Why is Inventory Important?

Inventory at Successive Stocking Points

Water Tank Analogy Flow of Receipts (Raw Materials & Parts) Demand Flow (Finished Goods) Scrap or Reject Flow Inventory Level

Outflow exceeds Inflow Flow of Receipts (Raw Materials & Parts) Demand Flow (Finished Goods) Scrap or Reject Flow

Inflows exceed Outflows Flow of Receipts (Raw Materials & Parts) Demand Flow (Finished Goods) Scrap or Reject Flow

Types of Demand Independent Item’s demand is influenced ONLY by market conditions and is NOT related to production decisions for any other items. Only end items Demand must be forecast Examples –Cars, TVs, Bicycles, Number of Seats in a restaurant

Types of Demand Dependent Item’s demand derives from the production decisions of its parents. All intermediate and purchased items in manufacturing Demand should be derived Examples –Car doors, Tv remotes, Bicycle tires, Number of T-bones for a given night

A Bill of Materials A B(3) C(2) C(1) D(3) E(2) F(2) G(1)

Pressures for Small Inventories Interest/Opportunity Cost Storage and handling Property Taxes Insurance premiums Shrinkage Spoilage

Pressures for Large Inventories Customer Service Order/Setup Cost Labor/Equipment Utilization Transportation Cost Cost of Materials/Quantity Discounts

The Gaming Co.

How Much? When! When!

Economic Order Quantity Annual cost (dollars) Lot Size (Q)

Economic Order Quantity Annual cost (dollars) Lot Size (Q) Holding cost (HC)

Economic Order Quantity Annual cost (dollars) Lot Size (Q) Holding cost (HC) Ordering cost (OC)

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

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

Economic Order Quantity Annual cost (dollars) |||||||| — 2000 — 1000 — 0 — Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ Lot Size (Q) Birdfeeder costs(Current System) C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units

Economic Order Quantity Annual cost (dollars) |||||||| Lot Size (Q) 3000 — 2000 — 1000 — 0 — Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ Birdfeeder costs (Current System) C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $ $108 = $3033

Economic Order Quantity |||||||| 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 Birdfeeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $ $108 = $3033

Economic Order Quantity |||||||| 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 |||||||| 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 Birdfeeder costs (Optimal) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = EOQ C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H

Economic Order Quantity |||||||| 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 Birdfeeder costs (Optimal) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H

Economic Order Quantity |||||||| 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 Birdfeeder costs (Optimal) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units C = $562 + $562 = $1124 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H

Economic Order Quantity |||||||| 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 Birdfeeder costs (Optimal) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units C = $562 + $562 = $1124 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H

Economic Order Quantity |||||||| 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 Birdfeeder costs (Optimal) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units C = $562 + $562 = $1124 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Lowest cost Best Q (EOQ)

Economic Order Quantity |||||||| Annual cost (dollars) Lot Size (Q) 3000 — 2000 — 1000 — 0 — Current cost Lowest cost Best Q (EOQ) Current Q Total cost = (H) + (S) DQDQ Q2Q2 Holding cost = (H) Q2Q2 Ordering cost = (S) DQDQ

Five Assumptions of the EOQ CONSTANT demand rate Two relevant COSTS Item INDEPENDENCE CERTAINTY in demand, lead time and supply Whole LOTS

Realistic? No Way BUT, since EOQ is relatively insensitive to errors, IT WORKS ANYWAY!

How Much? When! When!

Reorder Point On-hand inventory Time R Order received Q OH

Reorder Point On-hand inventory Order received Q OH Order placed IP TBO L R

Reorder Point On-hand inventory Time Order received Order received QQ OH Order placed Order placed IP TBO L L L R

Reorder Point Time On-hand inventory Order received Order received Q OH Order placed Order placed IP R TBO 1 TBO 2 TBO 3 L1L1 L2L2 L3L3

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability Cumulative Probability

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability Cumulative Probability Desired Cycle-Service Level = 95%

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability Cumulative Probability Desired Cycle-Service Level = 95% Reorder Point = 500 units

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability Cumulative Probability Desired Cycle-Service Level = 95% Reorder Point = 500 units

Reorder Point / Safety Stock Lower Florida Keys Health System Basic Surgery Cart Demand During Lead Time (units) Probability Cumulative Probability Desired Cycle-Service Level = 95% Reorder Point = 500 units Safety stock = Reorder point - DDLT DDLT= 100(0.10) + 200(0.15) (0.05) = 355 units Safety stock = = 145 units

Reorder Point / Safety Stock Probability of stockout ( = 0.15) Cycle-service level = 85% Average demand during lead time zLzL R

Reorder Point / Safety Stock Demand during lead time = 36 units  L = 15 Cycle/service level = 90% Time On-hand inventory R

Reorder Point / Safety Stock Demand during lead time = 36 units  L = 15 Cycle/service level = 90% Time On-hand inventory R z = 1.28 Safety stock = z  L = 19.2  20 Reorder point = = 56

Reorder Point / Safety Stock Demand during lead time = 36 units  L = 15 Cycle/service level = 90% Time On-hand inventory 56 z = 1.28 Safety stock = z  L = 19.2  20 Reorder point = = 56

Reorder Point / Safety Stock Demand during lead time = 36 units  L = 15 Cycle/service level = 90% Time On-hand inventory 55 z = 1.28 Safety stock = z  L = 19.2  19 Reorder point = = 55 When  L not given, but L and  t are known:  L =  t L

Current Practice Papers