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1 Lecture 6 Inventory Management Chapter 11

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2 Economic production quantity (EPQ) model: variant of basic EOQ model Production done in batches or lots Replenishment order not received in one lump sum unlike basic EOQ model Inventory is replenished gradually as the order is produced hence requires the production rate to be greater than the demand rate This model's variable costs are annual holding cost, and annual set-up cost (equivalent to ordering cost). For the optimal lot size, annual holding and set-up costs are equal. Economic Production Quantity (EPQ)

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3 EPQ = EOQ with Incremental Inventory Replenishment

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4 EPQ Model Assumptions Demand occurs at a constant rate of D items per year. Production capacity is p items per year. p > D Set-up cost: $C o per run. Holding cost: $C h per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Set-up time (lead time) is constant. Planned shortages are not permitted.

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5 EPQ Model Formulae Optimal production lot-size (formula of book) Run time: Q */p Time between set-ups (cycle time): Q */D years Total cost (formula of book)

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6 Example: Non-Slip Tile Co. Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tiles annually. The set-up cost is $5,000 per run Holding cost is estimated at 10% of the manufacturing cost of $1 per tile. The production capacity of the machine is 500,000 tiles per month. The factory is open 365 days per year. Determine Optimal production lot size Annual holding and setup costs Number of setups per year Loss/profit that NST is incurring annually by using their present production schedule

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7 Management Scientist Solutions Optimal TC = $28,868 Current TC =.04167(100,000) + 5,000,000,000/100,000 = $54,167 LOSS = 54, ,868 = $25,299

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8 Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production occurs periodically Production rate is constant Lead time does not vary No quantity discounts Economic Production Quantity Assumptions

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9 Too much inventory Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain Wise strategy Reduce lot sizes Reduce safety stock Operations Strategy

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10 The Balance Sheet – Dell Computer Co.

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11 Income Statement – Dell Computer Co.

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12 Debt Ratio What It Measures: The extent to which a firm uses debt financing How You Compute: The ratio of total debt to total assets

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13 Inventory Turnover Ratio What It Measures: How effectively a firm is managing its inventories. How You Compute: This ratio is computed by dividing sales by inventories Inventory turnover ratio =

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14 Lecture 6 MGMT 650 Simulation – Chapter 13

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15 Simulation Is … Simulation – very broad term methods and applications to imitate or mimic real systems, usually via computer Applies in many fields and industries Simulation models complex situations Models are simple to use and understand Models can play what if experiments Extensive software packages available ARENA, ProModel Very popular and powerful method

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16 Applications Manufacturing facility Bank operation Airport operations (passengers, security, planes, crews, baggage, overbooking) Hospital facilities (emergency room, operating room, admissions) Traffic flow in a freeway system Waiting lines - fast-food restaurant, supermarkets Emergency-response system Military

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17 Example – Simulating Machine Breakdowns The manager of a machine shop is concerned about machine breakdowns. Historical data of breakdowns over the last 100 days is as follows Simulate breakdowns for the manager for a 10-day period Number of BreakdownsFrequency

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18 Simulation Procedure Expected number of breakdowns = 1.9 per day

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19 Statistical Analysis 95 % confidence interval for mean breakdowns for the 10-day period is given by:

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20 Monte Carlo Simulation Monte Carlo method: Probabilistic simulation technique used when a process has a random component Identify a probability distribution Setup intervals of random numbers to match probability distribution Obtain the random numbers Interpret the results

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21 Example 2 – Simulating a Reorder Policy The manager of a truck dealership wants to acquire some insight into how a proposed policy for reordering trucks might affect order frequency Under the new policy, 2 trucks will be ordered every time the inventory of trucks is 5 or lower Due to proximity between the dealership and the local office, orders can be filled overnight The historical probability for daily demand is as follows Simulate a reorder policy for the dealer for the next 10 days Assume a beginning inventory of 7 trucks Demand (x)P(x)

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22 Example 2 Solutions

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23 In-class Example 3 using MS-Excel The time between mechanics requests for tools in a AAMCO facility is normally distributed with a mean of 10 minutes and a standard deviation of 1 minute. The time to fill requests is also normal with a mean of 9 minutes and a standard deviation of 1 minute. Mechanics waiting time represents a cost of $2 per minute. Servers represent a cost of $1 per minute. Simulate arrivals for the first 9 mechanic requests and determine Service time for each request Waiting time for each request Total cost in handling all requests Assume 1 server only

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24 AAMCO Solutions

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25 Simulation Models Are Beneficial Systematic approach to problem solving Increase understanding of the problem Enable what if questions Specific objectives Power of mathematics and statistics Standardized format Require users to organize

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26 Different Kinds of Simulation Static vs. Dynamic Does time have a role in the model? Continuous-change vs. Discrete-change Can the state change continuously or only at discrete points in time? Deterministic vs. Stochastic Is everything for sure or is there uncertainty? Most operational models: Dynamic, Discrete-change, Stochastic

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27 Discrete Event Simulation Example 1 - A Simple Processing System

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28 Advantages of Simulation Solves problems that are difficult or impossible to solve mathematically Flexibility to model things as they are (even if messy and complicated) Allows experimentation without risk to actual system Ability to model long-term effects Serves as training tool for decision makers

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29 Limitations of Simulation Does not produce optimum solution Model development may be difficult Computer run time may be substantial Monte Carlo simulation only applicable to random systems

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30 Fitting Probability Distributions to Existing Data Data Summary Number of Data Points= 187 Min Data Value = 3.2 Max Data Value = 12.6 Sample Mean = 6.33 Sample Std Dev = 1.51 Histogram Summary Histogram Range = 3 to 13 Number of Intervals= 13

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31 ARENA – Input Analyzer Distribution Summary Distribution:Gamma Expression:3 + GAMM(0.775, 4.29) Square Error: Chi Square Test Number of intervals= 7 Degrees of freedom = 4 Test Statistic = 4.68 Corresponding p-value= Kolmogorov-Smirnov Test Test Statistic= Corresponding p-value> 0.15 Data Summary Number of Data Points= 187 Min Data Value = 3.2 Max Data Value = 12.6 Sample Mean = 6.33 Sample Std Dev = 1.51 Histogram Summary Histogram Range = 3 to 13 Number of Intervals= 13

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32 Simulation in Industry

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33 Course Conclusions Recognize that not every tool is the best fit for every problem Pay attention to variability Forecasting Inventory management - Deliveries from suppliers Build flexibility into models Pay careful attention to technology Opportunities Improvement in service and response times Risks Costs involved Difficult to integrate Need for periodic updates Requires training Garbage in, garbage out Results and recommendations you present are only as reliable as the model and its inputs Most decisions involve tradeoffs Not a good idea to make decisions to the exclusion of known information

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