Chapter VI. Independent Demand Inventory Systems

- Inventory is a store of goods held for future use. Types of inventory include raw materials, work-in- process, finished goods, and supplies.

- Among some firms, inventory carrying costs represent from 10 to 40 percent of the cost of goods sold.

- Why hold inventories? Benefits include:

1. Meet expected customer demand

2. Improve customer service

3. Uncertain sources of supply

4. Economies of scale (production, purchase, transportation)

5. Stable (smooth) rates of production

6. An inability to backlog demand

7. Decouple operations (internal and external)

8. Forward buying (hedge)

9. Display items

- Costs to have inventory include:

1. Costs to: insure, finance, warehouse, manage or control, security

2. Foregone return of alternative investments

3. Shop congestion

4. Tendency to hide quality related problems

5. Delays in meeting customer deliver dates

A. Independent demand inventory systems

- Due to the nature of demand, an important distinction is made between independent and dependent demand

- Independent demand inventory control procedures rely upon unbiased forecasts of uncertain demand. Demand and lead times may be treated as random variables. Forecasts are used to develop production and purchase schedules for end items.
- Dependent demand inventory control techniques utilize material requirements planning (MRP) logic.

- MRP converts a production schedule for end items that experience independent demand into known requirements for “lower level” items in order to determine production and purchase schedules.

- Regardless of the nature of demand (independent, dependent, seasonal, terminal, lumpy, etc.) two fundamental issues underlie all inventory planning:

- How much to order (Q)
- When to order

B. Methods of Stock Control

1. Push inventory control

- A centralized form of inventory control whereby the distribution network (points) is viewed collectively.

- Available inventories are allocated to distribution points according to some criterion such as projected needs, historical use, or available space.
- Push may afford greater economies of scale in production and purchase orders.

2. Pull inventory control

- A decentralized approach, whereby each point in the distribution network is treated independently of all other points.

- Inventory policy decisions are made independently.

3. Benefits of centralized (push) inventory location strategies

a. Reduction of safety stocks

b. Greater opportunity to use private warehousing (volume)

c. Reduction of transshipment costs

d. Improvement of in-stock position in filling customer orders

4. Benefits of decentralized inventory location strategies

a. Improvement in order-cycle response time

b. Stimulation of sales

c. Reduction of warehouse-to-customer transport costs

d. Greater opportunity for public warehousing (larger proportion of costs which vary with volume)

C. Inventory control objectives (2)

- Remember: two fundamental issues underlie all inventory planning: (1) how much to order (Q), and (2) when to order.

- Cost Objective: Minimize sum of relevant costs

- Service objective: Maximize customer service

- Four potential costs: holding (carrying), order, shortage, and item acquisition (purchase)

a. Holding (Carrying) costs: H = C(i)

- C is the unit cost and i is the annual holding cost expressed as a percent of C
- Determined for an average inventory level and divided into 3 classes: (1) space costs, (2) capital costs, and (3) risk costs

b. Order (Set-Up): S

- Fixed costs associated with the acquisition of goods and include costs for processing, transmitting, handling, transportation, receipt, and inspecting orders.

c. Shortage Costs

- Costs incurred when a customer order cannot be filled from the inventory to which the order in assigned.

- There are two classes: (1) lost sales, and (2) backorder costs

d. Acquisition Cost (Manufacture or Purchase) - C represents the unit cost

e. Total Cost = Holding Cost + Order Cost + Shortage Cost + Acquisition Cost

- Service Level (SL): defined several ways

a. The probability of satisfying all of demand during the lead-time period (the complement of a stock out)

b. The number of orders per year that were completely filled

c. The time between customer order transmittal and order receipt

- Note impact of customer service level on inventory levels.

D. Pull Strategy Inventory Control Models

- Remember: 2 important issues in inventory control: order quantity and order timing.

- 2 general classes of models: continuous review (fixed-order quantity) and periodic review (fixed-order-period)

1. Continuous Review (*Q*-systems or fixed-order-quantity systems)

a. Multi-period models

(1) Fixed order quantity, variable time between orders

(2) Perpetual inventory count

(3) On-hand inventory balance serves as order trigger (R)

(4) Example: 2-bin system

- When inventory on-hand drops to a predetermined level, a replenishment order is placed for a fixed amount of inventory. EOQ in conjunction with reorder point (R) is used to determine inventory policy (order quantity and order release determination).

b. Single-period model

- Places orders for a fixed amount of inventory, but does so every period. “Marginal analysis” is used to determine inventory policy (order quantity determination).

2. Periodic Review (*P*-systems or fixed-order-period systems)

a. Variable order quantity, fixed time between orders

b. Periodic inventory count

c. Time serves as order trigger

- When a predetermined amount of time,
*P*, has elapsed a physical inventory count is taken. Based upon the number of units in stock at that time (A) and an upper inventory unit target (*T*), an order is placed for Q units, where Q = (T-A).

E. Pull strategy and *Q*-Systems: How much to order (Q)

- Multi-period inventory model: order decisions for infinite length planning period address how much to order as well as when to place an order. Economic Order Quantity (EOQ) model is commonly used as basis for determining Q.

- Single-period model: order decisions for finite length (1 period) inventory planning address how much to order. Marginal analysis commonly used as modeling basis.

1. Economic Order Quantity (EOQ)

- Goal: to identify an order size (Qo) that will minimize the sum of the
*relevant*costs.

