. Batch Size Q Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost **EOQ** **EOQ** Model: if there is a lead time L ROP = Reorder point L = Lead time (constant) Q = **Economic** **order** **quantity** L L ROP Time # Units on hand Q **EOQ** **Economic** **Order** **Quantity** (**EOQ**) Model **Economic** **Order** **Quantity** (**EOQ**) Model –Robust, widely used –Insensitive to errors in estimating parameters (40-20-2 Rule): 40% error in/

**Economic** **Order** **Quantity** **EOQ** Model **EOQ** Model Equations (part - 1) Equations (part - 1) Equations (part – 2) Equations (part – 2) **EOQ** Model Total Inventory cost is the minimum. Annual demand of the item is constant and known. Annual demand of the item is uniformly distributed through out the year. Lead time is zero. Total OC (P) = Total CC (R) Equations For **EOQ**, Total OC (P) = Total CC (R) Total/

constant; 5.That replenishment is made instantaneously, i.e. batch is delivered whole **Economic** **Order** **Quantity** (**EOQ**) GRAPHICAL APPROACH To calculate **EOQ** graphically, the following ingredients are necessary: -Total costs per annum (i.e. **ordering** cost plus carrying costs) -Number of **orders** required per annum (i.e. Annual DD / **Order** Qty) -Average stock (i.e. **Order** Qty / 2) Example: A company uses 50000 bottles per annum which costs N10/

DC IP Per Unit Carrying Cost: 2DC * Q = C h Percentage Carrying Cost: IP DC 2 Inputs and Outputs of the **EOQ** Model Models Input Values Output Values Annual Demand (D) **Ordering** Cost (Co) Carrying Cost (Ch) Lead Time (L) Demand Per Day (d) **Economic** **Order** **Quantity** (**EOQ**) Reorder Point (ROP) The Reorder Point (ROP) Curve ROP = (Demand per day) x (Lead time for a new/

is two weeks. What is the **economic**-**order**-**quantity**? Cost Management System Relevant **ordering** cost per purchase **order**: $209 Relevant carrying costs per package per year: Required annual ROI (15% × $15)$2.25 Relevant other costs 3.25 Total$5.50 Cost Management System = 988 packages **EOQ** = Cost Management System What are the relevant total costs (RTC)? RTC = Annual relevant **ordering** costs + Annual relevant carrying costs RTC/

demand. As an example of deterministic models, we will demonstrate in detail Model 1, the basic **EOQ** model, In this model the firm **orders** the product. The goal of the firm is to determine Q, the **Economic** **Order** **Quantity** that minimizes the firm’s total cost. Determining the **economic** **order** **quantity** uniquely determines the cycle’s length T. The determination depends on the relative cost of making an/

Chapter 6 **Economic** **Order** **Quantity** (**EOQ**) provides _____ number of units to **order**. a.Minimum b.Maximum c.Optimum d.None of the above **Economic** **Order** **Quantity** (**EOQ**) provides _____ number of units to **order**. a.Minimum b.Maximum c.Optimum d.None of the above Cost associated with **ordering** and receiving goods: a.Procurement cost b.Inventory cost c.Holding cost d.None of the above Cost associated with **ordering** and receiving/

and supply **Economic** **Order** **Quantity** (**EOQ**) A: annual demand Q: **order** **quantity** CP: **ordering** (preparation) cost per **order** CH: carrying cost per unit per year Annual inventory carrying cost= (Q/2)·CH Annual **ordering** cost= (A/Q) ·CP Total annual cost (TAC) = (A/Q)·CP + (Q/2)·CH Finding the optimal **order** **quantity** that minimizes TAC using Calculus Observation (Fig 11.4) **Economic** time between **order** (TBO) in weeks = **EOQ**/(A/52) **EOQ** Sensitivity What/

