economic order quantity is derived and explained. An example application to a coffee maker order at SaveMart is provided to illustrate calculating optimal order quantity and reorder point using EOQ equations. Factors that could impact the EOQ are also listed.
The document discusses inventory management concepts including the reasons for holding inventory, types of inventory, costs of inventory, and inventory control systems. It describes the economic order quantity (EOQ) model which aims to minimize total inventory costs by balancing ordering and holding costs. The EOQ model assumes constant demand, lead times, and avoids stockouts. ABC analysis prioritizes inventory items based on their value to focus management efforts on the most important items. Cycle counting helps maintain accurate inventory records by regularly counting samples of inventory.
This document discusses inventory problems and the economic order quantity (EOQ) model. It covers:
- Types of inventory costs and notations used in EOQ models.
- The basic EOQ model which assumes constant demand rate and minimizes total inventory costs. This model is used to determine the optimal order quantity.
- Extensions of the basic EOQ model which relax some assumptions, such as models allowing for finite replenishment rates, shortages, quantity discounts, etc.
- Examples demonstrating how to apply the EOQ model to determine optimal order quantity and total costs for different inventory situations.
1. The document discusses quantity discount models, where the price per unit decreases as the order quantity increases. It presents the total cost curve approach to determine the optimal order quantity under different discount levels.
2. A two-step solution procedure is outlined: (1) calculate the EOQ for each price level to find the first feasible one, (2) compare the total cost of the feasible EOQ to the total costs at higher discount price break points to determine the lowest cost option.
3. An example application demonstrates finding the optimal order quantity for a hospital item given price discounts at 300, 500, and over 500 units that minimizes total purchase and holding costs.
This document discusses inventory management concepts including types of inventory, ABC analysis for inventory classification, and inventory control models. It provides examples of deterministic and probabilistic inventory control problems involving determining economic order quantity, reorder levels, and dominant sequences for dynamic demand. The key tradeoffs considered are between inventory carrying costs and ordering/shortage costs.
The document discusses cycle inventory and economies of scale in supply chains. Cycle inventory is the average inventory that builds up due to purchasing or producing goods in batches larger than customer demand. This allows companies to benefit from economies of scale by reducing production and transportation costs. While cycle inventory lowers costs, it also increases the average time goods spend in the supply chain before being sold. The optimal lot size balances order and holding costs to minimize total supply chain costs.
The document discusses the economic order quantity (EOQ) model, which is used to determine the optimal order quantity and time to place orders to minimize total inventory costs. The EOQ model balances ordering costs with carrying costs using formulas to calculate the economic order quantity, total annual inventory costs, reorder point, and other metrics. The document also provides examples of using the EOQ model formulas to analyze inventory management for different companies.
The document discusses the economic order quantity (EOQ) model, which aims to determine the optimal lot size that minimizes total annual inventory holding and ordering costs. It provides the assumptions of the EOQ model and guidelines for when to use, modify, or not use the EOQ. It also gives an example calculation of the EOQ, total costs, and time between orders for a bird feeder item carried by a museum gift shop. The optimal lot size, or EOQ, balances annual holding and ordering costs and results in lower total annual inventory costs compared to the shop's current large lot size policy.
This document discusses inventory management concepts including independent vs dependent demand, objectives of inventory management, relevant inventory costs, order quantity strategies, and mathematical models for determining order quantity. It provides examples and explanations of economic order quantity (EOQ), economic production quantity (EPQ), and quantity discount models. It also discusses how to determine safety stock and reorder points when demand is uncertain.
This document discusses inventory control models and techniques for determining optimal order quantities and reorder points. The Economic Order Quantity (EOQ) model is introduced as a method to determine how much of an item to order to minimize total inventory costs. The EOQ model balances ordering costs and carrying costs. It assumes demand is known and constant. The Economic Production Quantity (EPQ) model extends the EOQ model to situations where inventory is produced rather than ordered. Safety stock models account for uncertain demand by holding extra inventory to prevent stockouts. ABC analysis classifies inventory items into important and less important groups.
