Inventory Models Assumptions of EOQ model Shortages are allowed

EOQ Model with Quantity Discounts Deterministic Inventory Models EOQ Model with Quantity Discounts

Inventory Models Assumptions of EOQ model EOQ Model with Quantity Discount Assumptions Assumptions of EOQ model Purchase cost is NOT independent of the order quantity Unit holding cost is NOT independent of the order quantity

Inventory Models Example – Brewery EOQ Model with Quantity Discount Example – Brewery Monthly production of beer = 4 000 hl Filling into glass bottles = 25% of production Empty bottles stored in plastic cases (20 pcs.) Ordering cost – transportation = 11 000 CZK per order – other = 1 000 CZK per order Lead time = ½ of month Objective: minimize total annual cost

Inventory Models Example – Brewery EOQ Model with Quantity Discount Example – Brewery Unit purchase price – quantity discount schedule: Discount category Order quantity [cases] Purchase price [CZK per case] 1 1 – 4 999 46 2 5 000 – 14 999 40 3 15 000 + 36 Unit holding cost [CZK per case] 23 20 18 Annual holding cost per case = = 50% of unit purchase price

Inventory Models Example – Brewery Annual demand Q = 120 000 cases EOQ Model with Quantity Discount Example – Brewery Annual demand Q = 120 000 cases Purchase price cq = 46/40/36 CZK per case Annual holding cost c1 = 23/20/18 CZK per case Ordering cost c2 = 12 000 CZK per order Lead time d = 1/2 of month = 1/24 of year

Inventory Models Example – Brewery Total annual cost EOQ Model with Quantity Discount Example – Brewery Total annual cost Total annual HOLDING cost Total annual ORDERING cost Total annual PURCHASE cost

Inventory Models Example – Brewery Total annual cost EOQ Model with Quantity Discount Example – Brewery Total annual cost

cq= 46 cq= 40 cq= 36

Inventory Models q* Example – Brewery EOQ Model with Quantity Discount Example – Brewery Optimum order quantity for EACH CATEGORY Discount category q* 1 11 191 2 12 000 3 12 650

cq= 46 4 999 11 191 cq= 40 cq= 36

cq= 46 cq= 40 cq= 36 12 000

cq= 46 cq= 40 cq= 36 15 000 12 650

TC = 5  865 546 TC = 5  040  000 TC = 4  551  000

Economic Production Lot Size Model Deterministic Inventory Models Economic Production Lot Size Model

Inventory Models Assumptions of EOQ model Economic Production Lot Size Model Assumptions Assumptions of EOQ model Inventory is NOT replenished through the single batch

Inventory Models Time Inventory Level Maximal Inventory Level Economic Production Lot Size Model Time Inventory Level Maximal Inventory Level Production Phase Nonproduction Phase Average Inventory Level t t1 t2

Inventory Models Production phase - production (production rate) Economic Production Lot Size Model Assumptions Production phase - production (production rate) - demand (demand rate) - replenishment Nonproduction phase - demand (demand rate) - depletion

Production rate  Demand rate Inventory Models Economic Production Lot Size Model Assumptions Production rate  Demand rate

Inventory Models Holding cost Production setup cost Economic Production Lot Size Model Cost Holding cost Production setup cost Objective: minimize total annual cost

Inventory Models Example – Brewery Economic Production Lot Size Model Example – Brewery Monthly production of beer = 4 000 hl Filling into glass bottles = 25% of production Empty bottles are processed on the cleaning line (daily output = 8 000 bottles) Setup cost – 12 000 CZK per one cleaning process Annual holding cost per case = 20 CZK Lead time (preparation of cleaning line) = ½ of month Objective: minimize total annual cost

Inventory Models Filling bottles Example – Brewery Store Economic Production Lot Size Model Example – Brewery Production phase Filling bottles Cleaning line Store

Inventory Models Filling bottles Example – Brewery Store Economic Production Lot Size Model Example – Brewery Nonproduction phase Filling bottles Cleaning line Store

Inventory Models Example – Brewery What is the optimum LOT SIZE? Economic Production Lot Size Model Example – Brewery What is the optimum LOT SIZE? What is the maximum inventory level? What is the minimum total annual cost ? How long time does a cleaning run take? When to start the preparation process for the cleaning run?

Inventory Models Example – Brewery Demand rate Economic Production Lot Size Model Example – Brewery Demand rate h = 120 000 cases per year Production rate p = 146 000 cases per year Annual holding cost c1 = 20 CZK per case Setup cost c2 = 12 000 CZK per cleaning lot Lead time d = 1/2 of month = 1/24 of year

Inventory Models Example – Brewery Total annual cost Economic Production Lot Size Model Example – Brewery Total annual cost Total annual HOLDING cost Total annual SETUP cost

Inventory Models Example – Brewery Economic Production Lot Size Model Example – Brewery Production lot size – number of cleaned cases in a cleaning lot (within period t1) Demand within period t1 – Maximum inventory level

Inventory Models Example – Brewery Average inventory level Economic Production Lot Size Model Example – Brewery Average inventory level Total annual HOLDING cost

Inventory Models Example – Brewery Economic Production Lot Size Model Example – Brewery Number of production lots within a year Total annual SETUP cost

Inventory Models Example – Brewery Total annual cost Economic Production Lot Size Model Example – Brewery Total annual cost

Inventory Models Example – Brewery Optimum (economic) lot size Economic Production Lot Size Model Example – Brewery Optimum (economic) lot size

Inventory Models Example – Brewery Maximum inventory level Economic Production Lot Size Model Example – Brewery Maximum inventory level

Inventory Models Example – Brewery Optimum total annual cost Economic Production Lot Size Model Example – Brewery Optimum total annual cost

Inventory Models Example – Brewery Optimum length of production period Economic Production Lot Size Model Example – Brewery Optimum length of production period

Inventory Models Example – Brewery Optimum length of depletion period Economic Production Lot Size Model Example – Brewery Optimum length of depletion period

Inventory Models Example – Brewery or Optimum cycle Economic Production Lot Size Model Example – Brewery Optimum cycle or

Optimum starting setup point Time Inventory Level Time Inventory Level

Inventory Models Example – Brewery Optimum starting setup point Economic Production Lot Size Model Example – Brewery Optimum starting setup point