**Economic** **ORDER** QuantityEconomic REPAIR **Quantity** **Quantity** **economical** to Procure at the Reorder Point Used to provide an **economical** tradeoff between Holding Cost and Admin Procurement Cost Larger **EOQ**= Increased Holding Cost Smaller **EOQ**= Increased Admin Cost **Quantity** **economical** to Repair at the RAP Used to provide an **economical**/ ACTION POINT AMSAA 8 / 13 PROCUREMENT DECISIONS: REPAIR DECISIONS: Assets Time **Economic** **Order** **Quantity** FebMarJan BUY Reorder Point = SL + Net Leadtime Demand Applicable Assets Time /

costs gives a total cost curve that is an asymmetric ‘U’ shape with a distinct minimum ● this minimum cost shows the optimal **order** size – which is the **economic** **order** **quantity**, **EOQ**. 9.2 **ECONOMIC** **ORDER** **QUANTITY** The standard analysis of **EOQ**: The cost changes with different **order** **quantity** Worked example John Pritchard buys stationery for Penwynn Motors. The demand for printed forms is constant at 20 boxes a month. Each box/

buy in multiples of 12. Policy Code D-Fixed **Order** **Quantity** Based on **EOQ** (**Economic** **order** **quantity**) calculation. Maintained in Fixed **Order** **Quantity** Field Similar to Minimum **Order** **Quantity** Use when: –Demand is fairly steady –Cost is insignificant –Packaging or handling constraints might determine **order** size –An **EOQ** type of **order** **quantity** is required **Order** Policy D - FOQ 400 **Order** Policy D Fixed **Order** **Quantity** - Multiple 12 - FOQ 400 **Order** Policy Code F-Part Period Balancing Std. Cost MRP/

/p During production, d units are sold or used each day. (p – d) units go into inventory. Maximum inventory: Total cost: **Economic** production **quantity** (EPQ): **EOQ** vs. EPQ When to use **economic** **order** **quantity** (**EOQ**): Demand is independent Compute how much to **order** (**order** **quantity**) When to use **economic** production **quantity** (EPQ): Parts or products will be produced: demand is dependent Compute how much to make at one time (production lot size)

= hQ max /2= hQ (1- D / P )/2 Total **ordering**/setup cost = AD / Q Total production/purchasing cost = cD Total cost = AD / Q + hQ (1 - D/P )/2 + cD Unit cost = A / Q + hQ (1 - D / P )/2 D + c Costs 7 The **Economic** Production **Quantity** 8 The EPQ is equivalent to an **EOQ** model with holding cost h’=h(1-D/P). Consequently/

fees The Role of **Quantity** Discounts in Channel Coordination **Economic** literature Marketing literature Production management literature **Quantity** Discounts Price discrimination Effect on the profit Demand decreases in price Operating cost is fixed Effect on the operating costs Demand is fixed Operating cost is a function of **order** **quantities** **Quantity** discounts are effective and necessary mechanisms to achieve channel coordination Assumptions The buyer uses **EOQ** model as her/

Basic concepts. Management issues. Inventory-related costs. **Economic** **order** **quantity** model. **Quantity** discount model. **Order** timing decisions. **Order** **quantity** and reorder point interactions. Multi-item management. Multiple/**Economic** **Order** **Quantity** Model (**EOQ**) TAC=(A/Q)C P + (Q/2)C H = annual **ordering** cost + annual carrying cost. **Quantity** Discount Model TAC=(v)A + (A/Q)C P + (Q/2)C H =annual purchase cost + annual **ordering** cost + annual carrying cost Calculating the minimum-cost **order** **quantity**: 1. Calculate **EOQ**/

Sensitivity of **EOQ** Models Holding and setup costs are fairly insensitive to lot size Errors caused by restricting lot sizes to powers of 2 are minimal (no more than 6%) Powers of 2 **ordering** can facilitate sharing truck resources (one week, two weeks, four weeks…) Extensions involve non-instantaneous production (**economic** production lot model), backorders, major and minor setups, and **quantity** discounts Dynamic Lot/

cost per unit: The setup cost per unit: The production cost per unit: **Economic** **order** **quantity** Exercise Each is invited to analyze the following insights, based on the **EOQ** model (20 minutes): 1. “There is a tradeoff between lot size and inventory/ obtained by using the **economic** **order** **quantity** is $952.50, so increasing the **order** **quantity** by 10% leads a total cost increase of only $4.30. Changing the **order** **quantity** by a small amount has very little effect on the cost, because **EOQ** formula gives robust solutions./

