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Topic 6. INVENTORY MANAGEMENTPowerPoint Presentation

Topic 6. INVENTORY MANAGEMENT

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I. Introduction

- What is inventory?
- stored resource used to satisfy current or future demand

- Types of Inventories:
- Raw Materials/Components
- In-Process Goods (WIP)
- Finished Goods
- Supplies

Introduction

- Inventory Related Costs:
- Holding Cost -- cost to carry a unit in inventory for a length of time (annual), includes interest opportunity cost, insurance, taxes, depreciation, obsolescence, deterioration, May be expressed as a percentage of unit price or as a dollar amount per unit

Introduction

- Inventory Related Costs (continued):
- Order Cost -- Cost of ordering and receiving inventory, Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality, Generally expressed as a fixed dollar amount, regardless of order size
- Inventory may also influence purchasing cost
- Inventory is costly

Introduction

- Inventory Related Costs (continued):
- Shortage Cost-- result when demand exceeds the inventory on hand, Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime, difficult to measure, thus may have be subjectively estimated

Introduction

- Why Hold Inventories?
- Meet anticipated demand
- Lead time – the time period between place an order until receive the order
- Average lead time demand is considered as anticipate demand

- Protect against stock-out
- Safety stock – more than average lead time demand inventory

- Meet anticipated demand

Introduction

- Why Hold Inventories (continued)?
- De-couple successive operations - separate production from distribution
- Wine production and inventory

- Smooth production process
- Snowmobile production and inventory

- Buy/Produce in economic lot sizes - take advantage of quantity discounts
- Hedge against price increases

- De-couple successive operations - separate production from distribution

Introduction

- JIT Inventory – minimum inventory needed to keep a system running, small lot sizes
- Advantages
- lower inventory costs
- easy to identify problems and potential problems

- Disadvantages
- requires accurate timing and cooperation
- breakdowns stop everything

- Advantages

A

Annual

$ volume

of items

B

C

Low

Few

Many

Number of Items

Introduction- Inventory Classification
- Identify important
Items and more inventory

control on important items

- Measure of importance:
- ABC analysis:
- A = 70-80% of total inventory value, but only 15% of items
- B = 15-25% of total inventory value, but 30% of items
- C = 5% of total inventory value, but 55% of items

- Identify important

214800 232087768

Introduction- Monitor Inventory
- As important as demand forecast for decision making
- Universal Product Code - Bar code printed on a label that hasinformation about the item to which it is attached
- Cycle counting: taking physical counts of items and reconciling with records on a continual rotating basis, regular inventory audits, ABC approach

Introduction

- Inventory Systems
- Objective: minimize annual total inventory cost and maintain satisfied service level.
- service level: probability of no shortage
Total Inventory Cost is not Inventory Cost

- Annual total inventory cost (TC) = annual product cost + annual inventory cost
- Annual product cost = annual demand * unit price
- Annual inventory cost = annual holding cost + annual setup (order) cost + annual shortage cost

- service level: probability of no shortage

- Objective: minimize annual total inventory cost and maintain satisfied service level.

Introduction

- Possible performance measures
- customer satisfaction
- number of backorders/lost sales
- number of customer complaints

- inventory turnover
- ratio of annual cost of goods sold to average inventory investment

- days of inventory
- expected number of days of sales that can be supplied from existing inventory

- customer satisfaction

Introduction

- Requirements for Effective Inventory Management :
- A system to keep track of the inventory on hand and on order
- A classification system for inventory items
- A reliable forecast of demand that includes an measure of forecast error
- Reasonable estimates of inventory holding costs, ordering costs, and shortage costs
- Knowledge of lead times and lead time variability

Introduction

- 1. Continuous (Perpetual) Review System: (event-triggered)
- Monitor the inventory level all the time, order a fixed quantity (Q) when the inventory level drops to the reorder point (ROP)
- Calculate: Q and ROP
- Re-Order Point (ROP) – an inventory level when actual inventory drops to it will trigger an activity of re-order.

Introduction

- 2. Periodic Review System: (time-triggered)
- Place an order every fixed period T. Each time bring the current inventory to a target level M
- Calculate: T and M

- 3. Advantages and Disadvantages?

