Food Purchasing & Inventory ISQA 458/558 Mellie Pullman

1. Food Purchasing & Inventory ISQA 458/558Mellie Pullman

2. Differences Between Food & other consumer goods

3. Purchasing Inventory Systems • Rules to manage inventory, specifically: • timing (when to order or purchase) • sizing (how much to order or purchase)

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 ?

5. Comparison of Periodic and Continuous Review Systems Continuous Review • Varying order intervals • Fixed order sizes (Q) • Allows individual review frequencies • Possible quantity discounts • Lower, less-expensive safety stocks Periodic Review • Fixed order intervals • Variable order sizes • Convenient to administer • Inventory position only required at review

6. Purchasing & Inventory Costs • Holding (or carrying) costs ($/unit) • Setup (ordering, transportation) costs • Shortage costs • Spoilage costs • Others?

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

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

9. What happens if he decides to place more orders but keep the same overall quantity?

11. Total Inventory Cost Equation 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).

12. Deriving the EOQ :Economic Order Quantity (Q) • Setting the total holding cost equal to the total setup cost and determining Q:

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 cases; $32.50 per case if > 90 • EOQ & Total annual cost ?

14. But if we go up to order size of 90, we get a price break. Calculate total cost

15. Approach for Quantity Discounts • 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 • Otherwise, compare the total cost at each price break above the EOQ to see if you can find a better overall cost.

16. Number of units on hand Q Q Q R L L Time R = Reorder point Q = Economic order quantity L = Lead time EOQ Model--Basic Fixed-Order Quantity Model (Q)

17. The Reorder Point Reorder point = (average period demand)*Lead Time periods = d * L

18. Another EOQ Example (say pet food) 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* sL) • where: d = average daily (or weekly) demandL = Lead time (matching days or weeks)sL = standard deviation of demand during lead time. sD = standard deviation of demand (days or weeks).

20. Service Level or % of time inventory will meet demand during lead time

21. Example • Annual Demand = 1000 units • 250 work days in the yeard=1000/250 = 4 units/day • Q= 200 unitsL=9 days sL = 3 units • z=2 (97.7% likelihood that we won’t run out during lead time)Reorder point= d*L +z*sL= (4*9) + (2*3) = 42 units

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?

23. P Method (periodic review) • R = restocking level • Current Inventory position = IP • Order Quantity= R-IP • How do we determine R?

24. Restocking Level • Needs to meet most demand situations • R= Restocking level = Average demand during lead time & review period+ safety stock= mP+L + z* sP+Lwhere:mP+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). sRP+L= standard deviation of demand during lead time + review period

25. Single period inventoryHow much to order when the item loses value after a certain period Shortage cost Excess cost Item cost +disposal cost - salvage cost • Value of item if demanded – item cost Goal is to determine a stocking level that strikes the best balance of these 2 costs Determine the target service level (SLT) that balances shortage & excess Use that level to determine the target stocking point (TS) for the item.

26. 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

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

28. Stocking point Standard dev= 67 Mean=422 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?

29. From a cumulative normal table (where 50% is a the mean + this Z value) 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.)