- A cost is only
*relevant*if it can be avoided.

- Numerous modeling variations

- Modeling assumptions: “Saw-Tooth Diagram”

a. 1 product

b. Annual demand (D) known, occurs at a constant rate (d)

c. Known and constant order lead time (LT)

d. Instantaneous replenishment (no split deliveries)

e. No stock outs allowed

f. No quantity discounts

g. All costs known and constant

- There are only two relevant costs: annual carrying and ordering costs.

- Total annual cost: TC = (Q/2)H + (D/Q)S

____________

- Basic model: Qo = 2(D)S /H

- Realism?

- Reorder point (R) quantity under certainty

- Example

2. Economic Production Lot-Size EOQ

- EOQ with Quantity Discounts

4. Joint Replenishment EOQ

F. Pull strategy and *Q*-Systems: When to order (R)

- When to place an order is determined relative to an on-hand balance or a Re-order Point (R) quantity.

- The R quantity is to be determined for a preferred customer service level rather than estimating stock out costs.

1. Four determinants of R quantities

a. Rate of demand (d)

b. Length of order (manufacturing) LT

c. Variability of demand and LT (d, LT, or DLT)

d. Degree of stock-out risk (preferred service level, SL)

2. Alternative demand during lead time probability distributions

a. Discrete distribution of __d__emand __d__uring __l__ead __t__ime (DDLT)

- May be used due to lack of demand history or item nature

- For a desired minimum service level, R is determined relative to the cumulative demand frequency.

Number of Frequency Cumulative

__DDLT__ __Observations __ __(Probability)__ __Probability__

3 10 .10 .10

4 20 .20 .30

5 40 .40 .70

6 20 .20 .90

7 __10__ __.10__ 1.00

100 1.00

b. Continuous distribution of demand during lead time

- May be used given sufficient demand history or due to nature of the item (e.g., divisible units)

- General Model Form: R =
*m*+*s*

Where, *m* is expected (mean) demand during lead time and s is safety stock. Safety stock is used to satisfy the variability in demand and/or lead time and is a function of: (1) rate of demand, (2) length of lead time, (3) variability of demand and/or lead time, and (4) desired service level. Safety stock is determined as:

*s* = Z(DLT)

- 4 Model Variations

- Constant Demand (d), Constant Lead Time (LT):

R = d(LT)

(2) Variable Demand (d), Constant Lead Time (LT):

__

R = d(LT) + Z(DLT) where DLT = sdÖLT

(3) Constant Demand (d), Variable Lead Time (LT):

R = d(LT) + Z(DLT) where DLT = d(LT)

(4) Variable Demand (d), Variable Lead Time (LT):

_______________

R = d(LT) + Z(DLT) where, DLT = LT(d2) + d2(LT2)

- Example

G. Pull strategy and *P*-Systems with Demand Uncertainty

- Orders are placed after an elapsed fixed period of time, the order interval (
*P*), has passed for a variable quantity of units.

- Other differences between
*Q*- and*P*-Systems:

(a) Perpetual versus periodic inventory accounting systems

(b) Higher than normal demand during the order cycle leads to a shorter time between orders for *Q*-Systems while in *P*-Systems it leads to larger order sizes

(c) *P*-Systems typically require larger safety stocks in order to provide the same level of customer service.

1. General model form with uncertain (variable) demand, constant lead time

Expected Demand

Q = During Protection + Safety Stock - Amount on hand

Interval (A)

2. Specific model form (uncertain demand, constant lead time)

____

Q = d(*P* + *L*) + Z(d)*P* + *L* - A

Where, d is rate of demand, *P* is the time between orders, *L* = lead time, Z reflects desired service level, d is the standard deviation of demand, and A = amount on hand at reorder time

- A reasonable approximation method for determining model parameter
*P*is to use the EOQ model to solve for the order size. The time between orders is then simply the order quantity divided by annual demand.*T*, or the upper inventory target, is determined for a specified service level. The standard deviation of demand during the “protection interval” is found by determining the daily standard deviation of demand and multiplying by the square root of the daily length of the protection interval.

- Example

3. Advantages of *P*-Systems versus *Q*-Systems

a. On-hand accuracy resulting from periodic physical inventory counts

b. Ability to group orders from a supplier resulting in potentially lower transportation and ordering

4. Disadvantages of *P*-Systems versus *Q*-Systems

a. Larger amount of safety stock for a given level of customer service

b. Periodic physical inventory review cost

H. Single period inventory model (Continuous Review, Fixed-Order-Quantity System)

- The approach used assumes units cannot be carried over to a subsequent period without penalty. The difference of this model is due to the finite length (1 period) planning horizon. Marginal analysis is used to determine order quantity.

- Shortage Costs (Cs) = revenue per unit – cost per unit

- Excess Costs (Ce) = cost per unit - salvage value per unit

- Service Level = Cs/(Cs+Ce)

- Uniform Demand Distribution:

So = Min. Demand + SL (Max - Min Demand)

2. Normal Demand Distribution: So = d + Zsd

3. Discrete Demand Distribution: compare SL with cumulative frequency. So established so that SL achieved as a minimum requirement.

I. ABC Inventory Classification

J. Cycle Counts

*Source: *http://www.sba.oakland.edu/Faculty/Fliedner/Vienna/Independent%20Inventory%20Demand%20Systems.doc

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