Everyday Inventory Food Gasoline Clean clothes… What else?
Inventory Stock or quantity of items kept to meet demand Takes on different forms Final goods Raw materials Purchased/component parts Labor In-process materials Working capital
Inventory Static – only one opportunity to buy and sell units Dynamic – ongoing need for units; reordering must take place
Demand Dependent Demand Items are used internally to produce a final product Independent Demand Items are final products demanded by external customers
Reasons To Hold Inventory To meet anticipated demand To smooth production requirements To decouple components of the production- distribution system To protect against stock-outs To take advantage of order cycles To hedge against price increases or to take advantage of quantity discounts To permit operations
Inventory Costs Carrying Costs Costs of holding an item in inventory Ordering Costs Costs of replenishing inventory Shortage (stockout) Costs Temporary or permanent loss of sales when demand cannot be met
Inventory Management Objective: To keep enough inventory to meet customer demand and also be cost-effective Purpose: To determine the amount of inventory to keep in stock - how much to order and when to order How much and when to order inventory?
Inventory Management Requirements A system to keep track of the inventory on hand and on order A reliable forecast of demand Knowledge of lead times Reasonable estimates of inventory costs A classification system for inventory items (ABC)
Inventory Control Systems Control the level of inventory by determining how much to order and when Continuous (Perpetual) Inventory System - a continual record of the inventory level for every item is maintained Periodic Inventory System - inventory on hand is counted at specific time intervals
Other Control Systems/Tools Two-Bin System - two containers of inventory; reorder when the first is empty Universal Product Code (UPC) - Bar code printed on a label that has information about the item to which it is attached RFID Tags 0 214800 232087768
Considerations Lead Time Time interval between ordering and receiving the order Cycle Counting Physical count of items in inventory Usage Rate Rate at which amount of inventory is depleted
Inventory Cycle Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time
Economic Order Quantity The EOQ Model determines the optimal order size that minimizes total inventory costs
Inventory Costs Carrying Costs – cost associated with keeping an item in stock Includes: storage, warehousing, insurance, security, taxes, opportunity cost, depreciation, etc. Ordering Costs – cost associated with ordering and receiving inventory Determining quantities needed, preparing documentation, shipping, inspection of goods, etc.
Optimal Order Quantity Q = 2DS H = 2 (Annual Demand) (Order Cost) Annual Holding Cost per unit o QoDQoD Length of order cycle = DQoDQo # Orders / Year =
Basic EOQ Model Annual carrying cost Annual ordering cost Total cost =+ QoQo 2 H D QoQo S TC = + Where: Q o = Economic order quantity in units H = Holding (carrying) cost per unit D = Demand, usually in units per year S = Ordering cost
Cost Minimization Goal The Total-Cost Curve is U-Shaped Ordering Costs QOQO Order Quantity (Q) Annual Cost ( optimal order quantity) Carrying Costs
EOQ Example 1 A local office supply store expects to sell 2400 printers next year. Annual carrying cost is $50 per printer, and ordering cost is $30. The company operates 300 days a year. A) What is the EOQ? B) How many times per year does the store reorder? C) What is the length of an order cycle? D) What is the total annual cost if the EOQ quantity is ordered?
Given: Demand = D = 2400 Holding Cost = H = $50 per unit per year Ordering Cost = S = $30 A.What is the EOQ? B. How many times per year does the store reorder? C. What is the length of an order cycle?
Given: Demand = D = 2400 Holding Cost = H = $50 per unit per year Ordering Cost = S = $30 D. What is the total annual cost if the EOQ quantity is ordered? TC = Carrying cost + Ordering cost
EOQ Example 2 A local electronics store expects to sell 500 flat-screen TVs each month during next year. Annual carrying cost is $60 per TV, and ordering cost is $50. The company operates 364 days a year. A) What is the EOQ? B) How many times per year does the store reorder? C) What is the length of an order cycle? D) What is the total annual cost if the EOQ quantity is ordered?
Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50 A.What is the EOQ? B. How many times per year does the store reorder? C. What is the length of an order cycle?
Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50 D. What is the total annual cost if the EOQ quantity is ordered? TC = Carrying cost + Ordering cost
Other Considerations Safety Stock Reorder Point Seasonality
Quantity Discounts A price discount on an item if predetermined numbers of units are ordered TC = Carrying cost + Ordering cost + Purchasing cost = (Q / 2) H + (D / Q) S + PD where P = Unit Price
Quantity Discount Example Campus Computers 2Go Inc. wants to reduce a large stock of laptops it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule as shown below. Given the discount schedule and its known costs, the bookstore wants to determine if it should take advantage of this discount or order the basic EOQ order size. QuantityPrice 1 – 49$1,500 50 – 89$1,000 90 +$800 Carrying Cost:$200 Ordering Cost$1,000 Annual Demand400 units
First, determine the optimal size and cost with the basic EOQ model. Q O = This order size is eligible for the discount price of $1,000… now we compute the total cost TC = Compare this cost to an ordering size of 90 @ $800: TC = (Q / 2) H + (D / Q) S + PD =
What if a new discount was offered where they would receive a price of $790 if they were to order 150 or more?
HW #13 A mail-order house uses 18,000 boxes a year. Carrying costs are $.60 per box per year and ordering costs are $96. The following price schedule is offered. Determine the EOQ and the # of orders per year. # BoxesUnit Price 1000-1999$1.25 2000-4999$1.20 5000-9999$1.15 10000+$1.10
EOQ with Incremental Replenishment (EPQ) Used when company makes its own product Considers a variety of costs/terms: Carrying Cost Setup Cost (analogous to ordering costs) Maximum and Average Inventory Levels Economic Run Quantity Cycle Time Run Time
EOQ with Incremental Replenishment (EPQ) Definitions S = Setup Cost H = Holding Cost I max = Maximum Inventory I avg = Average Inventory D = Demand/Year p = Production or Delivery Rate u = Usage Rate
EOQ with Incremental Replenishment Total Cost = Carrying Cost + Setup Cost (I max /2) H + (D/Q o ) S Economic run quantityQ o = 2DS/H * p/(p-u) Cycle time (time between runs) Q o /u Run time (production phase) Q o /p Maximum Inventory LevelI max = (Q o /p)(p-u) Average Inventory LevelI average = I max /2
Assumptions Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually, production periodically Production rate is constant Lead time doesn’t vary No quantity discounts
EOQ Replenishment Example A toy manufacturer uses 48,000 rubber wheels per year for its product. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the: Optimal run size Minimum total annual cost for carrying and setup Cycle time for the optimal run size Run time
D = 48,000 wheels per year S = $45 H = $1 per wheel per year p = 800 wheels per day u = 48,000 wheels per 240 days, or 200 wheels per day Q o = 2DS/H * p/(p-u) = I max = (Q o /p)(p-u) = TC min = (I max /2) H + (D/Q o ) S = Cycle time = Q o /u = Run time = Q o /p =
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