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Ch 12 - Inventory Management

1. Introduction (p529)
   1. Def - Inventory - any resource held to meet internal or external customer demand.
   2. Objectives - minimize total of:
      1. Item cost
      2. Order/setup cost
      3. Holding cost
      4. *Stockout cost
   3. Types of inventory (p530)
      1. Raw materials
      2. Purchased parts
      3. Work-in-process (partially completed products)
      4. Items being transported
      5. Tools, and equipment
      6. Finished goods.
   4. Functions of inventory (p530)
      1. Decoupling - when two processes cannot be synchronized, inventory can smooth fluctuations. Example, firm with high seasonal demand, produces some products in off-season.
      2. Hedge against inflation
      3. Quantity discounts
   5. Types of Demand (p531)
      1. Independent demand - typical finished product - demand from many small external independent customers. (Ch 12)
      2. Dependent demand - typical component of a finished product -demand for lawn mower wheels is dependent on demand for lawn mowers. (Ch 14 - Resource Planning)
2. Economic Order Quantity (p537)
   1. Def - EOQ - the order quantity which minimizes total ordering and holding costs.
   2. Assumptions
      1. Uniform demand
      2. Replenishment of Q units arrives as last unit is used. These assumptions imply (see Fig 12.2) Avg inventory level = Q/2
   3. Costs
      1. Annual ordering cost - preparing order, receiving shipment, placing in inventory.
         = C_o (D / Q)
             C_o - ordering cost for each order
             D - annual demand
             Q - order quantity
      2. Annual holding cost - storage, taxes, investment, insurance, obsolescence
         = C_c (Q / 2)
             C_c - holding (carrying) cost per unit per year
             Q/2 - average inventory level
   4. Fact: EOQ occurs when ordering cost = holding cost.

      

      

      Implies

      

   5. *EOQ

      

   6. See Example 12.2 - p539
              Do assigned HW - Problem 12-1.
3. Reorder Point with Variable Demand (p548)
   1. Definitions
      1. *Safety stock - extra stock carried to reduce the probability of stockout due to:
             · unexpectedly high demand during lead time and/or
             · unexpectedly long lead time.
      2. D_L - random variable denoting demand during lead time
      3. *ROP - reorder point - inventory level (point), at which order is placed
             ROP = mean(D_L) + safety stock
      4. *Service level - probability of supplying stock during lead time
             service level = Prob( D_L £ ROP )

      

   2. Example 12.6 - paint store - p549.  Determine safety stock and reorder point, if the desired service level is 95%.  Daily demand is normally distributed with a mean, µ_d, of 30 and a standard deviation, s_d, of 5.  Lead time, L, is 10 days.
      1. Mean(D_L) = µ = µ_d L = 30 * 10 = 300
              Standard deviation(D_L) = s = s_d sqrt(L) = 5 * sqrt(10) = 15.81
      2. Let SS denote safety stock and Z = ( D_L - µ ) / s.
              Then, service level = Prob( D_L £ ROP ) = Prob( Z £ SS/s )
      3. From Appendix A, p787, Z₁ = 1.65 satisfies Prob(Z £ Z₁) = 0.95
      4. Therefore, safety stock = Z₁ s = 1.65 (15.18) = 26.1 gallons
      5. ROP = mean(D_L) + safety stock = 300 + 26.1 = 326.1 gallons
                    Do assigned HW - Problem 12-33.
4. Independent-Demand Inventory Systems
   1. *Fixed-order-quantity System (Continuous Inventory System, p533)
      1. Procedure
             Establish reorder point, s_min, and order quantity, Q.
             Review inventory status with each transaction
             If inventory level, I  £  s_min
             then order Q.
      2. Advantage
             Least safety stock
      3. Disadvantages
             Requires perpetual record keeping
             Numerous independent orders
   2. *Fixed-time-period System (Periodic Inventory System, p534)
      1. Procedure
             Establish max inventory level, S_max
             Review inventory status at intervals of T
             Order   S_max - I   on each occasion.
      2. Advantage
             Consolidation of individual item orders
      3. Disadvantages
             Larger safety stock
             Possible small individual order size
   3. *Min-max system (discussed on bottom of p550)
      1. Procedure
             Review inventory status at intervals of T
             If   I  £  s_min
             then order  S_max - I.
      2. Advantage
             Less frequent orders than Fixed-time-period System
      3. Disadvantage
             Largest safety stock.
5. *ABC Analysis
   1. Procedure - p535
      1. List inventory items by decreasing value (annual dollar usage, investment, profit, . . .)
      2. Group items into classes (more specific than on page 535)
         1. Class A contains items in top 70% of value - Typically Class A contains 10-20% of inventory items
         2. Class B contains items in middle 20% of value - Typically Class B contains 20-35% of inventory items
         3. Class C contains items in bottom 10% of value.
   2. See Example 12.1 - spare parts inventory - p536
   3. Worksheet for Client ABC Analysis - click here to download my worksheet, ABCAnalysis.xls. 
   4. Typical use

   Establish:	Possible Inventory System:
   Tight control on A items	Fixed-order-quantity
   Moderate control on B items	Fixed-time-period (computerized)
   Loose control on C items	Fixed-time-period (manual)

                                                                   (This page was last edited on August 16, 2006 .)