Inventory is the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process
An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be
Firms invest 25-35 percent of assets in inventory but many do not manage inventories well
Event triggered (Example: running out of stock, or dropping below a “reorder point”)
EOQ, EOQ with reorder point (ROP) , and with safety stock
Multi-Period Models: Basic Fixed-Time Period Model
EOQ with Quantity Discounts
Inventory Control (Management)
Independent vs. Dependent Demand E(1) Independent Demand (Demand not related to other items or the final end-product) Dependent Demand (Derived demand items for component parts, subassemblies, raw materials, etc.)
UNC Charlotte basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game?
Determine C u = $10 and C o = $5 (this time, these were directly given)
Compute P ≤ $10 / ($10 + $5) = 0.667 66.7%
Order up to ~ 66.7% of the demand
How do you determine it?
Normal distribution, Z transformation,
Z 0.667 = 0.432 (use NORMSDIST(.667) or Appendix E)
Therefore we need 2,400 +0.432(350) = 2,551 shirts
Demand for the product is constant and uniform throughout the period.
Inventory holding cost is based on average inventory.
Ordering or setup costs are constant.
All demands for the product will be satisfied. (No back orders are allowed.)
Lead time (time from ordering to receipt) is constant (later, this assumption is relaxed with “safety stocks”).
Price per unit of product is constant.
Basic Fixed-Order Quantity Model and Reorder Point Behavior 17- R = Reorder point Q = Economic order quantity L = Lead time L L Q Q Q R Time Number of units on hand 1. You receive an order quantity Q. 2. Your start using them up over time. 3. When you reach down to a level of inventory of R, you place your next Q sized order. 4. The cycle then repeats.
Cost Minimization Goal Ordering Costs Holding Costs Q OPTIMAL Order Quantity (Q) C O S T Annual Cost of Items (DC) By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Q optimal (a.k.a. “EOQ”) inventory order point that minimizes total costs. Total Cost
Basic Fixed-Order Quantity (EOQ) Model Annual Holding Cost A little bit of calculus… A little bit of common sense… ROP with safety stock… Total Annual Cost = Annual Purchase Cost Annual Ordering Cost + + TC = Total annual cost D = Demand C = Cost per unit Q = Order quantity S = Cost of placing an order or setup cost H = Annual holding and storage cost per unit of inventory R or ROP = Reorder point L = Lead time (constant) = average (daily, weekly, etc) demand σ L = Standard deviation of demand during lead time
Basic EOQ & ROP Example Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15 Given the information below, what are the EOQ, reorder point, and total annual cost? EOQ 89.44 89 or 90 units ROP 2.74*7 19.18 19 or 20 units
Another example Days per year considered in average daily demand = 360 Average daily demand is 3.5 units Standard deviation of daily demand is 0.95 units Cost to place an order = $50 Holding cost per unit per year = $7.25 Lead time = 4 days Compute the EOQ, and ROP is the firm wants to maintain a 97% service level (probability of not stocking out)
Fixed-Time Period Model with Safety Stock q = Average demand + Safety stock – Inventory currently on hand
Example of the Fixed-Time Period Model Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units. Given the information below, how many units should be ordered? q = 20(30+10) + 1.75(25.30) – 200 644.27 units
Based on the same assumptions as the EOQ model, the price-break model has a similar EOQ (Q opt ) formula:
Annual holding cost, H, is calculated using H = iC where
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula above must be applied to each price-break cost value.
Determine the total cost for each price break
The lowest total cost suggests the optimal order size (EOQ)
Price-Break Example A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? Order Quantity(units) Price/unit($) 0 to 2,499 $1.20 2,500 to 3,999 $1.00 4,000 or more $0.98 Re-do the example with an order cost of $25 and an inventory carrying cost rate of 45%.