, computer systems, supply chain and network) Strategic approach Outsourcing Globalization and virtualization Customer orientation City logistics and non- conventional applications **EOQ** simple formula (Harris, Wilson) **Economic** **order** **quantity** formula helps to find the optimal number of units which should be **ordered** or made in **order** to minimize the total inventory costs Developed in 1913 by Harris and applied in industry by Wilson Many disadvantages and several/

*Lead time) 10,000 – (900 * 8) = 2800 units Danger Level Average daily consumption x Emergency time 900 x 2 = 1800 units **Economic** **Order** **Quantity** (E.O.Q) **Economic** **Order** **Quantity** is the **quantity** which an entitle **orders** to the suppliers. This **order** **Quantity** should be **Economical**. Methods for **EOQ** calculation **Economic** **Order** **Quantity** Formula Table Graph E.O.Q 2x RU x O.C U.C x C.C% RU Annual Required units O.C/

costs Shortage costs Inventory Management Questions What should be the **order** **quantity** (Q)? When should an **order** be placed, called a reorder point (ROP)? How much safety stock (SS) should be maintained? Inventory Models **Economic** **Order** **Quantity** (**EOQ**) Special Inventory Models With **Quantity** Discounts Planned Shortages Demand Uncertainty - Safety Stocks Inventory Control Systems Continuous-Review (Q,r) Periodic-Review (**order**-up-to) Single Period Inventory Model Inventory Levels For/

: every D/Q times per year Average Variable Cost/Year: TVC = h*Q/2 +A*D/Q The **EOQ** zUse Calculus to find the value of Q that minimizes TVC(Q) zOr... The **Economic** **Order** **Quantity** h Q/2 = A D/Q Q 2 = 2 A D/h Q = SQRT(2 A D/h) CAVEAT: Make sure you use commensurate units! An Example zRaw/

OMSAN LOJİSTİK **Economic** **Order** **Quantity** ‘**EOQ**’ Inventory Planning and Management Latin America Logistics Center Logistics Management Series - **Economic** **Order** **Quantity** 1.Constant Demand Rate 2.No Constraints on Lot Size 3.Only relevant costs are holding and **ordering**/setup 4.Decisions for items are independent from other items 5.No uncertainty in lead time or supply. Assumptions **Economic** **Order** **Quantity** On-Hand Inventory (Units) Time Average Inventory Q—2Q—2/

for proper management decisions. Under certain conditions, both coincide while under other conditions they differ. 7 The **economic** cost as an opportunity cost Example: Suppose that company A undertakes the production of aluminum frames and has for/ minimum (given the total cost and the **order** **quantity**). The intersection of the carrying costs with the **ordering** costs curve is represented by the following formula. **EOQ**=[(2ad/K)] 1/2, which a= variable cost per **order** (or production setup) d= Demand (periodical/

number of final units that will be produced (usually well known) Material Requirement Planning Independent Demand for items is determined by external customers (usually forecasted) **Economic** **Order** **Quantity** (**EOQ**) models Push/Pull View of Supply Chains Procurement, Customer **Order** Manufacturing and Cycle Replenishment cycles PUSH PROCESSES PULL PROCESSES In this view processes are divided based on their timing relative to the timing of a customer/

productivity and long-term contracts d. concentrate on core competencies 3). Simple **EOQ** is: a. efficient **order** **quantity** b. a balancing of inventory carrying cost and transportation cost c. a balancing of set-up cost and inventory carrying cost d. **economic** inventory level under conditions of uncertainty 3). Simple **EOQ** is: a. efficient **order** **quantity** b. a balancing of inventory carrying cost and transportation cost c. a/

be varied between products, according to lead times PERIODIC REVIEW Insert Figure 6.1 **ECONOMIC** **ORDER** **QUANTITY** (**EOQ**) **Order** **quantities** can be: large, placed infrequently small, placed frequently **EOQ** determines the most cost effective **quantity** to **order**, based on costs of **ordering** and possession Useful in conjunction with periodic review type system PRINCIPLES OF **EOQ** Costs of acquiring a product: **ordering** administration supplier search and selection expediting inspection increase with frequency of/

