FOOD PURCHASING & INVENTORY ISQA 458/558 MELLIE PULLMAN 1

FOOD PURCHASING & INVENTORY ISQA 458/558MELLIE PULLMAN

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DIFFERENCES BETWEEN FOOD & OTHER CONSUMER GOODS

Issue Food Consumer Goods

Pricing (what chain member pays producer)

Seasonality

Weather Influence

Perishability

Disease/Contamination

Inventory Models

Quantity Discounts

JIT

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Rules to manage inventory, specifically:

timing (when to order or purchase)

sizing (how much to order or purchase)

PURCHASING INVENTORY SYSTEMS

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THE AVAILABLE ANALYTICAL MODELS

Continuous Review or Fixed-Order Quantity Models (Q)Event triggered (Reach a certain level of inventory)Quantity DiscountsFood Types?

Periodic Review or Fixed-Time Period Models (P)Time triggered (Weekly sales call)Food Types?

Single Period ( excess inventory for that period loses value after the period passes)

Food Types ?

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Periodic Review

Fixed order intervals

Variable order sizes

Convenient to administer

Inventory position only required at review

Continuous ReviewVarying order intervalsFixed order sizes (Q)Allows individual review frequenciesPossible quantity discountsLower, less-expensive safety stocks

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COMPARISON OF PERIODIC AND CONTINUOUS REVIEW SYSTEMS

PURCHASING & INVENTORY COSTS

• Holding (or carrying) costs ($/unit)• Setup (ordering, transportation)

costs• Shortage costs• Spoilage costs• Others?

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INVENTORY COSTS

• C = Unit cost or production cost: cost for each unit purchased or produced.

• (i.e., average cost to buy a pound of lobster)

• H = Holding costs: cost of keeping items in inventory (both storage and capital costs)

• ( cost to hold a lobster along with opportunity cost)

•S = Purchasing or ordering costs: a fixed cost incurred every time you buy an order

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TOTAL COSTS OF CARRYING INVENTORY

Assumptionsdemand is constant and uniform throughout the period for your products (20,000 lobsters per month)

Price per unit is constant for the period ($2.50/loster)Inventory holding cost is based on an average cost.

Total Inventory Cost annually= purchase cost + order cost + holding cost

annual purchase cost = annual demand * Cost/item

annual order cost = annual # orders * Cost to order

annual holding cost = average units held*cost to carry one unit

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WHAT

HAPP

ENS IF

HE

DECID

ES

TO P

LACE

MORE ORDER

S BUT

KEEP

THE S

AME OVER

ALL

QUANTITY

?

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10Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Cost Minimization Goal

Ordering Costs

HoldingCosts

QOPT

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

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HQ

SQ

DCDTC

2*

D = yearly demand of unitsC = cost of each unitQ = quantity orderedS = cost to place orderH = average yearly holding cost for each unit = storage+interest*CD/Q = number of orders per yearQ/2 = average inventory held during a given period assuming with start with Q and drop to zero before next order arrives (cycle inventory).

Total Inventory Cost Equation

DERIVING THE EOQ :ECONOMIC ORDER QUANTITY (Q)

Setting the total holding cost equal to the total setup cost and determining Q:

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Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = EOQQ

QUANTITY DISCOUNTS (COMMON WITH FOOD)Pet Food demand = 1,200 cases per year

Holding cost = $10 per unit per year

Order cost = $30 per order

Cost = $35 per case if < 90 cases; $32.50 per case if > 90

EOQ & Total annual cost ?

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8510$

30$12002

xxEOQ

53.848,42$1200*35$30)$85

1200()10($

2

85TC

BUT IF WE GO UP TO ORDER SIZE OF 90, WE GET A PRICE BREAK. CALCULATE TOTAL COST

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?1200*50.32$30)$90

1200()10($

2

90TC

APPROACH FOR QUANTITY DISCOUNTS

1. Calculate the EOQ. If you can purchase that quantity at the lowest prices then you are all set; that is the lowest total order cost

2. Otherwise, compare the total cost at each price break above the EOQ to see if you can find a better overall cost.

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EOQ MODEL--BASIC FIXED-ORDER QUANTITY MODEL (Q)

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R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

THE REORDER POINT

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Reorder point = (average period demand)*Lead Time periods= d * L

ANOTHER EOQ EXAMPLE (SAY PET FOOD)

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Annual Demand = 1,000 casesDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per case per year = $2.50Lead time = 7 daysCost per unit = $15

Determine the economic order quantity & reorder point.

VARIATIONS IN LEAD TIME

If we have variations in lead time or demand, how should we change the reorder point so we rarely run out?

