Operations Management- Case 2
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topic_3_s.pptTypes of Inventories
- Raw materials & purchased parts
- Partially completed goods called
work in progress - Finished-goods inventories or merchandise
(manufacturing firms) (retail stores)
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Types of Inventories (Cont’d)
- Replacement parts, tools, & supplies
- Goods-in-transit to warehouses or customers
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Functions of Inventory
- To meet anticipated demand
- To smooth production requirements
- To decouple operations
- To protect against stock-outs
- To take advantage of quantity discounts
- To help hedge against price increases
- To permit operations
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Objective of Inventory Control
- To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
- Level of customer service
- Costs of ordering and carrying inventory
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Key Inventory Terms
- Lead time: time interval between ordering and receiving the order
- Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
- Ordering costs: costs of ordering and receiving inventory
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Economic Order Quantity Models
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Costs Associated with Inventory Control
- Three categories of costs associated with inventory:
Purchasing costs
Ordering costs
Carrying costs
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Purchasing Costs
- Purchasing costs are the costs of goods acquired from suppliers including incoming freight or transportation costs.
- These costs usually make up the largest single cost category of inventory.
- Discounts for different purchase-order sizes and supplier credit terms affect purchasing costs.
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Ordering Costs
- Ordering costs are the costs of preparing, issuing, and paying purchase orders, plus receiving and inspecting the items included in the orders.
- Purchase approval and special processing costs are related to the number of purchase orders processed.
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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Purchasing Process
MGT 504 by Dr. Bin Jiang
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Needs Identification
Purchasing requisition
Reorder point system
Statement of work/scope of work
2. Description by:
Market grade/industry standard
Brand
Specification
Performance characteristics
3. Supplier Selection/Contracting
Competitive bidding
Selecting
Negotiating
Contracting
4. Ordering
Purchase orders
EDI
5. Follow-up and Expediting
6. Receipt and Inspection
7. Settlement and Payment
8. Records Maintenance
Order Cycle
MGT 504 by Dr. Bin Jiang
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Carrying Costs
- Carrying costs arise when an organization holds an inventory of goods for sale.
- These costs include the opportunity cost of the investment tied up in inventory and the costs associated with storage such as space rental, insurance, obsolescence, and spoilage.
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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Economic-Order-Quantity Decision Model
- The economic-order-quantity (EOQ) is a decision model that calculates the optimal quantity of inventory to order under a restrictive set of assumptions.
- The simplest version of this model incorporates only ordering costs and carrying costs into the calculations.
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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Simplest EOQ Model
- The simplest EOQ model minimizes the relevant ordering costs and carrying costs.
- Relevant total costs = Relevant ordering costs + Relevant carrying costs
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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The Simplest EOQ Assumptions
- Assumptions:
- Demand is known
- Lead time is known & constant
- No quantity discounts are available
- Ordering (or setup) costs are constant
- All demand is satisfied (no shortages)
- The order quantity arrives in a single shipment
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MGT 504 by Dr. Bin Jiang
MGT 504 by Dr. Bin Jiang
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24.bin
The Inventory Cycle
MGT 504 by Dr. Bin Jiang
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Profile of Inventory Level Over Time
Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time
MGT 504 by Dr. Bin Jiang
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Costs
- Holding Cost:
- Setup Costs: A per lot
- Cost Function:
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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EOQ Model
How Much to Order?
MGT 504 by Dr. Bin Jiang
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Order Quantity
Annual Cost
Holding Cost Curve
Total Cost Curve
Order (Setup) Cost Curve
Optimal
Order Quantity (Q*)
MGT 504 by Dr. Bin Jiang
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Economic Order Quantity
MGT 504 by Dr. Bin Jiang
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EOQ Square Root Formula
MGT 504 by Dr. Bin Jiang
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Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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The Key Insight of EOQ
- There is a tradeoff between lot size and inventory costs.
- Large lot size = high inventory and infrequent orders.
- Small lot size = frequent orders lower average inventory
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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Example: A computer company has annual demand of 10,000. They want to determine EOQ for circuit boards which have an annual holding cost (H) of $6 per unit, and an ordering cost (S) of $75. They want to calculate TC and the reorder point (R) if the purchasing lead time is 5 days.
- EOQ (Q)
- Reorder Point (R)
- Total Inventory Cost (TC)
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MGT 504 by Dr. Bin Jiang
MGT 504 by Dr. Bin Jiang
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Example
A large bakery buys flour in 25-pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $10 per order. Annual carrying costs are $75 per bag.
- Determine the economic order quantity.
- What is the average number of bags on hand?
- How many orders per year will there be?
- Compute the total cost of ordering and carrying flour.
- If ordering costs were to increase by 10% per order, how much would that affect the minimum total annual cost?
- If holding costs were to increase by 10%, how much would that affect the minimum total annual cost?
- If holding costs were to increase by 10%, but ordering cost were to decrease 10%, how much would that affect the minimum total annual cost?
