Deterministic Inventory Models Operations Research Jan Fbry Deterministic

Deterministic Inventory Models ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models Basic EOQ Model ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) Ø How much to order? … Optimum quantity Ø When to order? … Optimum reorder point Ø What is the total cost? Ø What is the average inventory level? Ø What is the maximum inventory level? ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) Assumptions Ø Single item Ø Deterministic demand (static) Ø Deterministic lead time (constant) Ø Uniform depletion of the inventory ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) Assumptions Ø Constant order quantity (OQ) Ø Purchasing cost is independent of the OQ Ø Unit holding cost is independent of the OQ Ø No shortages, no surpluses ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) Inventory Depletion Replenishment Level q Maximum Level Average Level q/2 Order Arrives 0 Cycle 1 Cycle 2 Cycle 3 Time ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Monthly production of beer = 4 000 hl Ø Filling into glass bottles = 25% of production Ø Empty bottles stored in plastic cases (20 pcs. ) Ø Annual holding cost per case = 20 CZK Ø Ordering cost – transportation = 11 000 CZK per order – other = 1 000 CZK per order Ø Lead time = ½ of month Ø Objective: minimize total annual cost ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Annual demand Q = 120 000 cases Ø Annual holding cost c 1 = 20 CZK per case Ø Ordering cost Ø Lead time c 2 = 12 000 CZK per order d = 1/2 of month = 1/24 of year ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Total annual cost Total annual ORDERING cost Total annual HOLDING cost ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Inventory Level q Order quantity q/2 Maximum Level Average Level 0 Time ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Order quantity - q Ø Maximum inventory level Ø Average inventory level ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Total annual HOLDING cost Ø Total annual ORDERING cost ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Total annual cost ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Total cost 1 212 000 TC 624 000 HC OC 244 000 0 10 000 60 000 120 000 q ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Policy III Annual demand Q 120 000 Order quantity q 10 000 60 000 120 000 Annual unit holding cost c 1 20 20 20 Average inventory level q/2 5 000 30 000 60 000 Total annual holding cost HC 100 000 600 000 1 200 000 Unit ordering cost c 2 12 000 Number of orders Q/q 12 2 1 Total annual ordering cost OC 144 000 24 000 12 000 Total annual cost TC 244 000 624 000 1 212 000 ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level Policy I 10 000 0 6 12 Time ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level Policy II 60 000 0 6 12 Time ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level 120 000 Policy III 0 6 12 Time ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Optimum order quantity ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Ø Optimum total annual cost ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery cost TC 240 000 HC OC 0 12 000 q ______________________________________ Operations Research Jan Fábry

EOQ Model Example – Brewery Ø Optimum length of inventory cycle ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level 12 000 6 000 0 73 36. 5 146 109. 5 219 182. 5 292 255. 5 365 Time 328. 5 (days) ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level q* Order Delivery r* d t* Time ______________________________________ Operations Research Jan Fábry

EOQ Model Example – Brewery Ø Optimum reorder point q* r* d t* ______________________________________ Operations Research Jan Fábry

Deterministic Inventory Models EOQ Model Example – Brewery Inventory Level q* d > t* r* Time d t* ______________________________________ Operations Research Jan Fábry