Inventory Models

Inventory models Help to decide Help to decide How much to order How much to order When to order When to order Basic EOQ model Basic EOQ model POQ model POQ model

Basic EOQ model Assumptions Assumptions Known and constant demand Known and constant demand Known and constant lead time Known and constant lead time Instantaneous receipt of material Instantaneous receipt of material No quantity discounts No quantity discounts Only order (setup) cost and holding cost Only order (setup) cost and holding cost No stockouts No stockouts

Basic EOQ model Receive an order Receive an order Use the inventory at a constant rate Use the inventory at a constant rate Reorder same amount Reorder same amount Instantaneously receive the order Instantaneously receive the order

Economic Order Quantity On-hand inventory (units) Time

Economic Order Quantity On-hand inventory (units) Time

Economic Order Quantity On-hand inventory (units) Time Receive order Q

Economic Order Quantity On-hand inventory (units) Time Receive order Q 1 cycle

Economic Order Quantity On-hand inventory (units) Time Receive order Q 1 cycle

Economic Order Quantity On-hand inventory (units) Time Receive order Inventory depletion (demand rate) Q 1 cycle

Economic Order Quantity On-hand inventory (units) Time Receive order Inventory depletion (demand rate) Q 1 cycle

Economic Order Quantity On-hand inventory (units) Time Average cycle inventory QQ—2QQ—2 1 cycle Receive order Inventory depletion (demand rate)

Total Cost = Holding Cost + Order Cost

Annual cost (dollars) Lot Size (Q)

Annual cost (dollars) Lot Size (Q) Holding cost (HC) Total Cost = Holding Cost + Order Cost

More units must be stored if more are ordered More units must be stored if more are ordered Purchase Order DescriptionQty. Microwave1 Order quantity Purchase Order DescriptionQty. Microwave1000 Order quantity Why Holding Costs Increase

Annual cost (dollars) Lot Size (Q) Holding cost (HC) Ordering cost (OC) Total Cost = Holding Cost + Order Cost

If we order more when we place an order, then we order fewer times over the year. If we order more when we place an order, then we order fewer times over the year. Example: You expect to order 10 microwave ovens over a year for a retail store like Sears. It cost $10 to place an order. Example: You expect to order 10 microwave ovens over a year for a retail store like Sears. It cost $10 to place an order. Why Order Costs Decrease Order Cost $10 Purchase Order Description Qty. Microwave10 Order cost $10 Purchase Order Description Qty. 1Microwave If you order 1 microwave, how many orders will you place over the year? what is the ordering cost? What is the ordering cost per microwave? If you order 10 microwaves, how many orders will you place over the year? What is the ordering cost? What is the ordering cost per microwave?

Annual cost (dollars) Lot Size (Q) Ordering cost (OC) Holding cost (HC) Total cost = HC + OC Total Cost = Holding Cost + Order Cost

Gift Shop A museum of natural history is having problems managing their inventories. Low inventory turnover is squeezing profit margins and causing cash-flow problems. A museum of natural history is having problems managing their inventories. Low inventory turnover is squeezing profit margins and causing cash-flow problems. A Class A item, a birdfeeder is also a top- selling item. A Class A item, a birdfeeder is also a top- selling item. Sales: 18 units/week Sales: 18 units/week Purchase cost: $60 Purchase cost: $60 Order cost: $45 Order cost: $45 Annual holding cost: 25% of purchase cost Annual holding cost: 25% of purchase cost 52-week year 52-week year Management has been ordering in lots of 390 units. Management has been ordering in lots of 390 units.

