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Inventory Control

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Inventory Control

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**Inventory Control is everywhere.**

Fuel for the Car Milk to Drink Milk to Sell MotherBoards to Assemble Computers Production with Setups Inventory Control is everywhere. Fuel for the Car Milk to Drink Milk to Sell MotherBoards to Assemble Computers

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**Some youtube videos http://es.youtube.com/watch?v=qkZQxXJuqKo**

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Why we do store? Unplanned shocks (labor strikes, natural disasters, surges in demand, etc.) To maintain independence of supply chain Economies of production Improve customer service Economies of purchasing Transportation savings Hedge against future Why we do store? Unplanned shocks (labor strikes, natural disasters, surges in demand, etc.) To maintain independence of supply chain Economies of production Improve customer service Economies of purchasing Transportation savings Hedge against future

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**Costs Related with Inventory Control**

Inventory deteriorates, becomes obsolete, lost, stolen, etc. Order processing Shipping Handling Carrying Costs Capital (opportunity) costs Inventory risk costs Space costs Inventory service costs Out-of- Stock Costs Lost sales cost Back-order cost Complacency Why should not we store? Non-value added costs Opportunity cost Inventory deteriorates, becomes obsolete, lost, stolen, etc. Order processing Shipping Handling Carrying Costs Capital (opportunity) costs Inventory risk costs Space costs Inventory service costs Out-of- Stock Costs Lost sales cost Back-order cost Complacency

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**Nature of Inventory: Adding Value through Inventory**

Speed location of inventory has gigantic effect on speed Cost direct: purchasing, delivery, manufacturing indirect: holding, stockout. Quality inventory can be a “buffer” against poor quality; conversely, low inventory levels may force high quality Flexibility location, level of anticipatory inventory both have effects Nature of Inventory: Adding Value through Inventory Speed - location of inventory has gigantic effect on speed Cost - direct: purchasing, delivery, manufacturing indirect: holding, stockout. Quality - inventory can be a “buffer” against poor quality; conversely, low inventory levels may force high quality Flexibility - location, level of anticipatory inventory both have effects

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**Nature of Inventory:Functional Roles of Inventory**

Transit Buffer Seasonal Decoupling Speculative Lot Sizing or Cycle Mistakes Promotional

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**Logistics Costs Categoría de Coste Costes Totales % sobre Ventas**

% Costes Logísticos Transporte 636 5,4% (5.9%) 62,7% Almacenamiento 82 0,7% (0.8%) 8,1% Costes de Inventarios 250 2,1% (3%) 24,6% Administración 47 0,4% (0.4%) 4,6% Total 1015 8,6% (10.1%) 100% Source: 16th Annual State of Logistics Report, 2004 (Entre parentesis los datos del 2001)

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**http://www. loanational**

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**Costes Logísticos como**

Sectores diferentes tienen diferentes perfiles de coste Pero además la logística además también impacta en: Otros costes en la Cadena de suministro como los de fabricación materia prima o gestión de clientes. La cantidad de capital en el negocio. Y una elevada proporción del riesgo global del negocio. Costes Logísticos como Porcentaje de ventas 20% Aerospacial Maquinaría Automovil 15% Comida&Bebida Electronica Sanidad Químicas 10% Gas y Petrol Distribución Banca 5% 0% Source: ILT, McKinsey, LCP Consulting analysis

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Visión general

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**Which are the main factors**

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**Main Factors defining an Inventory Policy**

Demand Average Forecasted Demand Error on Forecasted Demand Setup Cost Time Storage Capacity Expiration Lead Time Lead Time (LT) Basic Period Period of Forecasting Horizon Finite and Infinite Horizon Finite or Infinite Production Rate

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EOQ Formula

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**Why to do it with Formulae what has always been done by head?**

Reduce Cost Number of Different units Time to do Added Value tasks Computer Aid Management Why to do with Formulae what has always been done by head? Reduce Cost Number of Different units Time to do Added Value tasks

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**Assumptions to derive the EOQ formula**

Production is Instantaneous. Delivery is inmediate Demand is deterministic Demand is constant over time A production run incurs a fixed setup cost Products can be analyzed individually

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**Inventory Order Cycle Demand rate Time Lead time Order placed**

Order receipt Inventory Level Reorder point, R Order quantity, Q

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**EOQ Cost Model Co - cost of placing order D - annual demand**

Cc - annual per-unit carrying cost Q - order quantity Annual ordering cost = CoD Q Annual carrying cost = CcQ 2 Total cost =

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**EOQ Cost Model TC = + CoD Q CcQ 2 = + Q2 Cc TC Q 0 = + C0D Qopt =**

= Q2 Cc TC Q 0 = C0D Qopt = 2CoD Deriving Qopt Proving equality of costs at optimal point = CoD Q CcQ 2 Q2 = 2CoD Cc Qopt =

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**EOQ Cost Model (cont.) Annual cost ($) Total Cost Slope = 0 CcQ 2**

Order Quantity, Q Annual cost ($) Total Cost Ordering Cost = CoD Q Slope = 0 Minimum total cost Optimal order Qopt Carrying Cost = CcQ 2

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**EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Qopt = 2CoD**

