OM4 Ch 12

CHAPTER 12

OM4CHAPTER 12

DAVID A. COLLIER

AND

JAMES R. EVANS

MANAGING INVENTORIES

Inventory is any asset held for future use or sale.

Objectives:

Maintain sufficient inventory

Incur lowest possible cost

Inventory Management involves planning,coordinating, and controlling the acquisition,storage, handling, movement, distribution, andpossible sale of raw materials, component partsand subassemblies, supplies and tools, replacementparts, and other assets that are needed to meetcustomer wants and needs.

Understanding Inventory

Raw materials, component parts, subassemblies,and supplies are inputs to manufacturing and service-delivery processes.

Work-in-process (WIP) inventory consists ofpartially finished products in various stages ofcompletion that are awaiting further processing.

Finished goods inventory is completed productsready for distribution or sale to customers.

Safety stock inventory is an additional amount ofinventory that is kept over and above the averageamount required to meet demand.

Exhibit 12.1 Role of Inventory in the Value Chain

Managing Inventories in Global Supply Chains

Purchasing, tracking, and managing such a variety of items inglobal supply chains requires good technology, processes, andinformation technology (IT) support.

Purchasing must focus on global sourcing and total systemcost; ensure quality, delivery performance, and technicalsupport; and seek new suppliers and products and be able toevaluate their potential to the company.

Environmentally Preferable Purchasing (EPP), orgreen purchasing, is the affirmative selection andacquisition of products and services that most effectivelyminimize negative environmental impacts over their life cycleof manufacturing, transportation, use, and recycling ordisposal.

Inventory managers deal with two fundamental decisions:

1. When to order items from a supplier or when to initiate production runs if the firm makes its own items

2. How much to order or produce each time a supplier or production order is placed

Inventory Management Decisions and Costs

Inventory Management Decisions and Costs

Four categories of inventory costs:

1. Ordering or setup costs

2. Inventory-holding costs

3. Shortage costs

4. Unit cost of the stock-keeping units (SKUs)

Inventory Management Decisions & Costs

Ordering costs or setup costs are incurred as a result of the work involved in placing purchase orders with suppliers or configuring tools, equipment, and machines within a factory to produce an item.

Inventory-holding costs or inventory-carrying costs are the expenses associated with carrying inventory.

Chapter 12 Managing Inventories

Inventory Management Decisions & Costs

Shortage costs or stockout costs arethe costs associated with a SKU being unavailable when needed to meet demand.

Unit cost is the price paid for purchased goods or the internal cost of producing them.


Inventory Characteristics

Number of items: each item is identified by a unique identifier, called a stock-keeping unit (SKU).

A stock-keeping unit (SKU) is a single item or asset stored at a particular location.



Nature of Demand:

Independent demand is demand for an SKU that is unrelated to the demand for other SKUs and needs to be forecast.

Dependent demand is demand directly related to the demand for other SKUs and can be calculated without needing to be forecast.

Demand can either be constant (deterministic) or uncertain (stochastic)

Static demand is stable demand.

Dynamic demand varies over time.



Number and Duration of Time Periods:

Single period

Multiple time periods

Lead Time:

The lead time is the time between placement of an order and its receipt.



Stockouts:

A stockout is the inability to satisfy demand for an item.

A backorder occurs when a customer is willing to wait for an item.

A lost sale occurs when the customer is unwilling to wait and purchases the item elsewhere.


ABC Inventory Analysis

ABC inventory analysis categorizes SKUs into three groups according to their total annual dollar usage

1.A items account for a large dollar value but a relatively small percentage of total items

2.C items account for a small dollar value but a large percentage of total items

3.B items are between A and C

Chapter 12 ABC Inventory Analysis

ABC Inventory (Pareto) Analysis

A items account for a large dollar value but relatively small percentage of total items (e.g., 10% to 30 % of items, yet 60% to 80% of total dollar value).

C items account for a small dollar value but a large percentage of total items (e.g., 50% to 60% of items, yet about 5% to 15% of total dollar value). These can be managed using automated computer systems.

B items are between A and C.

Chapter 12 ABC Inventory Analysis

Exhibit 12.2 Excel ABC Template Before Sorting

Solved Problem

The data show projected annual dollar usage for 20 items. Exhibit 12.3 shows the data sorted, and indicates that about 70% of total dollar usage is accounted for by the first 5 items.