This document discusses inventory management models. It describes opposing views on holding inventory, including reasons for and against it. It also covers the nature of inventory, including independent and dependent demand systems. Different inventory models are explained, including fixed order quantity and period systems. Key factors in inventory like order quantities, order points, and costs are defined.
This document discusses inventory management concepts including:
- Defining inventory and providing examples of inventory levels in different industries.
- The costs of holding inventory and pressures to reduce inventory levels.
- The economic order quantity (EOQ) model for determining optimal order sizes to minimize total costs of ordering and holding inventory.
- Key factors that influence the EOQ like demand, ordering costs, holding costs.
- How the EOQ is applied in examples and the insights from sensitivity analysis.
- Extensions of the EOQ model when lead times are present.
- Different inventory control systems for handling demand uncertainty.
This document discusses inventory models, including the basic economic order quantity (EOQ) model and quantity discounts. It begins by defining inventory and explaining the importance of inventory control. It then covers the basic EOQ model assumptions and formulas for calculating optimal order quantity, expected number of orders per year, time between orders, total cost, and average inventory value. The document also discusses using a reorder point and provides an example calculation. Finally, it introduces quantity discount models, where purchasing larger quantities results in decreased unit costs.
This document discusses the economic order quantity (EOQ) model, which aims to minimize total inventory costs by balancing order processing costs and inventory holding costs. It provides the EOQ formula and assumptions, including known constant demand and lead times. An example is shown for a company ordering coffee makers with annual demand of 1000 units. The optimal order quantity is calculated as 80 coffee makers with an expected reorder point of 14 units. Factors that could impact the EOQ are also listed.
This document discusses managing inventory and cycle inventory in supply chains. It describes how cycle inventory is held to take advantage of economies of scale and reduce costs. Cycle inventory is the average inventory that builds up because supply chain stages purchase in lot sizes larger than customer demand. This adds to the average time products spend in the supply chain. The optimal lot size balances ordering, holding, and transportation costs to minimize total supply chain costs.
This document discusses inventory management in supply chains. It begins by defining inventory as materials awaiting future sale or use. It then describes the different types of inventory held at various stages of the supply chain, from raw materials to finished goods.
The document outlines the costs associated with holding inventory, including purchase, ordering, and holding costs. It introduces concepts like economic order quantity (EOQ) and economic production quantity (EPQ) models to determine optimal lot sizes that minimize total costs.
The role of cycle inventory is explained, which allows different supply chain stages to purchase in larger lots than customer demand to take advantage of economies of scale. However, this increases total inventory levels and costs across the supply chain. Finally, the
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Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
2. After reading this chapter, you should
be able to:
Explain what inventory management entails.
Describe the difference between static and dynamic inventory
models.
Discuss demand distribution effects on inventory situations.
Differentiate inventory costs by process types.
Describe all costs relevant to inventory models.
2
3. After reading this chapter, you should
be able to (continued):
Discuss the use of economic order quantity (EOQ) models.
Discuss the use of economic production quantity (EPQ)
models.
Describe the discount model and explain how it indicates when
a discount should be taken.
Perform ABC classification of materials.
3
4. After reading this chapter, you should
be able to (continued):
Discuss lead-time effects on inventory situations.
Explain order point policies (OPP) and when they are used.
Explain the operation of the periodic inventory model.
Explain the operation of the perpetual inventory model.
Discuss reorder points.
Discuss and calculate safety stocks.
Describe a two-bin system.
4
5. Types of Inventory Situations
o Order repetition—static versus dynamic situations.
o Demand distribution—certainty, risk, and uncertainty.
o Stability of demand distribution—fixed or varying.
o Demand continuity—smoothly continuous or sporadic and
occurring as lumpy demand; independent.
o Lead-time distributions—fixed or varying.
o Dependent or independent demand.
