Economic Order Quantity and Economic Production Quantity Models for Inventory Management

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1 Economic Order Quantity and Economic Production Quantity Models for Inventory Management Inventory control is concerned with minimizing the total cost of inventory. In the U.K. the term often used is stock control. The three main factors in inventory control decision making process are: The cost of holding the stock (e.g., based on the interest rate). The cost of placing an order (e.g., for row material stocks) or the set-up cost of production. The cost of shortage, i.e., what is lost if the stock is insufficient to meet all demand. The third element is the most difficult to measure and is often handled by establishing a "service level" policy, e. g, certain percentage of demand will be met from stock without delay. The ABC Classification The ABC classification system is to grouping items according to annual sales volume, in an attempt to identify the small number of items that will account for most of the sales volume and that are the most important ones to control for effective inventory management. Reorder Point: The inventory level R in which an order is placed where R = D.L, D = demand rate (demand rate period (day, week, etc), and L = lead time. Safety Stock: Remaining inventory between the times that an order is placed and when new stock is received. If there are not enough inventories then a shortage may occur. Safety stock is a hedge against running out of inventory. It is an extra inventory to take care on unexpected events. It is often called buffer stock. The absence of inventory is called a shortage.

2 Quantity Discount Model Calculation Steps: Compute EOQ for each quantity discount price. Is computed EOQ in the discount range? If not, use lowest cost quantity in the discount range. Compute Total Cost for EOQ or lowest cost quantity in discount range. Select quantity with the lowest Total Cost, including the cost of the items purchased. The following This JavaScript compute the optimal values for the decision variables based on currently available information about the above factors. Enter the needed information, and then click the Calculate button. In entering your data to move from cell to cell in the datamatrix use the Tab key not arrow or enter keys. MENU: 1. The Classical Model 2. Shortages Permitted Model 3. Production and Consumption Model 4. Production and Consumption with Shortages Model 5. EOQ with Shortages and Lead Time 6. The ABC Classification 7. Inventory Control with Uncertain Demand The Classical Model Demand rate: x 5000 Ordering cost: C

3 Optimal Ordering Is: Q* Optimal Cycle Is: T* Number of Orders Is: n* Total Cost Is: TC Shortages Permitted Model Demand rate: x Ordering cost: C Shortage cost: C 3 0 Backorder cost: C 4 2 Optimal Ordering Is: Q* Optimal Shortage Is: S* Total Cost Is: TC Shortage Period Is: T 2 Period per Cycle Is: T Production and Consumption Model

4 Production rate: K 600 Demand rate: x Set-up cost: C Optimal Run Size Is: Q* Production Cycle Is: T 1 * Optimal Cycle Is: T* Cost per Cycle Is: TC Production and Consumption with Shortages Model Production rate: K 6000 Demand rate: x 600 Setup cost: C Backorder cost: C 4 2 Optimal Production Is: q* Optimal Inventory Is: Q* Optimal Shortage Is: P* Total Cost Is: TC Period per Cycle Is: T

5 EOQ with Shortages and Lead Time I: Base Economic Order Quantity Total Demand 500 Ordering Cost 15 Holding Cost/unit/year 20 Unit Price 250 EOQ Average Periodic Ordering Intervals Total Number of Orders Total Cost II: EOQ with Shortages and Lead Time Estimated Lead Time in Days 15 Shortage Cost/unit/year 5 EOQ Level for Reorder Point Maximum Inventory Level Total Cost Longest Delay Time in Days

6 For Technical Details, Back to: Decision Making in Economics and Finance Kindly your comments to: Professor Hossein Arsham Decision Tools in Economics & Finance Europe Mirror Site MENU Statistics Europe Mirror Site ABC Inventory Classification Autoregressive Time Series Beta and Covariance Computations Bivariate Discrete Distributions Break-Even Analysis and Forecasting Categorized Probabilistic, and Statistical Tools Detecting Trend & Autocrrelation Determination of the Outliers Forecasting by Smoothing Inventory Control Models Linear Optimization Solvers to Download Linear Optimization with Sensitivity Maths of Money: Compound Interest Analysis Matrix Algebra, and Markov Chains Mean, and Variance Estimations Measuring Forecast Accuracy Other Polynomial Regressions Optimal Age for Replacement Parametric System of Linear Equations Performance Measures for Portfolios Plot of a Time Series Predictions by Regression Proportion Estimation Quadratic Regression Regression Modeling Seasonal Index Single-period Inventory Analysis Summarize Your Data System of Equations, and Matrix Inversion Test for Random Fluctuations Test for Seasonality Test for Stationary Time Series Time Series' Statistics Probabilistic Modeling Europe Mirror Site Analysis of Covariance ANOVA for Condensed Data Sets ANOVA for Dependent Populations ANOVA: Testing the Means Bayesian Statistical Inference Bivariate Sampling Statistics Chi-square Test for Relationship Compatibility of Multi-Counts Confidence Intervals for Two Populations Descriptive Statistics Determination of the Outliers Empirical Distribution Function Equality of Multi-variances Estimations With Confidence Goodness-of-Fit for Discrete Variables Identical Populations Testing Index Numbers with Applications K-S Test for Equality of Two Populations Lilliefors Test for Exponentially Multiple Regressions Percentage: Estimation & Testing Paired Proportion Test Polynomial Regressions Pooling Means, and Variances P-values for the Popular Distributions Quadratic Regression Sample Size Determination Revising the Mean and the Variance Scattered Diagram and the Outliers Simple Linear Regression Subjective Assessment of Estimates Subjectivity in Hypothesis Testing Test for Several Correlation Coefficients Test for Homogeneity of a Population Test for Normality Test for Uniform Distribution Testing Poisson Process Test for Randomness

7 Bayesian Inference for the Mean Bayes' Revised Probability Bivariate Discrete Distributions Comparing Two Random Variables Decision Making Under Uncertainty Determination of Utility Function Making Risky Decisions Measure the Quality of Your Decision Multinomial Distributions Two-Person Zero-Sum Games Testing Several Proportions Testing the Mean Testing the Medians Testing the Correlation Coefficient Testing Two Populations Testing the Variance The Before-and-After Test The Other Means Two-Way ANOVA Test Two-Way ANOVA with Replications

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