INVENTORY MANAGEMENT

Transcription

1 INVENTORY MANAGEMENT Professor Robert Saltzman Operations Analysis Inventory What is it? Idle goods, waiting to be used or sold Inventory can take many forms: Finished Goods: Food, clothes, cars, electronics, Unfinished Goods: Raw materials, parts, WIP, Do banks have any? Items with Independent demand: Focus of current chapter Dependent demand: See MRP chapter

2 Why Hold Inventory? It takes time to make & deliver stuff Better customer service & selection Protection against: High product demand, High prices Shortage of parts, Unreliable suppliers Labor strike, Inefficient workers Take advantage of quantity discounts Achieve economies of scale Why Study Inventory? Most businesses holds some Are there businesses that don t hold any? May represent 20-30% of company assets EX: AA holds $500 Million+ in spare parts Holding costs = 20-50% of inventory s value Managing it better could save a lot of money Plays a big role in US economy Current inventory = about 20% of GDP

3 Holding Inventory Isn t Free Inventory Costs include things such as: Lost opportunity costs (tied up capital) Losses due to breakage & theft Losses due to spoilage & obsolescence Warehousing costs, e.g., rent, operating costs, insurance, taxes on building, Material handling costs, e.g., equipment, power, labor, supervision, 2 Key Inventory Decisions How you monitor Continuous Review (event-triggered) Periodic Review (fixed-period) 1. When to order or produce? Whenever stocks fall to Reorder Point R* At the end of each period (e.g., month) 2. How much to order (produce)? Order a fixed amount Q* each cycle Order a variable amount each period

4 Inventory Costs P = Unit Price (if purchasing), or Unit Cost (if producing) S = Order cost (if purchasing), or Setup cost (if producing) Order Costs: Postage/phone/fax, shipping & handling, inspection, accounting, labor Setup Costs: Adjust equipment, changeover time, cleaning costs, hiring & training, labor H =Holding cost per item per unit of time H is sometimes expressed as a % of P Other Inventory Symbols D = Demand rate: items/year, month or week d = Daily demand rate: items/day Q = Order Quantity (each time you order) R = ROP = Reorder Point (triggers an order) Be consistent with units: Don t mix $ and cents Don t mix years and months

5 Basic Example Camera Store sells a certain type of film P = $3/package (unit cost) S = $30/order (overnight delivery) H = $0.25/package/month ( film spoils!) D = 200 packages/month (average demand) No backorders allowed How Much & When To Order? Order 6 or 7 packages every day? Order 2,400 packages once per year? Happy medium between these 2 extremes: Order once per month (we ll see why soon)

6 The EOQ Model Q* = EOQ = Economic Order Quantity R* = Optimal Reorder Point Due to Ford W. Harris (1913) Main Assumptions: 1. Constant demand rate D 2. Continuous Review: Monitor inventory all the time 3. Entire order arrives together 4. Lead time L = 0 days: Order arrives immediately 5. Unit price P is constant for all Q: No quantity discounts EOQ Model: Inventory vs. Time Inv. months

7 EOQ: How to find best Q? Q* is found by minimizing total costs per unit time, e.g., $/month, in this example Monthly Purchasing Costs = DP Monthly Ordering Costs = (D/Q)S, or (DS)Q -1 Monthly Holding Costs = (Q/2)H, or (H/2)Q Total Costs = Purchasing + Ordering + Holding: TC(Q) = DP + (DS)Q -1 + (H/2)Q Q is the only variable; D, P, S, H are given data Find Q* using calculus Set the derivative dtc/dq = 0 and solve for Q: TC(Q) = DP + (DS)Q -1 + (H/2)Q dtc/dq = 0 1(DS)Q -2 + (H/2) = 0 So, H/2 = (DS)Q -2 So, Q 2 (H/2) = DS So, Q 2 = 2DS/H Thus, Q* = 2DS / H In film example: Q* =

8 Notes about EOQ Model If the lead time L is 0 days, then R* = 0 packages Optimal policy can be stated simply as: Order Q* whenever inventory falls to R* Q* does not depend on the unit price P (unless quantity discounts are offered) T* = Cycle Length = Time between orders = Q*/D At Q*, ordering costs = holding costs: DS/Q* = HQ*/2 What if Lead Time L > 0? Not difficult to deal with, e.g., suppose L = 3 days Essentially, just order 3 days earlier in the cycle R* = dl = Demand that occurs during L Remember, d = daily demand Here, (200/month)(1 month/30 days) = 6.67 packages/day R* = dl = (6.67 pkgs./day)(3 days) = 20 packages So, order Q* whenever inventory falls to 20 pkgs.