Exhibit 12.3 Excel ABC Template After Sorting

Exhibit 12.4 ABC Histogram for the Results from Exhibit 12.3

In a fixed quantity system (FQS), the order quantity or lot size is fixed; the same amount, Q, is ordered every time.

The fixed order (lot) size, Q, can be a box, pallet, container, or truck load.

Q does not have to be economically determined, as we will do for the EOQ model later.


Managing Fixed Quantity Inventory Systems


The process of triggering an order is based on the inventory position.

Inventory position (IP) is the on-hand quantity (OH) plus any orders placed but which have not arrived (scheduled receipts, or SR), minus any backorders (BO).

IP = OH + SR BO [12.1]



When inventory falls at or below a certain value, r, called the reorder point, a new order is placed.

The reorder point is the value of the inventory position that triggers a new order.


Exhibit 12.5 Summary of Fixed Quantity System (FQS)

Exhibit 12.6 Fixed Quantity System (FQS) under Stable Demand

Exhibit 12.7 Fixed Quantity System (FQS) with Highly Variable Demand

The Economic Order Quantity (EOQ) model is a classic economic model developed in the early 1900s that minimizes total cost, which is the sum of the inventory-holding cost and the ordering cost.


The EOQ Model


The EOQ Model

Assumptions:

Only a single item (SKU) is considered.The entire order quantity (Q) arrives in the inventory at one time. Only two types of costs are relevantorder/setup and inventory holding costs.No stockouts are allowed.The demand for the item is deterministic and continuous over time. Lead time is constant.

Cycle inventory (also called order or lot size inventory) is inventory that results from purchasing or producing in larger lots than are needed for immediate consumption or sale.

Average cycle inventory = (Maximum inventory + Minimum inventory)/2 = Q/2 [12.2]


The EOQ Model

Exhibit 12.8 Cycle Inventory Pattern for the EOQ Model


The EOQ Model

Inventory Holding Cost

The cost of storing one unit in inventory for the year, Ch, is

Ch = (I)(C) [12.3]

where I = annual inventory-holding charge expressed as a percent of unit costC = unit cost of the inventory item or SKU

Annual inventory-holding cost is computed as:


[12.4]annual inventory

holding costaverageinventory

annual holdingcost per unit= ( ) = 12 QCh( )

The EOQ Model

Ordering Cost

If D = annual demand and we order Q units each time, then we place D/Q orders/year.

Annual ordering cost is computed as :

( )( ) ( )annual ordering cost = number oforders per year costper order = D Co [12.5]Q

The EOQ Model

where C0 is the cost of placing one order

Total Annual Cost

Total annual cost is the sum of the inventory holding cost plus the order or setup cost:


TC2 Q

= QCh Co1

+D

[12.6]

The EOQ Model

Economic Order Quantity

The EOQ is the order quantity that minimizes the total annual cost


Ch

Q* = 2DCo [12.7]

The EOQ Model

Calculating the Reorder Point

The reorder point, r, depends on the lead time and demand rate.

Multiply the fixed demand rate d by the length of the lead time L (making sure they are expressed in the same units, e.g., days or months):

r = Lead time demand = (demand rate)(lead time)

= (d)(L) [12.8]


The EOQ Model


Solved Problem

D = 24,000 cases per year.Co = $38 per order.I = 18 percent.C = $12.00 per case.Ch = IC = $2.16.

EOQ = 2(24,000)(38)

2.16= 919 cases rounded to a whole number.

TC =1

2Q($2.16) +

24,000

Q($38.00)

Exhibit 12.9 Excel Spreadsheet from EOQ Model Template

Safety Stock and Uncertain Demand in a Fixed Order Quantity System

When demand is uncertain, using EOQ based on the average demand will result in a high probability of a stockout.

Safety stock is additional planned on-hand inventory that acts as a buffer to reduce the risk of a stockout.

A service level is the desired probability of not having a stockout during a lead-time period.


When a normal probability distribution provides a good approximation of lead time demand, the general expression for reorder point is

r = mL + zsL [12.9]

where

mL = average demand during the lead time

sL = standard deviation of demand during the lead time

z = the number of standard deviations necessary to achieve the acceptable service level

zsL represents the amount of safety stock.