Q – order quantity Q – order quantity TC – Total cost TC – Total cost Annual Annual Monthly Monthly ?? ?? What is the annual cost of the current policy? Time Q

Holding Cost

Holding cost |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Holding cost = (H) Q2Q2 Annual cost (dollars)

Ordering cost

Holding & Ordering Cost |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ Annual cost (dollars)

Total Cost |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ Annual cost (dollars)

Total cost:

What is the annual cost of the current policy? D – Total demand Q – Order quantity S – Setup/order cost H – Holding cost

What is the annual cost of the current policy? D – Total demand 936/year Q – Order quantity 390/order S – Setup/order cost $45/order H – Holding cost = 0.25*60 = $15/unit/year

Total Cost for Q = 390 Annual cost (dollars) |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Current cost Current Q Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ

Can the gift shop do better? Annual cost (dollars) |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Current cost Current Q Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ

Economic Order Quantity – Q* Annual cost (dollars) |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Q* Setup cost = Holding Cost

Economic Order Quantity (EOQ) – Q*

Total Cost of Economic Order Quantity (EOQ) – Q* When Q = 390

When to order? Reorder point (ROP) Reorder point (ROP) Lead time – amount of time from order placement to receipt of goods Lead time – amount of time from order placement to receipt of goods Lead time demand – the demand the occurs during the lead time Lead time demand – the demand the occurs during the lead time

Reorder point Order received OH On-hand inventory

Reorder point Order received OH TBO On-hand inventory Time between orders

Reorder point Order received OH TBO L On-hand inventory Lead time

Reorder point Order received OH Order placed TBO L R On-hand inventory

Gift shop reorder point Demand: 18 birdfeeders/week Demand: 18 birdfeeders/week Lead time: 2 weeks Lead time: 2 weeks Lead time demand: 36 birdfeeders Lead time demand: 36 birdfeeders ROP: 36 birdfeeders ROP: 36 birdfeeders

Gift shop order policy Place order when the on-hand inventory is 36 birdfeeders. Place order when the on-hand inventory is 36 birdfeeders. Order 75 birdfeeders Order 75 birdfeeders Order received in 2 weeks Order received in 2 weeks Place next order when the on-hand inventory is 36 birdfeeders Place next order when the on-hand inventory is 36 birdfeeders

Gift shop order policy Order received OH Order placed 2 wks 36 On-hand inventory 75

Distribution Game What is the EOQ for the central warehouse in the distribution game? What is the EOQ for the central warehouse in the distribution game? Order cost: S = Order cost: S = Holding cost: H = Holding cost: H = Demand: D = Demand: D = $200 $14.70/unit/year 2190

Distribution Game

Production Order Quantity

On-hand inventory Time Production Order Quantity

Production quantity On-hand inventory Q Time Production Order Quantity

Production quantity On-hand inventory Q Time Demand during production interval p – d Production Order Quantity

Production quantity Demand during production interval On-hand inventory Q Time p – d Production Order Quantity

Production quantity Demand during production interval On-hand inventory Q Time p – d Production and demand Demand only TBO Production Order Quantity

Production quantity Demand during production interval Production and demand Demand only TBO On-hand inventory Q Time p – d Production Order Quantity

Production quantity Demand during production interval Maximum inventory Production and demand Demand only On-hand inventory Q Time p – d Production Order Quantity (POQ Model)

POQ model Assumptions Assumptions Known and constant demand Known and constant demand Known and constant lead time Known and constant lead time Partial receipt of material Partial receipt of material No quantity discounts No quantity discounts Only order (setup) cost and holding cost Only order (setup) cost and holding cost No stockouts No stockouts

POQ model Producing and shipping product simultaneously until production quantity is reached. Producing and shipping product simultaneously until production quantity is reached. Ship the inventory at a constant rate (no production) Ship the inventory at a constant rate (no production) Reorder same amount Reorder same amount Begin production and shipping product simultaneously Begin production and shipping product simultaneously

POQ Model D – annual demand S – Setup cost H – Holding cost d – daily demand rate p – daily production rate

Chemical Plant A plant manager of a chemical plant must determine the lot size for a particular chemical that has a steady demand of 30 barrels/day. The production rate is 190 barrels/day, annual demand is 10,500 barrels, setup cost is $200, annual holding cost is $0.21/barrel, and the plant operates 350 days/year. Determine the production order quantity.

Chemical Plant Demand: Setup cost: Holding cost: Production: d = 30 barrels/day D = 10,500 barrels/year $200/setup $0.21/barrel/year 190 barrels/day

Chemical Plant