Ch. 13: Inventory Management
* Inventories are a vital part of business:
(1) necessary for operations and (2) contribute to customer satisfaction A "typical" firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory
*Annual setup cost =
(D/Q)S
*Annual ordering cost =
(D/Q)S *D = Demand *Q = order size *S = ordering cost per order
*EPQ average inventory level (Iaverage) =
(Imax/2)
*EPQ maximum inventory level (Imax) =
(Op/p)(p-u) or Qp - (Qp/p)u
*annual carrying cost =
(Q/2)H *Q = demand *H= holding/carrying costs per unit per year
*EPQ run time =
(Qp/p)
*EPQ Cycle time =
(Qp/u)
*Total cost (quantity discount) =
(carrying cost) + (ordering cost) + (purchasing cost) = (Q/2)H + (D/Q)S + (PD) *p = unit price
*TCmin =
(carrying cost) + (setup cost) = (Imax/2)H + (D/Q)S Imax = maximum inventory EPQ
Z(QdLT)
* z = number of standard deviations * (QdLT) = the standard deviation of lead time demand
* Two different kinds of inventories include the following:
-Raw materials and purchased parts -partially completed goods, work-in-process (WIP) -finished-goods inventory (manfacturing) -merchandise (retail) -tools and supplies -maintenance and repairs (MRO) inventory -goods-in-transit to warehouses, distributors, or customers (pipeline inventory)
*Requirements for effective inventory management:
1. A system to keep track of inventory 2. A reliable forecast of demand and forecast error 3. Knowledge of lead times and lead time variability 4. Estimates of inventory holding, ordering, and shortage costs 5. A classification system for inventory items
*Economic Production Quantity EPQ Assumptions of the EPQ model:
1. one product involved 2. annual demand requirements known 3. usage rate is constant 4. usage occurs continually, but production occurs periodically 5. production rate is constant 6. lead time does not vary 7. no quantity discounts
*The four determinants of (ROP) reorder point:
1. rate of demand 2. the lead time 3. extent or demand and/or lead time variation 4. degree of stockout risk acceptable to management
*Three EOQ economic order quantity models:
1. the basic EOQ model - fixed order size that will minimize costs( no quantity discounts) 2. the economic production quantity model 3. the EOQ model with quantity discounts
*Two main CONCERNS of inventory management:
1. the level of customer service -Having the right goods available in the right quantity in the right place at the right time 2. costs of ordering and carrying inventory
*Two basic FUNCTIONS of management concerning inventory:
1. to establish a system to keep track of items in inventory 2. to make decisions about when to order, how much, and when order should arrive 3. Inventory management tends to be "policy" oriented. -Type of inventory -Importance of item
List the eight functions of inventory:
1. to meet anticipated customer demands [anticipation stocks] 2. to smooth production requirements [seasonal inventories] 3. to decouple operations [inventory buffers] 4. to protect against stockouts [safety stocks] 5. to take advantage of order cycles [economic lot sizes] 6. to hedge against price increases 7. to permit operations 8. to take advantage of quantity discounts
Study Case problem examples. Know how to calculate 1. Economic order quantity EOQ 2. Number of orders each year 3. Cycle Time (how much time between two consecutive orders?) 4. Minimum total annual costs
1.Sqrt(2DS/H), annual demand, ordering cost S, holding costs H 2. Orders/yr = D/Qo 3. Time between orders= Q/D x Days worked per year 4.TC= (Q/2)H + (D/Q)S
Service Level =
100% - Stockout risk
*Inventory
A stock or store of goods
*Safety Stock increases=risk of stockout to decrease 2 methods of determining safety stock
As the amount of safety stock carried increases, the risk of stockout decreases. This improves customer service level 2 methods of determining safety stock: 1.Fixed amount 2.Service level The probability that demand will not exceed supply during lead time Service level = 100% - Stockout risk
*A-B-C approach
Classifying inventory according to some measure of importance, and allocating control efforts accordingly
*Number of orders per year =
D/Q *D = demand *Q = order size
*Reorder Point under uncertainty
Demand or lead time uncertainty creates the possibility that demand will be greater than available supply To reduce the likelihood of a stockout, it becomes necessary to carry safety stock ROP= d X LT + Safety Stock
*Optimal order quantity (Q0) =
Deriving EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Sqrt(2DS/H)
*How much Safety Stock?