5
6. 6
Functions of Inventory
Consider three subsystems of an organization representing the
supplier, manufacturer and the market.
These three subsystems are rigidly connected with each other,
without any inventories, as shown below.
Inventories reduce dependency of one subsystem over the other
in a supply chain.
Suppliers Manufacturer Market
7. Functions of Inventory (continued)
Production Planning – level production.
Take advantage of quantity (price) discounts.
Protect against anticipated increase in prices.
Protect against anticipated shortages.
7
8. Inventory Related Costs
o Costs of ordering
o Costs of setups and changeovers
o Costs of carrying inventory
o Costs of discounts
o Out-of-stock costs
o Costs of running the inventory system
8
9. 9
Data for Inventory Problems
• D: Annual Demand (units per year)
• C: Unit Price (purchase price of the item)
• S: Ordering or Setup Cost per Order
• H: Inventory Holding (Carrying) Cost/unit per year
• i: H may be given as i percent of C
• TC: Total Annual Cost
• TVC: Total Annual Variable Cost
• Q: Order Quantity
• EOQ: Economic Order Quantity (optimal value of Q)
11. 11
Inventory Level Variations
Suppose Annual Demand
D = 1200
Suppose Q units are purchased
at a time, where,
Q = 600
Q = 400 etc.
The figures on the RHS show
inventory variations for
different values of Q assuming
a constant and continuous
demand of 100 units per
month.
Order Size, Q = 600
Order Size, Q = 400
12. Average Inventory and Number of Orders
Average inventory = Q/2.
Number of orders = D/Q.
If Q = 400
Average Inventory
= 400/2 = 200
# Orders = 1200/400 = 3
12
Average Inventory during the first four months
is (400+0)/2 = 200.
For the next four months it is again (400+0)/2
= 200
Similarly for the last four months, the average
inventory is (400+0)/2 = 200
This means that the average inventory through
out the year is 200.
Order Size, Q = 400
13. 13
TC and TVC Formulae
Total Annual Cost (TC) = Annual Ordering Cost (D/Q)S +
Annual Holding Cost (Q/2)H+ Annual Purchase Cost (DC)
Total Annual Variable Cost (TVC) = Annual Ordering Cost +
Annual Holding Cost
Note: Annual purchase cost is not included in TVC.
H
Q
S
Q
D
TVC
2
DC
H
Q
S
Q
D
TC
2
14. 14
EOQ Formula
In the equations for TC and TVC, the values of D, H, S and C are known.
The only unknown variable is Q. Our objective is to minimize TC.
TC is minimized at that value of Q, where, Annual Ordering Cost = Annual Holding
Cost. See the equation below.
Solving the above equation for Q, gives the value of EOQ (QO) as shown below.
H
Q
S
Q
D
2
H
DS
EOQ
2
15. EOQ Example
Suppose D = 1,200 units, S = $5.00, H = $ 1.20 and C = $ 12.00.
EOQ (QO) for this problem is given below.
15
Qo =
2∗1200∗5
1.2
= 100
16. Graphs of Various Costs
The figure on RHS shows the
graphs of various costs as the
order quantity Q is changed.
The graphs for Annual
Ordering Cost and Annual
Inventory Cost intersect at
EOQ (=100).
16
17. Costs for Various Order Quantities
Order Size (Q)
Annual Ordering
Cost
Annual
Inventory
Costs
Total Annual
Variable Cost
(TVC)
50 $120 $30 $150
75 $80 $45 $125
100 $60 $60 $120
125 $48 $75 $123
150 $40 $90 $130
175 $34 $105 $139
200 $30 $120 $150
225 $27 $135 $162
250 $24 $150 $174
275 $22 $165 $187
300 $20 $180 $200
Note that minimum cost is
for Q = 100 (EOQ).
Ordering Cost = Inventory
Cost = 60 for Q = 100.