OF INVENTORIES 11 E O Q 12 Optimal Inventory Level The optimal **quantity** that should be **ordered** It is the **quantity** that will minimize the total inventory costs. **Economic** **Order** **Quantity** (**EOQ**) 13 Single product line Demand rate: recurring, known, constant Lead time: constant, known No **quantity** discounts - stable unit cost No stock-outs allowed Items **ordered**/produced in a lot or batch Batch received all at once Holding/

-50 % Elements of Inventory Carrying Costs Transportation/Logistic Strategy **Order** **Quantity** Cost of **Ordering** Cost of Carrying Inventory Total Cost $ (With Constant **Ordering** Costs) Zero Inventory JIT **Economic** **Order** **Quantity** Transportation/Logistic Strategy Total Cost = OC + CC OC = **Order** Placement Cost = A(R/Q) CC = Inventory Carrying Cost = 1/2(QVW) Where: Q = Optimal **Order** **Quantity** (**EOQ**) A = Cost of placing an **order** R = Annual Rate of use V = Value per unit/

Copyright 2013 John Wiley & Sons, Inc. Chapter 7: Supplement B The **Economic** **Order** **Quantity** 7B-2 The **Economic** **Order** **Quantity** Model (**EOQ**) **EOQ** model applier to items that are: –Replenished in batches or **orders** –Not produced and delivered instantaneously Only two costs are considered: 1.Carrying costs 2.**Ordering** costs Will decide 1.When to **order** 2.How many to **order** 7B-3 Assumptions 1.Constant rate of demand 2.Shortages not allowed/

awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors. Standard: With at least 80% accuracy: 1.Describe the concept of **economic** **order** **quantity** 2.Identify the key variables in the **EOQ** calculation © Dale R. Geiger 20113 Batch **Quantity** Concepts © Dale R. Geiger 20114 Batch Cost Assumptions Annual demand for units produced in batches is known Every batch is the same size i/

Lecture 6 Inventory Management Chapter 11 **Economic** Production **Quantity** (EPQ) **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 models variable costs are annual holding cost, and annual/

C c I max Total Cost ( ) = Cost Related to No. **Orders** ( ) Cost Related to Inventory Size ( ) + Spreadsheet Models for Managers: Session 11 11/12 Copyright © 1994-2011 Richard Brenner **Economic** **order** **quantity** **EOQ**: Lowest-cost **order** **quantity** for constant demand It can be shown mathematically that **EOQ** is the value of Q for which **Ordering** Costs = Carrying Costs. Readings: **Economic** **Order** **Quantity** 2DC 0 √ CcCc Spreadsheet Models for Managers: Session 11 11/

**Economic** **Order** **quantity** opgave 21-15 Tijn van der Zant How to calculate **EOQ** **EOQ** = √(2DP/C) Where: –D = Demand in units for a period –P = Relevant **ordering** costs per purchase **order** –C = Relevant carrying costs of 1 unit in stock for the same period used/costs (TRC) Total annual relevant cost (TRC) = DP/Q+QC/2 Where Q = **quantity** and in this example I assume it’s the same as **EOQ** (though that’s not necessary Calculate total **ordering** and carrying costs using **EOQ** DP/Q+QC/2 = 12000*120/1200+1200*2/2 = 12000 * 1/10 /

costs Shortage costs Inventory Management Questions What should be the **order** **quantity** (Q)? When should an **order** be placed, called a reorder point (ROP)? How much safety stock (SS) should be maintained? Inventory Models **Economic** **Order** **Quantity** (**EOQ**) Special Inventory Models With **Quantity** Discounts Planned Shortages Demand Uncertainty - Safety Stocks Inventory Control Systems Continuous-Review (Q,r) Periodic-Review (**order**-up-to) Single Period Inventory Model Inventory Levels For/