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
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Production Order Quantity Model
Assumptions:
- Demand is known
- Lead time is known & constant
- No quantity discounts are available
- Ordering (or setup) costs are constant
- All demand is satisfied (no shortages)
- The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Production Order Quantity Model
MGT 504 by Dr. Bin Jiang
Used when units are produced and sold simultaneously
Inventory level
Time
Demand part of cycle with no production
Part of inventory cycle during which production (and usage) is taking place
t
Maximum inventory
MGT 504 by Dr. Bin Jiang
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Production Order Quantity Model
MGT 504 by Dr. Bin Jiang
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days
Annual inventory holding cost
Holding cost
per unit per year
= (Average inventory level) x
Average inventory level
= (Maximum inventory level)/2
Maximum inventory level
Total produced during the production run
Total used during the production run
= –
= pt – dt
MGT 504 by Dr. Bin Jiang
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Production Order Quantity Model
MGT 504 by Dr. Bin Jiang
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days
Q = total produced = pt ; thus t = Q/p
Maximum inventory level
Total produced during the production run
Total used during the production run
= –
= pt – dt
Maximum inventory level
Q
p
Q
p
d
p
= p – d = Q 1 –
d
p
Q
2
Maximum inventory level
2
Holding cost = (H) = 1 – H
MGT 504 by Dr. Bin Jiang
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Production Order Quantity Model
MGT 504 by Dr. Bin Jiang
Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
D = Annual demand
Setup cost = (D/Q)S
Holding cost = (1/2)HQ[1 - (d/p)]
(D/Q)S = (1/2)HQ[1 - (d/p)]
2DS
H[1 - (d/p)]
Q2 =
2DS
H[1 - (d/p)]
Q* =
p
MGT 504 by Dr. Bin Jiang
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Quantity Discount Model
- Assumptions:
- Demand is known
- Lead time is known & constant
- No quantity discounts are available
- Ordering (or setup) costs are constant
- All demand is satisfied (no shortages)
- The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Quantity Discount Model
MGT 504 by Dr. Bin Jiang
- Reduced prices are often available when larger quantities are purchased
- Trade-off is between reduced product cost and increased holding cost
Total cost = Setup cost + Holding cost + Product cost
MGT 504 by Dr. Bin Jiang
Quantity Discount Model
MGT 504 by Dr. Bin Jiang
A typical quantity discount schedule
Total Annual Demand is 5000
| Discount Number | Discount Quantity | Discount (%) | Discount Price (P) |
| 1 | 0 to 999 | no discount | $5.00 |
| 2 | 1,000 to 1,999 | 4 | $4.80 |
| 3 | 2,000 and over | 5 | $4.75 |
MGT 504 by Dr. Bin Jiang
Quantity Discount Model
MGT 504 by Dr. Bin Jiang
- For each discount, calculate Q*
- If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount
- Compute the total cost for each Q* or adjusted value from Step 2
- Select the Q* that gives the lowest total cost
Steps in analyzing a quantity discount
MGT 504 by Dr. Bin Jiang
Quantity Discount Model
MGT 504 by Dr. Bin Jiang
1,000
2,000
Total cost $
0
Order quantity
Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b
a
b
1st price break
2nd price break
Total cost curve for discount 1
Total cost curve for discount 2
Total cost curve for discount 3
MGT 504 by Dr. Bin Jiang
Quantity Discount Example
MGT 504 by Dr. Bin Jiang
Calculate Q* for every discount
2DS
IP
Q* =
Q1* = = 700 units/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 units/order
2(5,000)(49)
(.2)(4.80)
Q3* = = 718 units/order
2(5,000)(49)
(.2)(4.75)
MGT 504 by Dr. Bin Jiang
Quantity Discount Example
MGT 504 by Dr. Bin Jiang
Calculate Q* for every discount
2DS
IP
Q* =
Q1* = = 700 units/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 units/order
2(5,000)(49)
(.2)(4.80)
Q3* = = 718 units/order
2(5,000)(49)
(.2)(4.75)
1,000 — adjusted
2,000 — adjusted
MGT 504 by Dr. Bin Jiang
Quantity Discount Example
MGT 504 by Dr. Bin Jiang
Choose the price and quantity that gives the lowest total cost
Buy 1,000 units at $4.80 per unit
| Discount Number | Unit Price | Order Quantity | Annual Purchase Cost | Annual Ordering Cost | Annual Holding Cost | Total |
| 1 | $5.00 | 700 | $25,000 | $350 | $350 | $25,700 |
| 2 | $4.80 | 1,000 | $24,000 | $245 | $480 | $24,725 |
| 3 | $4.75 | 2,000 | $23,750 | $122.50 | $950 | $24,822.50 |
MGT 504 by Dr. Bin Jiang
Safety Stock Model
- Assumptions:
- Demand is known
- Lead time is known & constant
- No quantity discounts are available
- Ordering (or setup) costs are constant
- All demand is satisfied (no shortages)
- The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Safety Stock Model
In the simplest EOQ model, ROP = dL
In the safety stock model, ROP = (safety stock)
MGT 504 by Dr. Bin Jiang
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SS
Q+SS
MGT 504 by Dr. Bin Jiang
Safety Stock Model
SS is decided by the following five factors:
- The variability of demand;
- The variability of lead time;
- The average demand;
- The average lead time;
- The desired service level.
