Chapter 12
demand per day (d)
= D / # working days a year
ROP formula with a service level %
Expected demand during lead time + Z(standard deviation (dLT)) Z - number of standard deviations standard deviation (dLT) - standard deviation of demand during lead time
4 Types of Inventory
(1) raw material inventory (2) work-in-process inventory (3) maintenance/repair/operating supply (MRO) inventory (4) finished-goods inventory.
Annual holding cost formula
(Average inventory level) * (Holding cost per unit per year) => (Order quantity/2) * (Holding cost per unit per year) => (Q/2)*H
Annual setup cost formula
(number of orders placed per year) * (setup or order cost per order) => (annual demand / number of units in each order) * (setup or order cost per order) => (D/Q)*S
assumptions of the economic order quantity (EOQ) model
1. Demand for an item is known, reasonably constant, and independent of decisions for other items. 2. Lead time—that is, the time between placement and receipt of the order—is known and consistent. 3. Receipt of inventory is instantaneous and complete. In other words, the inventory from an order arrives in one batch at one time. 4. Quantity discounts are not possible. 5. The only variable costs are the cost of setting up or placing an order (setup or ordering cost) and the cost of holding or storing inventory over time (holding or carrying cost). These costs were discussed in the previous section. 6. Stockouts (shortages) can be completely avoided if orders are placed at the right time. *graph of EOQ is sawtooth shape
Three situations for probabilistic models
1. Demand is variable and lead time is constant 2. Lead time is variable and demand is constant 3. Both demand and lead time are variable
Steps to find Q*
1. Develop an expression for setup or ordering cost. 2. Develop an expression for holding cost. 3. Set setup (order) cost equal to holding cost. 4. Solve the equation for the optimal order quantity. Q* = sqrt(2DS/H)
Techniques for inventory accuracy and control
1. Good personnel selection, training, and discipline 2. tight control of incoming shipments 3. effective control of all goods leaving the facility
Functions of Inventory
1. To provide a selection of goods for anticipated customer demand and to separate the firm from fluctuations in that demand. Such inventories are typical in retail establishments. 2. To decouple various parts of the production process. For example, if a firm's supplies fluctu- ate, extra inventory may be necessary to decouple the production process from suppliers. 3. To take advantage of quantity discounts, because purchases in larger quantities may reduce the cost of goods or their delivery. 4. To hedge against inflation and upward price changes.
Three independent inventory models
1. basic economy order quantity (EOQ) model 2. production order quantity model 3. quantity discount model
service level (probability of not stocking out)
= Cost shortage / (cost shortage + cost overage)
ABC Analysis
A method for dividing on-hand inventory into three classifications based on annual dollar volume. -what is known as "Pareto principle"..."critical few, trivial many"... not realistic to monitor inexpensive items with the same intensity as very expensive items. -criteria other than annual dollar can determine item classification (high shortage/holding cost, anticipated engineering changes, delivery problems, or quality problems)
probabilistic model
A statistical model applicable when product demand or any other variable is not known but can be specified by means of a probability distribution.
single-period inventory model
A system for ordering items that have little or no value at the end of a sales period (perishables).
Fixed-quantity (Q) system
An ordering system with the same order amount each time.
ROP = ?
Demand per day * lead time for a new order in days => d * L
safety stock (ss)
Extra stock to allow for uneven demand; a buffer.
Independent vs. dependent demand
Dependent example: demand for toaster oven components dependent on requirements of toaster ovens Independent example: demand for refrigerators independent of demand for toaster ovens
Expected # orders = N = ?
Demand / Order Quantity => D / Q*
robust
Giving satisfactory answers even with substantial variation in the parameters. EOQ model is robust! It changes little in neighborhood of the minimum. Curve is very shallow. Variations in setup, holding, demand, or even EOQ make modest difference in total cost.
Lead time
In purchasing systems, the time between placing an order and receiving it; in production systems, the wait, move, queue, setup, and run times for each component produced.
Expected time between orders = T = ?
Number of working days per year / N
define each variable used to determine setup and holding costs: Q, Q*, D, S, H
Q = Number of units per order Q* = Optimum number of units per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year
ROP formula to use when demand and lead time are variable
ROP = (avg daily demand * avg lead time in days_ + Z(stand. dev. (dLT)) WHERE stand dev (d) = standard deviation of demand per day AND stand dev (LT) = standard deviation of lead time in days AND stand dev(dLT) = sqrt((avg lead time * stand. dev(d)^2) + (avg daily demand)^2*stand dev(LT)^2))
ROP formula to use when demand is variable and lead time is constant
ROP = (avg daily demand * lead time in days) + Z(stand. dev (dLT)) WHERE stand. dev(dLT) = standard deviation of demand during lead time = stand. dev (d) = sqrt(Lead time) AND stand. dev (d) = standard deviation of demand per day
ROP Formula to use when variable and demand is constant
ROP = (daily demand * avg lead time in days) + Z * daily demand * stand. dev (LT) WHERE stand. dev (LT) = standard deviation of lead time in days
Holding costs
The cost to keep or carry inventory in stock. -include obsolescence and storage costs like insurance, staffing, and interest payments
setup cost
The cost to prepare a machine or process for production. Includes time and labor to clean or change tools/holders.
reorder point (ROP)
The inventory level (point) at which action is taken to replenish the stocked item.
service level
The probability that demand will not be greater than supply during lead time. It is the complement of the probability of a stockout.
Annual stock cost = ?
The sum of the units short for each demand level * The probability of that demand level * The stockout cost/unit * The number of orders per year
setup time
The time required to prepare a machine or process for production.
Ordering cost
cost of ordering process. Includes supplies, forms, order processing, purchasing, clerical support, etc.
ROP formula w/ inclusion of safety stock
d * L + ss
ROP formula assuming demand during lead time and lead time itself are constant
expected demand during lead time + safety stock
MROs
inventories devoted to maintenance/repair/operating supplies necessary to keep machinery and processes productive. Exist because need and timing for maintenance and repair of some equipment are unknown. Although the demand for MRO inventory is often a function of maintenance schedules, other unscheduled MRO demands must be anticipated.
pilferage
inventory theft
Total annual cost = ?
setup (order) cost + holding cost => TC = (D/Q)*S + (Q/2)*H + PD PD is purchase cost, if applicable.
Fixed-period (P) system
system in which inventory orders are made at regular time intervals - have same assumptions as basic EOQ fixed Q system (only relevant costs are ordering and holding, lead times are known & constant, items are independent of one another) - advantage: no physical count of inventory after item withdrawn. convenient administratively...occurs when next review period comes up. - appropriate when vendors make routine visits to customers to take fresh orders or when purchasers want to combine orders to save ordering and transporation costs (example: vending machine restocked every 5 days) - disadvantage: no tally of inventory during review period, so possibility of stockout. Possible if large order draws inventory level down to zero right after order is placed. Therefore, higher level of safety stock needs to be maintained during time between reviews and lead time.
Perpetual inventory system
system that keeps track of each withdrawal or addition to inventory continuously, so records are always current