000 台（每週 250 台，一年 52 週） ＝ Carrying Cost ＝每台每年＄ 5.2 (Q/2)*$5.2 ＝ **Ordering** Cost 每訂購一次成本＄ 200 D/Q*$200 **EOQ** ＝ ＝ 1,000 台 Deliveries ＝ 13,000 台 /1,000 台 ＝ 13 次 **Order** Point ＝ Lead Time ( 250 台 × 2 週 ) ＝ 500 台 + Shortage Costs+ Quality CostsQuality Costs Purchasing Cost Payoff T. **EOQ** 2015/6/2816 經濟訂購量 (**EOQ**) : 採購存貨會發生訂購成本 (**Ordering** Cost) ，進貨之後會 發生持有成本 (Carrying Cost) ，考慮公司銷量、前置時 間後所計算出來可讓兩種成本之和最低之每次訂購量 每次訂購量 成本 訂購成本 持有成本 **EOQ** **Economic** **Order** **Quantity** 0 總成本 Back 2015/6/2817 Shortage Cost vs. Safety Stock 一週二週三週四週五週 250/

the actual arrival of goods Reorder level This is the time when we should place an **order** by taking into consideration the interval between placing the **order** and receiving the supply. **Economic** **Order** **Quantity**(**EOQ**) **EOQ** is that size of **order** which minimizes total annual cost of carrying inventory and the cost of **ordering** under the assumed conditions of certainty and that annual demands are known Inventory models Deterministic/

) cost Unit purchasing (Production) cost Holding (Carrying) cost Shortage (Penalty) cost Revenue (Selling price) Basic **EOQ** Model **EOQ**: **Economic** **Order** **Quantity** Assumptions of **EOQ** models: –Demand is constant (unvarying ), expressed as annual demand (units per year ). –Models use continuous review, not periodic review. –Lead time is constant & known. –**Quantity** discounts are not possible. –2 variable costs: setup cost and holding cost. Inventory Levels Inventory vs. time. Inventory/

per unit is Rs. 2 & it costs Rs. 36 to place an **order** and to process the delivery. The inventory carrying cost is estimated at 9% of average inventory investment. Determine (i) **Economic** **order** **quantity**. (ii) Optimum no. of **orders** placed per annum. (iii) Minimum total cost of inventory per annum. Sol : (i) **EOQ** ( Q*)= √ 2DCo / C p. I = √ 2. 10,000. 36 / 2. 0.09/

T HE MOT AND V ENTURE B USINESS Prof. Takao Ito, Doctor of **Economics**, PH.D. of Engineering, Graduate School of Engineering, Hiroshima University Thursday, October 16, 2014 T /**EOQ**) C h is the holding cost per unit. It is also called carrying costs. Q is the **order** **quantity** **Order** cost (Co) is derived from the number of **orders** placed (D/Q - demand p.a. divided by **order** **quantity**) multiplied by the cost of placing an **order**. Co……**ordering** cost D…… demand per year Q …… **order** **quantity** Total cost=Holding cost + **Order**/

Numbers Definition Time Between **Orders** (P)= Q / D Where :P = Time (in same period considered for demand) Q = **Order** **Quantity** (often, **Economic** **Order** **Quantity**) D = Demand (Annual, Monthly, Weekly, Daily) e.g. If D is daily demand, time between **orders** would be in days./ done on an annual or quarterly basis. The second approach (Perpetual System) uses an **order** **quantity** (such as **EOQ**) and annual demand to determine the time between **orders**. C ALCULATIONS IN A P ERIOD S YSTEM 9 Calculations in a Periodic System MBTN/

Cost of Stock outs Cost Trade off **Ordering** vs Holding **Economic** **Order** **Quantity** Assumptions Constant demand Lead time in known Instantaneous receipt of inventory Constant purchase cost No stock out Holding cost and **ordering** cost are constant **EOQ** Equation Reorder Point ROP = d x LT **Ordering** Cost = Holding Cost Holding Cost = (Q/2)C h **Ordering** Cost = (D/Q) C o **Quantity** Discounts Holding cost is dependent upon purchase/

handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors Standard: With at least 80% accuracy: Describe the concept of **economic** **order** **quantity** Identify the key variables in the **EOQ** calculation © 20113 Batch **Quantity** Concepts © 20114 Batch Cost Assumptions Annual demand for units produced in batches is known Every batch is the same size i.e. same/