Introduction

- Dependent and Independent Demand:
- Dependent demand: derived demand, lumpy (subassemblies and components)
- cars

- Independent demand: from customer side, smooth (end items and finished goods)
- tires

- Dependent demand: derived demand, lumpy (subassemblies and components)

II. Inventory Models On Order Quantity

- Model Basics (consider as annual)
- Total Cost (TC) = Product Cost + Inventory Cost
Inventory Cost = Holding Cost

+ Setup (Order) Cost + Shortage Cost

TC = Product Cost + Holding Cost

+ Setup (Order) Cost + Shortage Cost

- Total Cost (TC) = Product Cost + Inventory Cost

Inventory Models On Order Quantity

- Product Cost = Annual Demand * Unit Price
- Holding Cost = average inventory level * Holding Cost per unit per year
- Ordering Cost = # of orders * Setup Cost per order
- # of orders = annual demand / order quantity

- Shortage Cost = Shortage Cost per unit
* average # of shortage per year

Best Order Quantity = a quantity that minimizes TC

Inventory Models On Order Quantity

EOQ Model (Economic Order Quantity), Fixed-Order-Quantity Model

- Assumptions
- There is one product type
- Demand is known and constant
- Lead time is known and constant
- Receipt of inventory is instantaneous (one batch, same time)
- Shortage is not allowed

EOQ Model (continued)

Q

Reorder

point

Place

order

Receive

order

Receive

order

Place

order

Receive

order

Lead time

EOQ Model (continued)

- Notation and Terminology
- Q = order quantity(# of pieces per order)
- Q0 = Economic Order Quantity (EOQ)
- D = demand for the time period considered (units per year)
- S = setup/order cost ($ per order)
- H= holding cost per unit per year ($ per unit per year)
- in general proportional to the price, H = I*P

EOQ Model (continued)

- Notation and Terminology (continued)
- I = Interest rate (expanded) (% per year)
- P= unit price ($ per unit)
- IC = inventory cost = setup cost + holding cost
- TC = IC+ product cost
Find Out EOQ

EOQ Model (continued)

- Average Inventory Level =
- Holding Cost =
- Number of orders per year =
- Setup (Order) Cost =
- Shortage Cost = 0, why?

EOQ Model (continued)

- Product Cost =
- IC =
- Total Cost (TC) =
- Minimize TC Minimize IC, why?

EOQ Model (continued)

- Observation: at the best order quantity EOQ (Q0),
holding cost = setup cost

Solve Q0, we have

EOQ Model (continued)

The Inventory Cost Curve is U-Shaped

Annual Cost

Annual

Carrying Costs

Annual

Ordering Costs

QO

(EOQ)

Order Quantity (Q)

EOQ Model (continued)

- Example:
Annual demand = 10,000 unit/year, ordering cost = $50/order, unit cost (price) = $4/unit, expanded interest rate = 25%/year. EOQ? TC at EOQ?

EOQ Model (continued)

- Sensitivity of IC with related to Q
-- Example (continued)

EOQ Model (continued)

- Conclusion:
- 1. Inventory cost curve is flat around EOQ
- 2. Flatter when Q increases than when Q decreases from EOQ

- Thinking Challenge:
- If the order quantity Q = 2*EOQ, by how much IC will increase?

EOQ Model (continued)

- Sensitivity of EOQ with related to D, H, S, P, I
- 1. Insensitive to parameter change
- 2. Directions?

EPQ Model

EPQ (Economic Production Quantity) Model: Fixed Order Quantity Model with Incremental Replenishment

- Problem description:
- Assumptions
- There is one product type
- Demand is known and constant
- Receipt of inventory is gradual and at a constant replenishment (production) rate
- Shortage is not allowed

EPQ Model (continued)

Production rate

- usage rate

Q

Quantity

on hand

Usage

rate

Reorder

point

Time

Start to

produce

Start to

produce

Finish

production

Production run length

EPQ Model (continued)

- Notation and Terminology
- Qp = production quantity(# of pieces/production run)
- Qp0 = Best production quantity (EPQ)
- p = daily production rate (units per day)
- d = daily demand rate (units per day)
- D = demand rate (units per year)
- S = production setup (order) cost($ per setup)
- H = holding cost per unit per year (again H = I*P in general)
- T= production run length = Q/p

EPQ Model (continued)

- Maximum Inventory Level =
- Average Inventory Level =
- Annual Holding Cost =

EPQ Model (continued)

- Number of production runs per year =
- Order Cost =
- IC =
- TC =
- Minimize TC Minimize IC, why?