The amount of safety stock that is appropriate for a given situation depends upon: 1. The average demand rate and average lead time 2. Demand and lead time variability 3. The desired service level Safety Stock= +zó subscript (dLT) z= Number of standard deviations ódLT= Standard deviation of lead time demand
*Economic Production Quantity (EPQ)
The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate)
*Safety Stock
To reduce the likelihood of a stockout, it becomes necessary to carry safety stock, STOCK that is held in excess of expected demand due to variable demand and or lead time ROP= d X LT + Safety Stock
*Total Annual Cost (TC) =
Total Cost = (Annual carrying/holding costs) + (annual ordering costs) = (Q/2)H + (D/Q)S Q= Order quantity in units H= Holding (carrying) cost per unit, usually per year D= Demand, usually in unity per year S= Ordering cost per order [note: substitute Q for Q0 to find minimum total cost]
*Two-bin system
Two containers of inventory; reorder when the first is empty
*Basic economic order quantity, EOQ Model and Assumptions
Used to find a fixed order quantity that will minimize total annual inventory costs 1. one product involved 2. annual demand requirements known 3. demand rate spread evenly throughout year, reasonable constant 4. lead time known, constant 5. each order is received in a single delivery 6. no quantity discounts
days of inventory on hand
a number that indicates the expected number of days of sales that can be supplied from existing inventory
*Cycle counting
a physical count of inventory
Because inventories may represent a significant portion of total assets,
a reduction of inventories can result in a significant increase in ROI
*ABC items. In most instances, a relatively small number of items will
account for a large share of the annual dollar value A items(very important) 10-20% of # of items in inv. & about 60-70% of annual dollar value B items ( moderately important) C items (least important) 50-60% of # of items in inv., but only about 10-15 % of annual dollar value
When carrying costs are constant,
all points have their minimum points at the same quantity
*ordering costs are inversely
and nonlinearly related to order size
Universal Product Code (UPC)
bar code printed on a label that has information about the item to which it is attached
*Holding/Carrying cost
cost to carry an item in inventory for a length of time, usually a year 2 ways of defining: 1.Flat rate-$1.20 per item per year 2. % of price- an items price is $4 and carrying cost are 30% of price. 30% * $4= $1.20
*Ordering costs
costs or ordering and receiving inventory.
*Shortage costs
costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit
*Reorder Point (ROP) = Under Certainty
d X LT *d = Demand rate (units per period, per day, per week) *LT = Lead time (in same time units as d ) Example: An item has a demand of 50 per day And the lead time to replenish is 2 days. Then ROP = 50 x 2 = 100.
discrete distribution
demand is expressed in a number of units
continuous distribution
demand is expressed on a continuous scale
*excess cost
difference between purchase cost and salvage value of items left over at the end of a period C excess = Ce = Cost per unit - Salvage value per unit goes with single-period model
safety stock
extra inventory carried to reduce the probability of a stockout due to demand and/or lead time variability
*shortage cost
generally, the unrealized profit per unit C shortage= Cs= Revenue per unit- Cost per unit Goes with single-period model
Why wouldn't including purchasing cost in a basic EOQ model not change the EOQ?
including purchasing costs would merely raise the total-cost curve by the same amount (PD) at every point
*Independent-demand items
items that are ready to be sold or used
*Economic order quantity, EOQ models identify the optimal order quantity by
minimizing the sum of certain annual costs that vary with order size and order frequency
*Single-period-model
model for ordering perishables and other items with limited useful life Shortage cost Excess cost
*Carrying costs are linearly related to
order size
fixed-order-interval model (FOI)
orders are placed at fixed time intervals
*Quantity Discounts
price deductions for larger orders
Service Level
probability that demand will not exceed supply during lead time
return on investment is
profit after taxes divided by total assets
*The overall objective of inventory management is to achieve
satisfactory levels of customer service while keeping inventory costs within reasonable bounds 1. Measures of performance 2. Customer satisfaction -Number and quantity of backorders -Customer complaints 3. Inventory turnover
Cycle stock
the amount of inventory needed to meet expected demand
*Purchase cost
the amount paid to buy the inventory
Little's Law
the average amount of inventory in a system is equal to the product of the average demand rate and the average time a unit is in the system
*Setup costs
the costs involved in preparing equipment for a job, analogous to ordering costs
when carrying costs are stated as a percentage of unit price,
the minimum points do not line up
Fill rate
the percentage of demand filled by the stock on hand
*Goal: Total Cost Minimization The total cost curve reaches its minimum at
the quantity where carrying and ordering costs are equal Orders/yr =D/Qo
*Lead time
time interval between ordering and receiving the order
*the total cost curve is
u-shaped
*Reorder Point (ROP)
when the quantity on hand of an item drops to this amount, the item is reordered
Case study Problem How much safety stock would be required for the ingredient sausage if the average daily demand is 15 lbs. with a replenishment lead time is 5 days. The supplier for this ingredient is not always reliable. Data has shown that the standard deviation for demand during the normal lead time is 3 lbs. How much safety stock would be required if you wished to have a 95% service level.