2(150)(10,000) (0.75) Qopt = 2,000 yards TCmin = CoD Q CcQ 2 TCmin = (150)(10,000) 2,000 (0.75)(2,000) TCmin = $750 + $750 = $1,500 Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days

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**Required Data to generate a Policy**

Time Forecast Period Horizon Lead Time Demand for a given Period (average and Standard Deviation) Demand during Horizon Cost holding Cost (€ per unit per year) =K·Cu Unit Cost (€ per unit) Setup Cost S (€) Total Cost =Holding Cost + Setup Cost Service Level (max % of runouts that we are willing to afford)

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Policies

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**Reorder Point: if stock<ROP then Buy(Q)**

ROP=Level of inventory at which a new order is placed ROP= Maximun demand that we want to serve during Lead Time Average Demand during Lead Time Standard deviation of demand Safety Stock (ss) Q: Quantity that minimizes Total Cost R = dL+ss where d = demand rate per period L = lead time

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**Safety Stocks. Basic Concepts**

buffer added to on hand inventory during lead time Stockout an inventory shortage Service level probability that the inventory available during lead time will meet demand

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**Variable Demand with a Reorder Point**

point, R Q LT Time Inventory level

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**Reorder Point with a Safety Stock**

point, R Q LT Time Inventory level Safety Stock

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**Reorder Point With Variable Demand**

R = dL + zd L where d = average daily demand L = lead time d = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zd L = safety stock

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**Reorder Point for a Service Level**

Probability of meeting demand during lead time = service level a stockout R Safety stock dL Demand zd L

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**Reorder Point for Variable Demand**

The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 yards per day L = 10 days d = 5 yards per day For a 95% service level, z = 1.65 R = dL + z d L = 30(10) + (1.65)(5)( 10) = yards Safety stock = z d L = (1.65)(5)( 10) = 26.1 yards

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**Periodic Review Policies: if time then Buy(OUL-Stock)**

OUL: Max Demand we cover during next Review Period + Lead Time Time Review Period that minimizes Total Cost Economic Order Period (T*) Power of Two Policies

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**Order Quantity for a Periodic Inventory System**

Q = d(tb + L) + zd tb + L - I where d = average demand rate tb = the fixed time between orders L = lead time sd = standard deviation of demand zd tb + L = safety stock I = inventory level

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**Fixed-Period Model with Variable Demand**

d = 6 bottles per day sd = 1.2 bottles tb = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) Q = d(tb + L) + zd tb + L - I = (6)(60 + 5) + (1.65)(1.2) = bottles

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**Problem If the supplier has a lead time of 20 days?**

A toy manufacturer uses aproximately silicon chips annually. The Chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is 60 cents per chip and ordering cost is 24$. A year has 288 days. How muchh should we order each time? How many times per year are we to order? What is the length of an order cycle. What is the total cost? If the supplier has a lead time of 20 days? Which is the reorder point? Should do we have a safety stock? To prevent what?

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Problem Determine optimal number to order D = 1,000 units S = $10 per order H = $.50 per unit per year The pack has 150 units each Management underestimated demand by 50% C = $5/unit There is a discount of 5% per unit if you buy more than 500 units

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Problem A company substitutes in a regular way a component of a given machine to ensure quality parameters of the product. Machine works during the whole year and needs 40 parts per week. The component supplier offers a price of 10 € per unit for orders with less than 300 units, and a price of 9.70 € per unit for bigger orders. The cost of setting each order is stimated on 25 €, and the holding cost is of 0.26 €/ €/ year. How many units should you request each time? If the supplier wants you to make orders bigger than 500 units ¿which is maximum unit price that should stablish for orders bigger than 500 units?

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Karbonicas JuPe Karbonicas JuPe is a company bottling drinks where you work. To simplify we are to consider only one product. Our company has a warehouse where store product just manufactured and from where we serve the three logistics platforms that our client holds. The logistics platforms are cross-dock warehouses, where storing products has a high cost, and from where there associated retail stores are served. The lead time at the manufacturing side for Karbonicas JuPe is 7 days (i.e. it takes one week from we have been asked to produce until the product is ready at the warehouse. Each of the logistics platforms faces a demand (measured in pallets) that might be approximated by a normal distribution. (Data can be found at Table I). Each logistic platform knows the demand and the stock levels of each associated retail store. It takes two (2) days since the platform asks for products until the product reaches each retail store through the logistic platform. The inventory system is Reorder Point at each echelon. (i.e. the platforms work with ROP logic to the central warehouse of Karbonicas JuPe, and the central warehouse works with ROP to the manufacturing facility). The relation between the logistic platform and the retail stores is not considere in this problem. You are considering the posibility of eliminate the central warehouse echelon. To do that the three logistics platforms should agree a joint review period (considering all the costs) with a power-of-two policy. The factory consolidates the three orders (that have been done simultaneously) and will bottle them together. From the factory docks and without passing through the central warehouse the product will be sent directly to each logistic platform. Key questions are: how much does it cost now, how much will it cost the new system.

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**Karbonicas JuPe (ctnd)**

Data

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Chapter 12 Inventory Management.

To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Chapter 12 Inventory Management.

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