2. 1 Material Management Class Note # 3-A ( In review ) ~ Inventory control, analysis, and management ~ Prof. Yuan-Shyi Peter Chiu Feb. 2011

3. 2 § I1 :Types of Inventories § I1 : Types of Inventories (A) Raw Materials (B) Components (C) Work in process (D) Finished goods ◇ § I2 : Inventory Relevant Costs (A) Holding Cost (B) Order Cost (C) Penalty Cost (D) Outdate Cost

4. 3 § I3 : Motivation for Holding Inventories 1. Economies of Scale 2. Uncertainties ． Excess demand 3. Speculation 4. Transportation 5. Smoothing 6. Logistics ． safety stock ． minimum purchasing quantity 7. Control Costs ． record keeping & ． management costs ◇

5. 4 § I4 : Characteristics of Inventory System (A) Demand ． Constant versus Variable ． Known versus Random (B) Lead Time ． Zero, Constant, Variable, Random (C) Review Time ． Continuous, Periodic (D) Excess Demand ． Backordered, Lost (E) Ordering Policy. (r,Q), (s,S), etc. (F) Issuing Policy. FIFO, LIFO, etc. (G) Changing Inventory ． Shelf life (expired), obsolete ◇

6. 5 § I5: EOQ(Economic Order Quantity) K : setup (ordering) cost (per cycle) c : unit cost (per item) h : holding cost ( per item per year ) λ: demand per unit time (eg. year ) Q T I(t) t where T = Q / λ (cycle length) ◇

7. 6 § I5.3 : EOQ EOQ model : Balances order cost and holding cost The basic model: 1. The demand rate is known and is constant λ items per unit time 2. Shortages are not permitted 3. No order lead time 4. Costs include ◆ setup (ordering) cost K per order ◆ holding cost h per item held per unit time ◆ unit cost c per item ordered.◇

8. 7 § I6 : Sensitivity How cost increases if not using Q* recall [Eq.5.2] Drop λC for now if we use Q rather than Q*, then

9. 8 § I6 : Sensitivity

10. 9 § I7 : Order Lead Time : τ To order “τ” time in advance. or to consider a reorder point (I.e. level of inventory = “R”) (A) For τ < T 4 month R =1040 Q * =3870 t I(t) T = 1.24 year ◇

11. 10 Let τ = 4 months = 0.3333 year R = λτ = 3120 （ 0.3333) = 1040 (B) When τ > T (1) From the ratio τ / T (2) Consider only the fractional remainder (f - r) of the ratio. Convert this (f - r) back to year. (3) use R = λ * τ (f-r) § I7 : Order Lead Time : τ ◇

12. 11 § I8 : Finite Production Rate (E.P.Q.) P : production rate (per unit time) λ: demand rate (per unit time) P > λ

13. 12 § I8 : Finite Production Rate..[Eq.8.1] …….[Eq.8.2] ………...[Eq.8.3]

14. 13 A local company produces a programmable EPROM for several industrial clients. It has experienced a relatively flat demand of 2,500 units per year for the product. The EPROM is produced at a rate of 10,000 units per year. The accounting department has estimated that it costs $50 to initiate a production run, each unit cost the company $2 to manufacture, and the cost of holding is based on a 30 % annual interest rate. Determine the optimal size of a production run, the length of each production run, and the average annual cost of holding and setup. What is the maximum level of the on-hand inventory of the EPROMs? [Eg. 8.1]

15. 14 λ = 2500 / year P = 10,000 /year K = $50 / setup c = $ 2 / unit i = 30% Solution to [Eg.8.1] : ～ Finite Production Rate ～ Use [Eq.9.3]

16. 15 Use [Eq.9.2] setup cost / year holding cost / year Solution to [Eg.8.1] : ～ Finite Production Rate ～

17. 16 §. I 8.1: Class Problems Discussion Chapter 4 : ( # 12 ) p.201 ( # 19 ) p.204 ( # 33 ) p.224 The End