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Safety Stock: Two Uncertainties
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Safety Stock Model
MGT 504 by Dr. Bin Jiang
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| z-Value | Associated Service Level |
| 0.84 | 80% |
| 1.28 | 90% |
| 1.65 | 95% |
| 2.33 | 99% |
MGT 504 by Dr. Bin Jiang
Safety Stock Model Example
A retailer sells, on average, 16 Panasonic microwave ovens a day ( ), with a standard deviation in daily demand of 3 ( ). If a retailer reorders suppliers directly from its supplier, they will take, on average, nine days to arrive ( ), with a standard deviation in lead time of 2 ( ). The retailer has decided to maintain a 95% service level.
How many safety stock should the retailer hold?
What is the retailer’s reorder point?
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Safety Stock Model Example
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Warehouse Effect in Supply Chain
Risk Pooling and Inventory Impact
Consider a distribution supply chain consisting of a set of n downstream retailers linked to a common source warehouse. Suppose the supplier lead time is L and every retailer faced a demand with a mean of µ and a variance of σ2
MGT 504 by Dr. Bin Jiang
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Supplier
Warehouse
Lead time: L
Retailer 1
Retailer 2
………….
Retailer n
………….
………….
Customer
µ, σ2
Customer
µ, σ2
Customer
µ, σ2
MGT 504 by Dr. Bin Jiang
Warehouse Effect in Supply Chain
Risk Pooling and Inventory Impact
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Net Requirements Plan
MGT 504 by Dr. Bin Jiang
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MGT 504 by Dr. Bin Jiang
Lot-Sizing Techniques
MGT 504 by Dr. Bin Jiang
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Lot-for-lot techniques order just what is required for production based on net requirements
May not always be feasible
If setup costs are high, costs may be high as well
Economic order quantity (EOQ)
EOQ expects a known constant demand and MRP systems often deal with unknown and variable demand
MGT 504 by Dr. Bin Jiang
Lot-for-Lot Example
MGT 504 by Dr. Bin Jiang
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| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| Gross requirements | 35 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Scheduled receipts | |||||||||||
| Projected on hand | 35 | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Net requirements | 0 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Planned order receipts | 30 | 40 | 10 | 40 | 30 | 30 | 55 | ||||
| Planned order releases | 30 | 40 | 10 | 40 | 30 | 30 | 55 |
MGT 504 by Dr. Bin Jiang
Lot-for-Lot Example
MGT 504 by Dr. Bin Jiang
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No on-hand inventory is carried through the system
Total holding cost = $0
There are seven setups for this item in this plan
Total setup cost = 7 x $100 = $700
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| Gross requirements | 35 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Scheduled receipts | |||||||||||
| Projected on hand | 35 | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Net requirements | 0 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Planned order receipts | 30 | 40 | 10 | 40 | 30 | 30 | 55 | ||||
| Planned order releases | 30 | 40 | 10 | 40 | 30 | 30 | 55 |
MGT 504 by Dr. Bin Jiang
EOQ Lot Size Example
MGT 504 by Dr. Bin Jiang
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Holding cost = $1/week; Setup cost = $100;
Average weekly gross requirements = 27; EOQ = 73 units
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| Gross requirements | 35 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Scheduled receipts | |||||||||||
| Projected on hand | 35 | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Net requirements | 0 | 30 | 0 | 0 | 7 | 0 | 4 | 0 | 0 | 16 | |
| Planned order receipts | 73 | 73 | 73 | 73 | |||||||
| Planned order releases | 73 | 73 | 73 | 73 |
MGT 504 by Dr. Bin Jiang
EOQ Lot Size Example
MGT 504 by Dr. Bin Jiang
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Holding cost = $1/week; Setup cost = $100;
Average weekly gross requirements = 27; EOQ = 73 units
Annual demand = 1,404
Total cost = setup cost + holding cost
Total cost = (1,404/73) x $100 + (73/2) x ($1 x 52 weeks)
Total cost = $3,798
Cost for 10 weeks = $3,798 x (10 weeks/52 weeks) = $730
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| Gross requirements | 35 | 30 | 40 | 0 | 10 | 40 | 30 | 0 | 30 | 55 | |
| Scheduled receipts | |||||||||||
| Projected on hand | 35 | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Net requirements | 0 | 30 | 0 | 0 | 7 | 0 | 4 | 0 | 0 | 16 | |
| Planned order receipts | 73 | 73 | 73 | 73 | |||||||
| Planned order releases | 73 | 73 | 73 | 73 |
MGT 504 by Dr. Bin Jiang
2
cost holding annual
2
inventory average
HQ
Q
Q
SD
D
Q
S
cost setup annual
demand annual
cost setupunit
Q
SDHQ
QY
2
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Q
S
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DS
H
=
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(
Annual Demand
)
(
Order or Setup Cost
)
Annual Holding Cost
OPT
units
500
$6
$75
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10,000
*
2
H
2DS
Q
=
=
=
units
200
days
5
*
days
250
10,000
Time
Lead
x
Demand
Daily
R
=
=
=
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$1500
$1500
$6
2
500
$75
500
10,000
TC
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