TC can be calculated as
TC = TVC + DC.
DC is a constant term and
is independent of Q.
17
19. 19
Economic Production Quantity
The economic production quantity (EPQ) model is used in
manufacturing situations where inventory is replenished at a
finite rate given by the production rate of the item under
consideration.
We define two more variables:
p: Production rate per day (daily production)
d: Demand rate per day (daily demand)
Note: p and d must be defined in the same time unit. For example
these could be weekly instead of daily rates.
20. 20
Economic Production Quantity continued
Suppose
p = 50 units/day
d = 10 units/day
EPQ = 500 (production quantity, Q); Note: the optimal value of
Q is EPQ or QP
In this case we will need 10 days to produce 500 units
(EPQ/p = 500/50).
21. Economic Production Quantity continued
During these ten days, we produce 50 units per day but also use
10 units per day.
Therefore, we are building up inventory at the rate of 40 (p-d
=50-10) units per day.
At the end of 10 days, the total number of units in inventory is
400 (40 * 10). This is the maximum inventory level, Imax.
After 50 days, the next batch consisting of EPQ units is
scheduled for production. This is how the cycles continue.
21
22. Economic Production Quantity continued
At the end of the 10th day, we stop producing this item and then
continue to meet the demand from the inventory. The inventory
will last for 40 days (400/10) because we have 400 units in stock
and the demand rate is 10 units/day.
The production cycle thus consists of 50 days. For the first 10
days we produce and use the item. For the next 40 days, there is
no production and there is only the usage of the item.
22
23. 23
Economic Production Quantity continued
The maximum inventory level as explained
earlier is Imax = Q (1- d/p) = 400.
Average Inventory = (Imax)/2
Annual Setup Cost = (D/Q)S
Annual Holding Cost =
EPQ is obtained by equating the annual setup
cost with annual holding cost and then solving for
Q. The expression for EPQ is given on the RHS.
p
d
H
DS
EPQ
1
2
p
d
Q
H
H
ax
1
2
2
Im
p
d
Q
H
S
Q
D
TVC 1
2
24. Example: EPQ
Annual Demand (D) = 50,000 units, Setup Cost (S) =$25.00 per
set up, Inventory Holding Cost (H) = $5.00 per unit per year.
Production rate (p) = 500 units per day.
Number of working days = 250. Demand occurs only during the
working days. Therefore, (d) = 50,000/250 = 200.
EPQ (QP) = 912.87 =
Imax = 548.
24
26. 26
Quantity (Price) Discount Model
Quantity discount model is used when the vendor (supplier)
offers a discount for buying in large quantities.
For example, the supplier may quote a price of $ 10.00 per unit
for order size 1 to 999 and $ 9.50 for order size of 1,000 or more.
This scenario is also called a “price break” at quantity 1,000.
There could be several price breaks.
27. Example: Quantity (Price) Discounts
The annual demand (D) for an item is 240,000 units. The ordering cost per order (S) is
$ 30.00. The inventory carrying cost per unit per year (H) is 30% of the cost (price) of
the item, that is, H = 30% of C.
The vendor has quoted the following costs (prices).
Price 1: $ 2.80 for order quantity less than or equal to 29,999.
Price 2: $ 2.77 for order quantity 30,000 and above.
Find the Economic Order quantity.
27
28. Example: Quantity (Price) Discounts
(continued)
To solve this problem we will compare the total costs for both
prices. As in the EOQ model, the economic order quantity is
given by the following equation,
QO =
and, the total cost (TC) is given by the following equation:
TC = (D/Q)*S + (Q/2)*H + D*C
28
29. Example: Quantity (Price) Discounts
(continued)
Start calculations by finding EOQ at the lower price ($ 2.77).
The inventory carrying cost for this price is $0.83 (= 30% of $ 2.77) per unit
per year and the economic order quantity for this price is 4,163.