Reorder Point = Average demand during lead time(d*L) + safety stock (Z* L)

where: d = average daily (or weekly) demandL = Lead time (matching days or weeks)L = standard deviation of demand during lead time. D = standard deviation of demand (days or weeks).

LDL

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SERVICE LEVEL OR % OF TIME INVENTORY WILL MEET DEMAND DURING LEAD TIME

Z Value Resulting Service Level

1.28 90%

1.65 95%

2.33 99%

3.08 99.9%

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EXAMPLE

Annual Demand = 1000 units

250 work days in the yeard=1000/250 = 4 units/day

Q= 200 unitsL=9 days L = 3 units

z=2 (97.7% likelihood that we won’t run out during lead time)

Reorder point= d*L +z*L = (4*9) + (2*3) = 42 units

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P METHOD (PERIODIC REVIEW)

You have a predetermined time (P) between orders

(sales rep comes by every 10 days) or the average time between orders from EOQ is Q/D (Q=100 orders; D =1200 orders per year so P=Q/D = 1/12 year or every month.

How much should you order to bring inventory level up to some predetermined level, R?

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P METHOD (PERIODIC REVIEW)

R = restocking level

Current Inventory position = IP

Order Quantity= R-IP

How do we determine R?

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RESTOCKING LEVEL

Needs to meet most demand situations

R= Restocking level = Average demand during lead time & review period+ safety stock= P+L + z* P+Lwhere:

P+L = average demand during lead time and review period z = # of standard dev from mean above the average demand (higher z is lower probability of running out).

RP+L = standard deviation of demand during lead time + review period

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SINGLE PERIOD INVENTORYHOW MUCH TO ORDER WHEN THE ITEM LOSES VALUE AFTER A CERTAIN PERIOD

SHORTAGE COST

Value of item if demanded – item cost

EXCESS COST

Item cost +disposal cost - salvage cost

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Goal is to determine a stocking level that strikes the best balance of these 2 costs1.Determine the target service level (SLT) that balances shortage & excess2.Use that level to determine the target stocking point (TS) for the item.

TARGET SERVICE LEVEL (SLT)

Expected Shortage cost = expected excess cost

(1-p) C shortage = p C excess

Where:

p = probability that there are enough units to meet demand

(1-p) = probability that there is a shortage

C shortage = shortage cost

C excess = excess cost

Note: when these two costs are equal; p becomes the target service level or

26excessshortage

shortageT CC

CSL

EXAMPLE: SALAD

Jeff needs to determine how much salad to make for the deli counter each day (if it does not sell; it is tossed out)

Costs to make a pound of salad: $2.50 but makes $10/pound if sold.

C shortage= Revenue per pound - cost per pound= $10-$2.50 = $7.50

C excess = cost per pound = $2.50

SLT= C shortage /(C shortage + C shortage )= .75 or 75%

Jeff should make enough salad to meet demand 75% of time.

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STOCKING POINT

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-4 -3 -2 -1 0 1 2 3 4

Number of Standard Deviations above or below the mean

To meet the demand 75% of the time, we need to know the meanAnd standard deviation of demand.Mean is 422 gallons; standard deviation is 67 gallons (M-F) What part of the curve would that represent?

Mean=422

Standard dev= 67

FROM A CUMULATIVE NORMAL TABLE (WHERE 50% IS A THE MEAN + THIS Z VALUE)

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z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0

0.00000.004

00.008

00.012

00.016

00.019

90.023

90.027

90.031

90.035

90.1

0.03980.043

80.047

80.051

70.055

70.059

60.063

60.067

50.071

40.075

30.2

0.07930.083

20.087

10.091

00.094

80.098

70.102

60.106

40.110

30.114

10.3

0.11790.121

70.125

50.129

30.133

10.136

80.140

60.144

30.148

00.151

70.4

0.15540.159

10.162

80.166

40.170

00.173

60.177

20.180

80.184

40.187

90.5

0.19150.195

00.198

50.201

90.205

40.208

80.212

30.215

70.219

00.222

40.6

0.22570.229

10.232

40.235

70.238

90.242

20.245

40.248

60.251

70.254

90.7

0.25800.261

10.264

20.267

30.270

40.273

40.276

40.279

40.282

30.285

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Jeff should prepare: mean + Z* std dev = 422 + .68 (67)467.56 pounds of salad

FOR ONE PERIOD MODEL

• Need historical data for the period that you are considering to create the mean and standard deviation

• demand for days, weeks or months. If your period is only 1 week, you many need to consider different targets for different seasons (holiday periods, etc.)

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