**ECONOMIC** **ORDER** **QUANTITY** Unni Krishnan Pillai - 16 Meaning: **Economic** **order** **quantity** is the level of inventory that minimizes the total inventory holding costs and **ordering** costs. It is one of the oldest classical production scheduling models. The framework used to determine this **order** **quantity** is also known as Wilson **EOQ** Model or Wilson Formula. Overview **EOQ** only applies where the demand for a product is constant over the year and that each/

and the frequency and size of additions to that stock, how many rockets ought Hezbollah fire off each day? The Standard **EOQ** Cost Function The **Economic** **Order** **Quantity** (**EOQ**) Modifications to Cost Function Demand (D) adjusted for casualty rate z of rockets at launch. **Order** Cost (c) adjusted for proportion n of shipments intercepted. Holding Cost (h) adjusted for daily casualty rate s of rockets in/

, and taxes. Shortage cost Potential disruption in Lost sales, lost production schedules goodwill Overstock cost Adverse changes in prices, obsolescence, pilferage **Economic** **Order** **Quantity**: (1) Direct relationship between carrying cost and **order** size. (2) Inverse relationship between **ordering** cost and **order** size. (3) **Economic** **order** **quantity** (**EOQ**) is the **order** size, which will minimize the total inventory cost and is determined at the point where the carrying cost curve and the/

in inventory, warehousing costs, shrinkage, deterioration, obsolescence, etc. backorder cost - cost of alienating customers THREE BASIC DECISIONS When to review? When to **order**? How much to **order**? Continuous Reorder point Fixed **EOQ** (**Economic** **order** **quantity**) Continuous review (Q,R) Periodic At review time Variable **Order**-up-to Periodic review (T, TI) 4 Policy Simple Continuous Review Continuous Review (Q,R) Policy in a deterministic system with no/

Sizing Techniques Lot-for Lot **EOQ**/EPQ Periodic **Order** **Quantity** Fixed Interval, Variable **Quantity** **EOQ**/Avg Use Fixed **Order** **Quantity** Variable Interval, Fixed **Quantity** Standard Package **Quantities** Price Break Levels **EOQ** Quality How would you define ‘/Manufacture Fluid Decision Revisit at Regular Intervals As **Economic** Conditions Change As Internal Conditions Change Always Maintain Internal Capability Reasons to Make **Quantities** Too Small Quality Too Critical Timing Too Critical /

the cut-out fabrics Buttons, which will be sewed on the blouses. Procurement Logistics Example Contd – Determine **Economic** **Order** **Quantity** (**EOQ**) (Carrying) Costs of -Transport -Storage -Cost of tied capital Total Costs Purchasing Price Costs **Quantity** **Economic** **Order** **Quantity** Example (Contd…): Optimal **Order** **Quantity** for the Fabrics ParametersPart **Order** (In Rs.’0000s)Total **Order** (In Rs.’0000s) Purchase Price 2.502.40 Transport Costs 0.250.20 Storage Costs 0.100.25/

**EOQ** History –Interest on capital tied up in wages, material and overhead sets a maximum limit to the **quantity** of parts which can be profitably manufactured at one time; “set-up” costs on the job fix the minimum. Experience has shown one manager a way to determine the **economical**/’t want to tie up too much precious capital in inventory. Question: how many racks should MedEquip **order** at once? **EOQ** Modeling Assumptions 1. Production is instantaneous – there is no capacity constraint and the entire lot is produced/

1 INVENTORY MODELS Outline Deterministic models –The **Economic** **Order** **Quantity** (**EOQ**) model –Sensitivity analysis –A price-break Model Probabilistic Inventory models –Single-period inventory models –A fixed **order** **quantity** model –A fixed time period model 2 / Trade-off Given costs of overestimating/underestimating demand and the probabilities of various demand sizes how many units will be **ordered**? 7 Consider an **order** **quantity** Q Let P = probability of selling all the Q units = probability (demand Q) Then, (1-/

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