Inventory Control Models

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Inventory Control Models

• Chapter 6

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Types of Inventory
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Uses of Inventory

• As a buffer to decouple
• suppliers and users,
• manufacturers and customers,
• two workstations in a workshop.

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Costs Related to Inventory

• Carrying (holding) cost
• Ordering cost
• Stockout cost
• Purchase (material) cost

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Carrying Cost

• Includes
• Capital cost
• Opportunity costs,
• Storage space rental, and labor and facilities
  for storage,
• Cost of obsolescence and damage,
• Insurance.
• Varies with the amount of inventory.

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Ordering Cost

• Includes
• Shipping and handling cost,
• Cost of processing orders, such as forms, papers,
  labor.
• Typically, this cost varies with number of
  orders, not with number of units in an order.

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Stockout Cost

• Includes
• Lost profit,
• Expediting and back ordering expenses,
• Cost of reputation and goodwill

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Inventory Profile
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Average Inventory

• Inventory level changes everyday.
• Average inventory is often used to measure
  inventory level
• Average daily inventory level

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Some Basic Calculations (1 of 2)

• Dannual demand in units
• Coordering cost per order
• Chcarrying cost per unit per year
• Qorder quantity number of units in an order.
• Number of orders required in a year

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Some Basic Calculations (2 of 2)

• Total annual holding cost
• Total annual ordering cost
• Total annual inventory cost

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Economic Order Quantity (EOQ)

• EOQ is the order quantity at which the total
  annual cost (annual holding cost annual
  ordering cost) is minimized.

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EOQ Total Costs

• Total annual costs
• annual ordering costs annual holding costs

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Formula for EOQ

• Let Q be Economical Order Quantity (EOQ)

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Simco Pump Example (p.197)

• Annual demand 1,000 units
• Ordering cost 10 / order
• Annual holding cost 0.5 / unit
• What is the best order quantity?

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Simco Pump Example (p.197)

• With order quantity Q200 units,
• (a) How many orders would be made annually?
• (b) What is the total annual ordering cost?
• (c) What is the average daily inventory?
• (d) What is total annual holding cost?
• (e) What is the total annual inventory cost?

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Simco Pump Example (p.197)

• We have found the EOQ is 200 units per order,
  and the associated total annual inventory cost is
  100.
• If the company orders 250 units each time, what
  is total inventory cost then?
• If the company orders 100 units each time, what
  is total inventory cost then?

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Purchase Cost, C

• Purchase cost, C, of inventory items is not in
  the EOQ formula, since the order quantity Q does
  not affect the annual purchase cost, D?C. That
  is, C is not relevant in determining the order
  quantity.
• Sometime, unit carrying cost is a percent, I, of
  the purchase cost of the item, i.e., ChIC.

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Reorder Point

• Reorder point is in terms of number of units on
  hand, at which an order should be placed.
• Reorder point must be at least the demand during
  the lead time (delivery time).

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Safety Stock

• Safety stock is the extra stock to help in
  avoiding stockout, when there exist uncertainties
  in demand and lead time.

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Safety Stock and Uncertainties
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Formula for Reorder Point

• Reorder Point
• d?L SS
• where
• d average daily demand in units
• L lead time in days
• SS safety stock in units

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Example (p.201 extended)

• Procomps annual demand is 8,000 units. There are
  200 work days per year. So, daily demand is 40
  units.
• Lead time 3 days
• Safety stock 20 units
• What is the reorder point (ROP)?

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How Does EOQ Work in Inventory Control?

• For each item k, calculate its economic order
  quantity Qk and its reorder point ROPk.
• Keep watching the inventory on hand. If the
  stock of item k drops to ROPk, order Qk units of
  item k.

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EOQ Assumptions (p.193)

• Demand rate is constant.
• The ordered units are delivered in a single
  shipment (instantaneous).
• No quantity discount is available
• All demand is satisfied (no shortages)

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EOQ without Instantaneous Receipt Assumption
(p.201)

• The ordered units arrive piece by piece.
• Application example
• A company's finished good inventory that is
  supplied by its production department.
• It is called Production Run Model
• The best order quantity is called Optimal
  Production Quantity (OPQ).

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OPQ Formula

• d daily demand in units,
• p daily production capacity in units,
• Cs setup cost (similar to Co)
• D and Ch are defined same as before,
• then

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Meaning of Q in OPQ

• Q here is still the order quantity (number of
  units in an order), but the order is issued to
  the production department of the same company.
• Therefore, Q can also be understood as the
  production batch size.

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Formulas in Production Run Model

• Maximum Inventory Level
• Average Inventory Level

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Formulas in Production Run Model

• Total annual ordering cost
• (same as for EOQ)
• Total annual holding cost
• Total annual inventory cost

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Example of Brown Manuf. (p.203)

• Annual demand 10,000 units
• Setup (ordering) cost 100/order
• Carrying cost 0.50/unit/year
• Daily production rate 80 units
• Daily demand rate 60 units.
• Once a unit is finished, it is counted into the
  inventory.

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To Find EOQ under Quantity Discount (p.206 209)

• Trial-and-error method in general
• May develop a spreadsheet that calculate the
  total cost for each possible order quantity.
  Then, pick up the order quantity with the lowest
  total cost. (See class demonstration)

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