For a service level of 95%, z= 1.64 Std dev of lead time = 3 days LT = 5 days SS = 1.64 x 3 x 2.2 = 10.8 or 11 lbs.
*Cycle counting management
How much accuracy is needed? A items: ± 0.2 percent B items: ± 1 percent C items: ± 5 percent When should cycle counting be performed and who should do it?
economic order quantity (EOQ)
How much to order: the order size that minimizes total annual cost
*Forecasts
Inventories are necessary to satisfy customer demands, so it is important to have a reliable estimates of the amount and timing of demand
Case study problems. calculate EPQ, Max inv., cycle time. length of run, TC
Lunch rush time is the busiest time for the restaurant. Rush hour last for 2 hours. You need to keep the pizza buffet line supplied with pizzas to keep your customer satisfaction rating high. Assume your ovens have a capacity of 50 pizzas/hour and can hold up to 100 pizzas . At peak time your customers will consume on the average about 40 pizzas/hour. Setup costs consist of the cost of pre-heating the oven. Setup cost is estimated at $10 per day. Inventory carrying costs for cooked pizzas are estimated at $0.50 per pizza/day. Calculate the following: a) Economic production quantity, b) Maximum inventory, c) Cycle Time (i.e. the length of time between runs), d) Length of the pizza run, e) Total cost of baking pizza during rush hour.
*Periodic System
Physical count of items in inventory made at periodic intervals (weekly, monthly)
*Inventory Costs
Purchase cost, holding/carrying cost, ordering cost, setup costs, shortage costs,
*Length of order cycle =
Q/D
Study Case Problems Know how to calculate reorder point ROP
ROP= d X LT + Safety Stock
*ROP : Demand Uncertainty
ROP= d'LT+zsd sq.rt. (LT) z=number of st.dv d=average demand per period sd=The st.dev. of demand per period LT=lead time
*ROP: Lead Time Uncertainty
ROP= dXLT + zdo (LT) look at notes for correct version of equation variables
Inventory turnover
Ratio of average cost of goods sold to average inventory investment, indicates how many times a year the inventory is sold
* Point-of-Sale Systems (POS) FORECASTS
Record items electronically at time of actual sale. demand info Useful for enhancing forecasting and inv. mgmt.
*Stocking Levels
Service level equation= Cs/Cs+Ce Zizi's wants to keep a supply of Dallas Morning News papers available for their customers to read while eating. Zizi's will not stock the Sunday edition of the paper. See the table below for prices and demand data. Item( newspaper) Selling Price ($0.75) Unit Cost ( $0.15) Average Daily Demand ( Minimum 10, Max 25) Salvage Value $0.00 Cshortage = Cs = Revenue per unit - Cost per unit = $0.75 - $0.15 = $0.60 Cexcess = Ce = Cost per unit - Salvage value per unit = $0.15 - $0.00 = $0.15 a. Calculate optimum service level SL = $0.60/($0.60+$0.15) SL = 80% 5b. Calculate the quantity of newspapers to buy for this service level Quantity = Minimum demand + SL (Max - min demand) Quantity = 10 + .80 (25-10) = 22 newspapers
*EPQ quantity (Qp) =
Sqrt.(2DS/H)* Sqrt.(p/p-u) p = prodution/delivery rate u = usage rate
*Perpetual Inventory System
System that keeps track of removals continuously, thus monitoring current levels of each item An order is placed when inventory drops to a predetermined minimum level