Safety Stock and Uncertain Demand in a Fixed Order Quantity System


Safety Stock and Uncertain Demand in a Fixed Order Quantity SystemWe may not know the mean and standard deviation of demand during the lead time, but only for some other length of time, t, such as a month or year. Suppose that mtand st are the mean and standard deviation of demand for some time interval t, If the distributions of demand for all time intervals are identical to and independent of each other, then

mL = mtL [12.10]

sL = st L [12.11]

Solved Problem

Southern Office Supplies, Inc. distributes laser printer paper.

Ordering costs are $45.00 per order,

One ream of paper costs $3.80,

Annual inventory-holding cost rate is 20%.

The average annual demand is 15,000 reams, or about 15,000/52 = 288.5 per week

The standard deviation of weekly demand is about 71

The lead time from the manufacturer is two weeks.

Inventory-holding cost is Ch = IC = 0.20($3.80) = $0.76 per ream per year.


The average demand during the lead time is (288.5)(2) = 577 reams,

The standard deviation of demand during the lead time is approximately 712 = 100 reams.

The EOQ model results in an order quantity of 1333, reorder point of 577, and total annual cost of $1,012.92.


Solved Problem

Desired service level of 95%, which results in a stockout of roughly once every 2 years. For a normal distribution, this corresponds to a standard normal z-value of 1.645.

r = mL + zsL = 577 = 1.645(100) = 742 reams

This policy increases the reorder point by 742 577 = 165 reams, which represents the safety stock.

The cost of the additional safety stock is Ch times the amount of safety stock, or ($0.76/ream)(165 reams) = $125.40.


Solved Problem

Excel FQS Safety Stock TemplateExhibit 12.10

Managing Fixed Period Inventory Systems

An alternative to a fixed order quantity system is a fixed period system (FPS)sometimes called a periodic review systemin which the inventory position is checked only at fixed intervals of time, T, rather than on a continuous basis.

Two principal decisions in a FPS:

1. The time interval between reviews (T), and

2. The replenishment level (M)



Economic time interval: T = Q*/D [12.12]

Optimal replenishment level without safety stock:

M = d (T + L) [12.13]

where d = average demand per time period

L = lead time in the same time units

M = demand during the lead time plusreview period


Exhibit 12.10 Summary of Fixed Period Inventory Systems

Exhibit 12.11 Operation of a Fixed Period Systems (FPS)


Uncertain Demand

Compute safety stock over the period T + L. The replenishment level is computed as:

M = mT+L + zT+L [12.14]

mT+L = mt (T + L) [12.15]

T+L = t T + L [12.16]

Chapter 12 Special Models for Inventory Management

Excel FPS Safety Stock TemplateExhibit 12.13

Single-Period Inventory Model

Applies to inventory situations in which one order is placed for a good in anticipation of a future selling season where demand is uncertain.

At the end of the period, the product has either sold out or there is a surplus of unsold items to sell for a salvage value.

Sometimes called a newsvendor problem, because newspaper sales are a typical example.


Single-Period Inventory Model

Solve using marginal economic analysis.

cs = the cost per item of overestimating demand (salvage cost); this cost represents the loss of ordering one additional item and finding that it cannot be sold.

cu = the cost per item of underestimating demand (shortage cost); this cost represents the opportunity loss of not ordering one additional item and finding that it could have been sold.

The optimal order quantity Q* must satisfy:


P (demand Q*) =cu

cu + cs[12.17]

Solved Problem

A buyer orders fashion swimwear about six months before the summer season.

Each piece costs $40 and sells for $60.

At the sale price of $30, it is expected that any remaining stock can be sold during the August sale.

The cost per item of overestimating demand is equal to the purchase cost per item minus the August sale price per item:cs = $40 $30 = $10.

The per-item cost of underestimating demand is the difference between the regular selling price per item and the purchase cost per item; that is, cu = $60 $40 = $20.


Exhibit 12.12 Probability Distribution for Single Period Model

Assume that a uniform probability distribution rangingfrom 350 to 650 items describes the demand.

Solved Problem

Solved Problem

The optimal order size Q must satisfy:

P(demand Q*) = cu /(cu + cs)

= 20/(20+10) = 2/3

Because the demand distribution is uniform, the value of Q* is two-thirds of the way from 350 to 650. This results in Q* = 550.


Excel Single Period Inventory TemplateExhibit 12.15

OM4 Ch 12

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