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OPSM 301 Spring 2012 Class 13: Inventory Management

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Presentation on theme: "OPSM 301 Spring 2012 Class 13: Inventory Management"— Presentation transcript:

1 OPSM 301 Spring 2012 Class 13: Inventory Management

2 Inventory “The stock of any item or resource used in an organization”
“All the money that the system has invested in purchasing things it intends to sell” Inventory is the stock of any item or resource used in an organization. An inventory system is the set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. By convention, manufacturing inventory generally refers to materials entities that contribute to or become part of a firm's product output. Manufacturing inventory is typically classified into raw materials, finished products, component parts, supplies, and work in process. In services, inventory generally refers to the tangible goods to be sold and the supplies necessary to administer the service.

3 Types of Inventories Inputs - Raw Materials
Processes - Work-in-Process Outputs - Finished Goods

4 Definition of Inventory
Inventory: the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process Manufacturing inventory: refers to items that contribute to or become part of a firm’s product Inventory system: the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be 3

5 The Material Flow Cycle
Cycle time 95% 5% Input Wait for Wait to Move Wait in queue Setup Run Output inspection be moved time for operator time time

6 Flow time T = Inventory I / Throughput R
Chapter 6 Operational Flows Throughput R Inventory I Notes: FLOW TIME T I = R T Flow time T = Inventory I / Throughput R

7 Why do Buffers Build? Why hold Inventory?
Chapter 6 Why do Buffers Build? Why hold Inventory? Economies of scale Fixed costs associated with batches Quantity discounts Trade Promotions Uncertainty Information Uncertainty Supply/demand uncertainty Seasonal Variability Strategic Flooding, availability Cycle/Batch stock Notes: Safety stock Seasonal stock Strategic stock Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

8 Why do we need Inventory?
Variability (uncertainty) Demand Capacity availability Materials and lead times Processing times Time Delivery lead time, production lead time Economies of Scale Purchasing, production

9 Functions Provided by Inventories
Purpose /Reason Type Cost Transportation Pipeline Transportation Costs Economies in Setups Cycle Stocks Setup/Order Costs Seasonality in Demand Seasonal Stock Smoothing Costs Uncertainty in Demand Safety Stock Shortage/Stock-out Costs Economies in Purchase Cycle Stocks Price Discounts Inflation and/or Price Fluctuations Speculative Stock Costs due to Price

10 Inventory Costs The following costs affect the inventory size:
Ordering Cost Receiving and inspection Transportation Setup (or production change) costs Costs for arranging specific equipment setups etc. Holding (Carrying) Cost Cost of money Insurance Taxes Shrinkage, spoilage, obsolescence Stock-out (Shortage) Cost Lost sales, customers etc. Emergency shipment costs

11 Economies of Scale: Inventory Management for a Retailer
The South Face retail shop in Vermont has observed a stable monthly demand for its line of Gore-Tex jackets on the order of 100 jackets per month. The retail shop incurs a fixed cost of $2,000 every time it places an order to the California warehouse for stock replenishment. The marginal cost of a jacket is $200, and South Face’s cost of capital is approximately 25%. What order size would you recommend for The South Face? retailer warehouse

12 Parameters EOQ Model R (or D) demand rate (units per year)
C unit production cost, not counting setup or inventory costs (dollars per unit) S fixed or setup cost to place an order (dollars) H holding cost (dollars per year); if the holding cost is consists entirely of interest on money tied up in inventory, then H = iC where i is an annual interest rate. Q the unknown size of the order or lot size

13 Inventory Usage Over Time
Inventory Level Average Inventory (Q*/2) Minimum inventory Order quantity = Q (maximum inventory level) Usage Rate

14 Total Annual Cost Total Annual Cost = Annual Purchasing Cost Ordering Holding + Using calculus, we can take the derivative of the total cost function and set the derivative (slope) equal to zero We can also use economic intuition