However, we cannot buy 4,163 units at the price of $ 2.77 because the
minimum quantity specified by the vendor at this price is 30,000.
Therefore, we have to buy at least 30,000 units to obtain this price discount.
We calculate the total cost TC (at 30,000). Using the TC equation,
TC (at 30,000) = (240,000/30,000)*30 + (30,000/2)*0.83 + 240,000*2.77 = $ 677,505.00
29
30. Example: Quantity (Price) Discounts
(continued)
Now calculate the EOQ for the higher price $ 2.80.
The value of H for this price is $ 0.84 (30% of $ 2.80).
The economic order quantity is 4,140.
This quantity is feasible because we can by up to 29,999 units at $ 2.80 per
unit.
The total cost, TC(at 4,140) will be:
TC (at 4,140) = = (240,000/4,140)*30 + (4,140/2)*0.84 + 240,000*2.80 = $ 675,477.93.
The order quantity for this example is 4,140
since TC (at 4,140) < TC (at 30,000).
30
32. ABC Analysis
Some materials are more important than others.
Importance can be established in the following two
ways:
o Material Criticality
o Annual Dollar Volume of Materials
32
33. Material Criticality
There are various definitions of ‘‘critical’’ that fit different
situations. For example, a part is critical when:
o A part failure causes product or process failure.
o Part failure can have a probability (not a certainty) of stopping
the process or product.
o Part failure reduces production output by a significant amount.
o Danger involved in using materials. Flammability,
explosiveness, and toxicity of fumes are crucial safety factors
for materials management.
33
34. Material Criticality (continued)
Whichever definition of criticality is used, the procedure is to list first the
most critical parts.
Next, systematically rank-order parts according to their relative criticality.
The concept of criticality should reflect the costs of failures, including safety
dangers, loss of life, and losses in production output.
Curves similar to the figure on RHS
can be created for such situations.
34
35. Annual Dollar Volume of Materials
ABC categories are based on sorting materials by their annual dollar volume.
Dollar volume is the surrogate for potential savings that can be made by
improving the inventory management of specific materials.
Accordingly, all parts, components, and other materials used by a company
should be listed and then rank ordered by their annual dollar volume.
Start with those items that have the highest levels of dollar volume and rank
order them from the highest to the lowest levels.
o The top 25 percent of these materials are called A-type items.
o The next 25 percent are called B-type items.
o The bottom 50 percent are called C-type items.
35
36. Annual Dollar Volume of Materials
(continued)
However, there is no fixed convention that A, B, and C class breaks must
occur at 25 and 50 percent.
Companies differ with respect to what percent of all items stocked account for
75 percent of their total annual dollar volume.
The figure on RHS portrays a typical
case where 20 to 30 percent of all
items carried account for as much as
70 to 80 percent of the company’s
total dollar volume.
36
37. Annual Dollar Volume of Materials -
Example
Item Stock
Number
Annual
Volume
(Units)
Unit Cost
Annual Dollar
Volume
Percentage of
Annual Dollar
Volume
Cumulative % of
Annual Dollar
Volume
Percentage
of Number
of Items
Stocked
Cumulative % of
Number of Items
Stocked
Category
P 1250 $92.00 $115,000.00 40.17% 40.17% 10.00% 10.00% A
Q 530 $168.00 $89,040.00 31.10% 71.26% 10.00% 20.00% A
R 1970 $18.75 $36,937.50 12.90% 84.17% 10.00% 30.00% B
S 430 $42.20 $18,146.00 6.34% 90.50% 10.00% 40.00% B
T 990 $13.80 $13,662.00 4.77% 95.27% 10.00% 50.00% B
U 680 $12.50 $8,500.00 2.97% 98.24% 10.00% 60.00% C
V 2150 $0.98 $2,107.00 0.74% 98.98% 10.00% 70.00% C
W 210 $9.80 $2,058.00 0.72% 99.70% 10.00% 80.00% C
X 1250 $0.52 $650.00 0.23% 99.93% 10.00% 90.00% C
Y 335 $0.64 $214.40 0.07% 100.00% 10.00% 100.00% C
Total $286,314.90
37
38. Lead-Times
Lead time (LT) is the interval that elapses between the recognition that an
order should be placed and the delivery of that order. See Figure below.
