1. FOOD PURCHASING & INVENTORY ISQA 458/558 MELLIE PULLMAN 1

2. DIFFERENCES BETWEEN FOOD & OTHER CONSUMER GOODS IssueFoodConsumer Goods Pricing (what chain member pays producer) Seasonality Weather Influence Perishability Disease/Contamination Inventory Models Quantity Discounts JIT 2

3. Rules to manage inventory, specifically:  timing (when to order or purchase)  sizing (how much to order or purchase) PURCHASING INVENTORY SYSTEMS 3

4. THE AVAILABLE ANALYTICAL MODELS Continuous Review or Fixed-Order Quantity Models (Q)  Event triggered (Reach a certain level of inventory)  Quantity Discounts  Food 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 ? 4

5. Periodic Review Fixed order intervals Variable order sizes Convenient to administer Inventory position only required at review Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks 5 COMPARISON OF PERIODIC AND CONTINUOUS REVIEW SYSTEMS

6. PURCHASING & INVENTORY COSTS Holding (or carrying) costs ($/unit) Setup (ordering, transportation) costs Shortage costs Spoilage costs Others? 6

7. 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 7

8. TOTAL COSTS OF CARRYING INVENTORY Assumptions  demand 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 8

9. WHAT HAPPENS IF HE DECIDES TO PLACE MORE ORDERS BUT KEEP THE SAME OVERALL QUANTITY? 9

10. 10

11. 11 D = yearly demand of units C = cost of each unit Q = quantity ordered S = cost to place order H = average yearly holding cost for each unit = storage+interest*C D/Q = number of orders per year Q/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

12. DERIVING THE EOQ : ECONOMIC ORDER QUANTITY (Q) Setting the total holding cost equal to the total setup cost and determining Q: 12

13. 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 EOQ & Total annual cost ? 13

14. BUT IF WE GO UP TO ORDER SIZE OF 90, WE GET A PRICE BREAK. CALCULATE TOTAL COST 14

15. 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. 15

16. EOQ MODEL--BASIC FIXED-ORDER QUANTITY MODEL (Q) 16 R = Reorder point Q = Economic order quantity L = Lead time L L QQQ R Time Number of units on hand

17. THE REORDER POINT 17 Reorder point = (average period demand)*Lead Time periods =d * L

18. ANOTHER EOQ EXAMPLE (SAY PET FOOD) 18 Annual Demand = 1,000 cases Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per case per year = $2.50 Lead time = 7 days Cost per unit = $15 Determine the economic order quantity & reorder point.

19. 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) demand L = Lead time (matching days or weeks)  L = standard deviation of demand during lead time.  D = standard deviation of demand (days or weeks). 19

20. SERVICE LEVEL OR % OF TIME INVENTORY WILL MEET DEMAND DURING LEAD TIME Z ValueResulting Service Level 1.2890% 1.6595% 2.3399% 3.0899.9% 20

21. EXAMPLE Annual Demand = 1000 units 250 work days in the year d=1000/250 = 4 units/day Q= 200 units L=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 21

22. 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? 22

23. P METHOD (PERIODIC REVIEW) R = restocking level Current Inventory position = IP Order Quantity= R-IP How do we determine R? 23

24. RESTOCKING LEVEL Needs to meet most demand situations R= Restocking level = Average demand during lead time & review period+ safety stock =  P+L + z*  P+L where:  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 24

25. SINGLE PERIOD INVENTORY HOW 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 25 Goal is to determine a stocking level that strikes the best balance of these 2 costs 1.Determine the target service level (SL T ) that balances shortage & excess 2.Use that level to determine the target stocking point (TS) for the item.

26. TARGET SERVICE LEVEL (SL T ) 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 26

27. 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 SL T = C shortage /(C shortage + C shortage )=.75 or 75% Jeff should make enough salad to meet demand 75% of time. 27

28. STOCKING POINT 28 To meet the demand 75% of the time, we need to know the mean And 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

29. FROM A CUMULATIVE NORMAL TABLE (WHERE 50% IS A THE MEAN + THIS Z VALUE) 29 z0.000.010.020.030.040.050.060.070.080.09 0.00.00000.00400.00800.01200.01600.01990.02390.02790.03190.0359 0.10.03980.04380.04780.05170.05570.05960.06360.06750.07140.0753 0.20.07930.08320.08710.09100.09480.09870.10260.10640.11030.1141 0.30.11790.12170.12550.12930.13310.13680.14060.14430.14800.1517 0.40.15540.15910.16280.16640.17000.17360.17720.18080.18440.1879 0.50.19150.19500.19850.20190.20540.20880.21230.21570.21900.2224 0.60.22570.22910.23240.23570.23890.24220.24540.24860.25170.2549 0.70.25800.26110.26420.26730.27040.27340.27640.27940.28230.2852 Jeff should prepare: mean + Z* std dev = 422 +.68 (67) 467.56 pounds of salad

30. 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.) 30