15 Find most economical order quantity: Spreadsheet for The South Face
Number of units per order/batch Number of batches per year Annual Setup Cost Annual Holding cots Total Cost Q R/Q SR/Q hQ/2 50 24 48000 1250 49250 100 12 24000 2500 26500 150 8 16000 3750 19750 200 6 12000 5000 17000 250 5 9600 6250 15850 300 4 8000 7500 15500 310 7742 7750 15492 320 350 3 6857 8750 15607 400 6000 10000 450 5333 11250 16583 500 2 4800 12500 17300 550 4364 13750 18114 600 4000 15000 19000 650 3692 16250 19942 700 3429 17500 20929 750 3200 18750 21950 800 3000 20000 23000 850 1 2824 21250 24074 900 2667 22500 25167 950 2526 23750 26276 1000 2400 25000 27400 1050 2286 26250 28536 1100 2182 27500 29682

16 Accurate Response to Scale Economies: Economic Order Quantity EOQ
Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost Order Size Q Fixed cost per order The order quantity that minimizes total supply chain cost is: Annual unit demand Annual unit holding cost J.A. Van Mieghem/Operations/Supply Chain Mgt Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

17 Optimal Economies of Scale: For a South Face retailer
R = 100 units/ month = 1200 units/year C = $ 200 / unit r = 0.25/year S = $ 2,000 / order Unit annual holding cost = H = 0.25/yr x $200 = $50/yr Optimal order quantity = Q = sqrt(2 x 1200 x 2000/50) = 309.8 Number of orders per year = R/Q =3.87 Time between orders = Q/R = 0.25yr =13 weeks Annual order cost = (R/Q)S = $/year Average inventory I = Q/2 = 154.9 Annual holding cost = (Q/2)H = $/year Average flow time T = I/R = 0.12 yr = 6.7 weeks J.A. Van Mieghem/Operations/Supply Chain Mgt Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

18 An EOQ Example Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units
Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units

19 Expected number of orders
An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity D Q* N = = 5 orders per year 1,000 200

20 Expected time between orders Number of working days per year
An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year = T = Expected time between orders Number of working days per year N T = = 50 days between orders 250 5

21 An EOQ Example Determine optimal number of needles to order
D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = S H D Q 2 TC = ($10) ($.50) 1,000 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100

22 Learning Objectives: Batching & Economies of Scale
Increasing batch size Q of order (or production) increases average inventories (and thus flow times). Average inventory for a batch size of Q is Q/2. The optimal batch size minimizes supply chain costs by trading off setup cost and holding cost and is given by the EOQ formula. To reduce batch size, one must reduce setup cost (time). Economies of scale are manifested by the square-root relationship between QEOQ and (R, S): If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4. J.A. Van Mieghem/Operations/Supply Chain Mgt Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

23 Role of Leadtime L: South Face cont.
The lead time from when a South Face retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order? Inventory Profile: Two key decisions in inventory management are: How much to order? When to order? Inventory Q -R Time t J.A. Van Mieghem/Operations/Supply Chain Mgt Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

24 Continuous Review Policy: Ordering Decisions and the Re-order Point
ROP L -R Place order n I(t) Q time Receive order n+1 order n+2 Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

25 ROP and Inventory position
ROP = L × R But if lead time L is greater than time between orders, there will be more than one order outstanding Inventory position = Inventory level (On-hand inventory) + On-order inventory Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

26 Determine the economic order quantity and the reorder point
EOQ Example Annual Demand = 1,000 units Days per year considered in average daily demand = 250 Cost to place an order = $10 Holding cost per unit per year = $0.50 Lead time = 7 days Cost per unit = $15 Determine the economic order quantity and the reorder point

27 Number of working days in a year
Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days d = D Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units

28 Economic Order Quantity (EOQ) Model
Robust, widely used Insensitive to errors in estimating parameters ( Rule): 40% error in one of the parameters 20% error in Q < 2% of total cost penalty

29 An EOQ Example Management underestimated demand by 50%
D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days 1,500 units TC = S H D Q 2 TC = ($10) ($.50) = $75 + $50 = $125 1,500 200 2 Total annual cost increases by only 25%

30 An EOQ Example Actual EOQ for new demand is 244.9 units
D = 1,000 units Q* = units S = $10 per order H = $.50 per unit per year 1,500 units TC = S H D Q 2 Only 2% less than the total cost of $125 when the order quantity was 200 TC = ($10) ($.50) 1,500 244.9 2 TC = $ $61.24 = $122.48


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