The diminishing stock level reaches a threshold (or limen) called QRP - the
stock level of the reorder point.
The threshold triggers the order for replenishment.
The stock level at the reorder point, RP, is enough to meet orders until the
replenishment supply arrives and is ready to be used.
38
39. Lead-Times (continued)
Eight lead-time (LT) considerations that apply to EOQ or EPQ or
both:
The amount of time required to recognize the need to reorder.
The interval for doing whatever clerical work is needed to
prepare the order.
Mail, e-mail, EDI, or telephone intervals to communicate with
the supplier (or suppliers) and to place the order(s).
Time that takes the supplier’s organization to react to the
placement of an order?
39
40. Lead-Times (continued)
Delivery time including loading, transit, and unloading.
Processing of delivered items by the receiving department.
Inspection to be sure items match specifications.
Time delays in updating records The effect of such delays on
the production schedule must be considered.
The eight lead-time components are added to get the lead time.
Lead times are usually variable.
Safety stocks may be increased to deal with variable lead times.
40
41. Order Point Policies (OPP)
Order point policies (OPP) define the stock level at which an
order will be placed. The reorder point (RP), triggers an order for
more stock.
OPP systems specify the number of units to order and when to
order.
We will discuss the following two systems
Periodic, also known as fixed time, inventory systems.
Perpetual, also known as fixed quantity, inventory systems.
41
42. Periodic (Fixed Time) Inventory
Systems
The interval between orders is fixed while the ordered amount varies.
The order size is determined by the amount of stock on-hand when the record
is read.
It is the date that triggers the review and the order being placed.
See the figure on RHS.
42
43. Perpetual (Fixed Quantity) Inventory
Systems
Perpetual, also known as fixed quantity, inventory systems continuously
record inventory received from suppliers and withdrawn by employees.
An order is placed when reorder point is reached.
The amount ordered is same (generally EOQ or EPQ) in each cycle.
The interval between placing orders is different in each cycle because of
demand variability.
See the figure on RHS.
43
44. Reorder Point and Safety (Buffer) Stock
Shortages occur whenever actual demand in the lead-time period exceeds QRP.
The likelihood of a shortage will be decreased by increasing the value of
safety( buffer) stock.
Determining safety (buffer) stock level requires an economic balancing
situation between the cost of going out of stock versus the cost of carrying
more inventory.
The large buffer stock means that the carrying cost of stock is high to make
sure that the actual cost of stock-outages is small.
The stock level of the reorder point (QRP) is equal to the expected (average)
demand during the lead time period plus the safety stock (SS) quantity.
Thus,
44
QRP = LT + SS
45. Expected Demand During Lead Time
The expected demand during lead time is a function of average demand per
day (d) and the magnitude of lead time (LT) and is determined as
It may be noted that calculation of demand during lead time becomes complex
if lead time also varies.
45
46. Safety Stock Calculations
The value of SS depends on the variability of demand and the service level.
The service level is a measure of the stock-out situations allowed. For
example, a 95% service level means that there will be no out-of-stock situation
95% of the time during lead time.
Assuming that the demand follows a normal distribution the value of SS can be
determined as
SS = zσLT
where, σLT is the standard deviation of demand during lead time and z is a
measure of the service level that we want to provide. z is called standard
normal random variable and can be found from its statistical table. For the
95% service level the value of z = 1.65.
46
47. Two-Bin Perpetual Invenory Control
System
The two-bin system is a smart way of continuously monitoring
the order point.
It is a simple self-operating perpetual inventory system.
See the figure below.
47