EPQ Model (continued)

- Observation: at EPO,
holding cost = setup cost

- Best Production Quantity (EPQ) formula:

EPQ Model (continued)

- Remarks: EPQ > EOQ (why?)
- Example: D=2000 unit/year, S=$5/setup, H=$0.4/unit/year, p=100 unit/day, 200 working days/year. Find the best production batch size and the # of production runs/year.

EOQ with discount

EOQ with Discount Model:

- Assumptions: same as with EOQ, plus discount on all units
- Terminology
- Price breaks: the smallest order quantity to receive a discount price
- Feasibility: the order quantity matching the claimed price is feasible, otherwise infeasible.

EOQ with discount (continued)

- Example:
Order Price

0-399 $2.1/unit

400-699 $2.0

Great equal 700 $1.9

- Idea is to compare TC curves under different prices - why TC?

for Price 1

Total Cost Curve

for Price 2

Total Cost Curve

for Price 3

Order Quantity

EOQ with discount (continued)$ cost

400

700

for Price 1

Total Cost Curve

for Price 2

Total Cost Curve

for Price 3

Order Quantity

EOQ with discount (continued)$ cost

400

700

EOQ with discount (continued)

- Observations:
- EOQ with a lower price, if feasible, is better than any order quantity with the same or higher price.
- Potential best order quantity: cheapest feasible EOQ, price breaks associated with lower prices.

EOQ with discount (continued)

- Solution Procedure:
- 1. Find the feasible EOQ with cheapest possible price.
- 2. Calculate TCs of the EOQ (from Step 1) and price breaks above EOQ.
- 3. Pick the order quantity with lowest TC

EOQ with discount (continued)

- Example (continued) Annual demand = 10,000 unit/year, order cost = $5.5/order. Assuming holding costs are proportional to unit prices and annual interest rate = 20%. Find the best order quantity.

III. Models on Reorder Points - When to Order?

- Models on Reorder Points - When to Order?
- Find ROP (Re-Order Point)

- ROP depends on:
- Lead Time: time between placing and receiving an order
- Demand Distribution: how uncertain
- Desired Service Level: probability of no shortage = 1-P(s), where P(s) = probability of shortage

Models on Reorder Points - When to Order ? (continued)

- Constant Demand Rate:
- Constant daily demand rate = d, Lead time = L days
ROP = d * L = Lead time demand

- Constant daily demand rate = d, Lead time = L days
- Remark:
- no uncertainty in demand
- service level = 100%
- safety stock = 0

Models on Reorder Points - When to Order ? (continued)

- Variable Demand with Stable Average Rate
- How continuous review system works?
- Lead time demand: demand during the lead time
- ROP Lead time demand ==>
- ROP < Lead time demand ==>
- ROP = Average lead time demand + Safety Stock = m + SS

Models on Reorder Points - When to Order ? (continued)

- Remarks:
- Higher the desired service level --->
- More uncertain the demand --->

- Two methods to determine the SS

Models on Reorder Points - When to Order ? (continued)

- 1. Determine SS and ROP based on shortage cost inf. (if available)
- SS increases Holding cost ? Shortage cost ?
- Best SS minimizes total inventory cost

Models on Reorder Points - When to Order ? (continued)

- 1. Determine SS and ROP based on shortage cost inf. (continued)
-- Example: Consider a light switch carried by Litely. Litely sells 1,350 of these switches per year, and places order for 300 of these switches at a time. The carrying cost per unit per year is calculated as $5 while the stock out cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). Find the best SS level and ROP for Litely.

