Inventory Control Models

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Inventory Control Models
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Objectives

• Understand the importance of inventory control
  and ABC analysis.
• Use the economic order quantity (EOQ) to
  determine how much to order.
• Compute the reorder point (ROP) in determining
  when to order more inventory.
• Handle inventory problems that allow quantity
  discounts or noninstantaneous receipt.
• Understand the use of safety stock with known and
  unknown stockout costs.

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Introduction

• Inventory is any stored resource that is used to
  satisfy a current or future need.
• Stockout occurs when the inventory level is lower
  than customer demand.
• Cost minimization is the major factor in
  obtaining this delicate balance.
• Ex. Raw material, work in process and
  finished goods

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Inventory Planning and Control system
Planning on what Inventory to Stock And How
to Acquire It
Forecasting Parts/Product Demand
Controlling Inventory Levels
Feedback Measurements To Revise Plans and
Forecasts
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Importance of Inventory Control

• The decoupling function
• To decouple manufacturing processes
• Storing resources
• Resources can be stored in work-in-process
• Irregular supply and demand
• Quantity discounts
• purchasing in larger quantities, lower the cost
  of
• products
• Avoiding stockouts and shortages

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Inventory Decisions

• There are only two fundamental decisions for
  controlling inventory
• How much to order
• When to order
• The major objective is to minimize total
  inventory costs.

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Inventory costs

• Cost of the items (purchase cost or material
  cost)
• Cost of ordering the time to process the
  paperwork, pay the bill and so forth does not
  depend on the number of units ordered.
• Cost of carrying, or holding inventory varies as
  the size of the inventory varies.
• Cost of stockouts indicates the lost sales and
  goodwill

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Ordering Costs

• Developing and sending purchase orders
• Processing and inspecting incoming inventory
• Bill paying
• Inventory inquiries
• Utilities, phone bills, etc., - purchasing
  department.
• Salaries/wages - purchasing department employees
• Supplies (e.g., forms and paper) - purchasing
  department

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Carrying Costs

• Cost of capital
• Taxes
• Insurance
• Spoilage
• Theft
• Obsolescence
• Salaries/wages - warehouse employees
• Utilities/building costs - warehouse
• Supplies (e.g., forms, paper) - warehouse

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Inventory Usage Over Time
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Costs as Functions of Order Quantity
Total Cost
Carry Cost
Minimum Cost
Order Cost
Optimal Quantity
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Steps in Finding the Optimum Inventory

• Develop an expression for the ordering cost.
• Develop an expression for the carrying cost.
• Set the ordering cost equal to the carrying cost.
• Solve this equation for the optimum desired.

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Economic Order Quantity (EOQ)

• This is one of the oldest and most commonly known
  inventory control techniques.
• This technique will help us to determine how much
  to order

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Assumptions for EOQ

• Demand is known and constant
• The lead time is known and constant
• The receipt of inventory is instantaneous
• Quantity discounts are not possible
• The only variable costs are ordering cost and
  holding or carrying cost
• Orders are placed so that stockouts or shortages
  are avoided completely

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Developing the EOQ

• Annual ordering cost
• Annual holding or carrying cost
• Total inventory cost

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EOQ
0
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Inputs and Outputs of the EOQ Model
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The Reorder Point (ROP) Curve
ROP (Demand per day) x (Lead time for a new
order, in days) d x L
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• Ex. Ross whites machine shop uses 2,500 brackets
  during the course of a year, and this usage is
  relatively constant throughout the year. These
  brackets are purchased from a supplier 100 miles
  away for 15 each, and lead time is 2 days. The
  holding cost per bracket per year is 1.5 (or 10
  of the unit cost) and the ordering cost per order
  is 18.75. There are 250 working day per year.

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Questions

• What is the EOQ?
• Given the EOQ, what is the average inventory?
  What is the annual inventory holding cost?
• In minimizing cost, how many orders would be made
  each year? What would be the annual ordering
  cost?
• What is the time between orders?
• What is the ROP?

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The production run model

• inventory continuously flows or builds up over a
  period of the time after an order has been placed
  or when units are produced and sold
  simultaneously.
• This model is especially suited to the production
  environment.
• Setup cost the cost of setting up the production
  facility to manufacture the desired product.

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Inventory Control and the Production Process
Production Portion of Cycle
Maximum Inventory Level
Inventory Level
Demand Portion of Cycle
Demand Portion of Cycle
Time
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Production Quantity EOQ

• Annual Carrying Cost
• Annual Ordering Cost
• Setup Cost
• Ordering Costs

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Production Quantity EOQ
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Example

• Brown manufacturing
• Brown manufacturing produces commercial
  refrigeration units in batches. The firms
  estimated demand for the year is 10,000 units. It
  costs about 100 to set up the manufacturing
  process, and the carrying cost is about 50 cents
  per unit per year. When the production process
  has been set up, 80 refrigeration units can be
  manufactured daily. The demand during the
  production period has traditionally been 60 units
  each day. Brown operates its refrigeration unit
  production area 167 days per year. How many
  refrigeration units should Brown Manufacturing
  produce in each batch? How long should the
  production part of the cycle last?

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Quantity Discount Models
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Quantity Discount Steps

• 1. Calculate Q for each discount
• 2. Adjust Q upward if quantity is too low for
  discount
• 3. Compute total cost for each discount
• 4. Select Q with the the lowest total cost

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The Use of Safety Stock
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The Use of Safety Stock

• Known stockout costs
• Given probability of demand, find total cost for
  each safety stock alternative
• Unknown stockout costs
• Set service level use normal distribution

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Service Level versus Carrying Costs
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Summary of ABC Analysis

• Group A Items - Critical
• Group B Items - Important
• Group C Items - Not That Important

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ABC Inventory Analysis
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ABC Inventory Policies

• Greater expenditure on supplier development for A
  items than for B items or C items
• Tighter physical control on A items than on B
  items or on C items
• Greater expenditure on forecasting A items than
  on B items or on C items