food purchasing & inventory isqa 458/558 mellie pullman 1
TRANSCRIPT
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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