Models on Reorder Points - When to Order ? (continued)

Determine SS and ROP based on shortage cost inf. (continued)

- 1. Determine SS and ROP based on demand inf. during each lead time period:

Models on Reorder Points - When to Order ? (continued)

- Determine SS and ROP based on shortage cost inf. (continued)
- If SS = 0, ROP = m = 15 switches

Models on Reorder Points - When to Order ? (continued)

Determine SS and ROP based on shortage cost inf. (continued)

- # of orders per year =
- For no safety stock, Litely has the following shortage table. Why?

Models on Reorder Points - When to Order ? (continued)

- Determine SS and ROP based on shortage cost inf. (continued)
- Determine the best SS in following table

Models on Reorder Points - When to Order ? (continued)

- 2. Determine ROP and SS based on lead time demand distribution and desired service level:

Models on Reorder Points - When to Order ? (continued)

- Case 1. Empirical Lead time demand distribution
- -- Example:

Models on Reorder Points - When to Order ? (continued)

- Find R and SS to achieve the service level of 85% and 95%, respectively.

Models on Reorder Points - When to Order ? (continued)

- Case 2. Lead time demand is Normally distributed with (m, )
- SS = , ROP = m + SS, z = single tail normal score of desired service level.
( is the standard deviation)

- Example:
- Lead time demand is Normally distributed with mean = 4 and standard deviation = 3. Find ROP and SS to achieve the service level of 85% and 95%, respectively.

Homework (Additional problems) Problem)

- Problem 1: A toy manufacturer uses approximately 36,000 silicon chips annually. The chips are used at a steady rate during the 240 days the plant operates. Annual holding cost is 50 cents per chip, and ordering cost (per order) is $25/order. Assume that each of their orders comes in one batch. Determine:
- a. .the best order quantity
- b. demonstrate that your order quantity is optimal by showing that annual ordering costs = annual holding costs
- c. the average inventory level
- d. the number of orders per year
- e. the number of working days between orders (Hint: days between orders = # days in a year / # of orders per year. Why?)

Homework (Additional problems) Problem)

- Problem 2. The Dine Corporation is both a producer and a user of brass couplings. The firm operates 200 days a year and uses the couplings at a steady rate of 50 per day. Couplings can be produced at a rate of 150 per day. Inventory holding cost is estimated at $5 per unit per year. Machine setup costs are $40 per production run. Determine:
- a. the best production run size
- b. demonstrate that your production run size is optimal by showing that annual set up costs = annual holding costs (Hint: find the formula of holding and setup cost for EPQ model in my lecture note.)
- c. the maximum inventory level (Hint: find the formula in the derivation of EPQ)
- d. the number of production runs per year
- e. the cycle time and the production time within each cycle (Hint: cycle time is given by Q/d and production time is given by Q/p. Why? Think before using the formula)

Homework (Additional problems) Problem)

- Problem 3
- A small manufacturing firm used roughly 3,400 pounds of chemical dye each year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The supplier has just announced that orders of 1,000 pounds or more will be filled at a price of $2.5 per pound. The manufacturing firm incurs a cost of $100 each time it submits an order and assigns an annual holding cost of 20% of the purchase price per pound.
- a. determine the best order size that minimizes the total cost
- b. if the supplier offered the discount at 2,500 pounds instead of at 1,000 pounds, what order size would minimize total cost?

Homework (Additional problems) Problem)

- Problem 4: A product is ordered four times every year. Inventory carrying cost is $20 per unit per year, and the cost of shortage for each unit is $40. Given the following demand probabilities during the reorder period

Homework (Additional problems) Problem)

- Problem 4 (continued)
- a) What is the average lead time demand?
- b) What would be the reorder point without safety stock?
- c) What would be the probabilities of the following shortage levels if the company uses the reorder point without safety stock?

Homework (Additional problems) Problem)

- Problem 4 (continued)
- d) Follow the Litely example in my lecture to find out the best safety stock level to minimize the total cost.
- e) What is the reorder point to achieve the 95% service level? What is the associated safety stock? (Hint: you need to follow the example in my lecture note under Case 1)

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