ICORE Operations: Inventory Management - The Newsvendor Model (SINGLE period inventory model)

multi period inventory model steps

1. find Cu, Co, and p 2. find z value of the p 3. plug the z value, mean and st. dev into quantity equation to see how much to order

critical ratio (other equation)

P <= Cu / (Co + Cu)

P

P is referred to as the critical ratio in a newsvendor problem it is the prob that the next unit will not sell the prob that we will meet all demand the area under the curve of the standard normal curve of demand WE CONTINUE TO INCREASE THE SIZE OF THE ORDER AS LONG AS THE PROBABILITY OF SELLING WHAT WE ORDER IS EQUAL TO OR LESS THAN THIS RATIO low p = you order less than mean bc cost of stocking out is low compared to cost of holding inventory so dont want extra inventory high p = you order more than mean bc cost of stocking out is high compared to cost of holding inventory so want extra inventory

single period inventory model equation

P x Co <= (1-P) x Cu Co = the cost of being over (too much inventory) Cu =the cost of being under (too little inventory) P = the probability that the next unit will not be sold, or the probability of meeting demand REMEMBER - the goal is to find the inventory level where expected benefits from carrying the next unit are less than the expected costs for that unit

finding quantity equation

Q = mean + z * st dev. Q = order quantity mean = mean demand Z = z score of your critical ratio st dev = standard deviation of demand

multi period inventory model

fixed order quantity models - event triggered (ex: running out of stock) fixed time period models - time triggered (ex: monthly sales call by sales rep)

costs of inventory 4

holding (or carrying) costs - costs for storage, handling, insurance, and so on setup (or production change) costs - costs for arranging specific equipment setups and so on ordering costs - costs of placing an order shortage costs - costs of running out

Inventory

inventory can be visualized as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit for many businesses, inventory is the largest asset on the balance sheet at any given time inventory can be difficult to convert back into cash it is a good idea to try to get your inventory down as far as possible

key conceptual

one time purchase decision - no second period 3 definitions of critical ratio

fixed order quantity model

used when we want to maintain an item in stock, and when we restock, a certain number of units must be ordered

high Co and low Cu means

we have high inventory holding costs and low stockout costs so order less if we order less then the probability that the next unit will not be sold (P) goes down -- less probability that you will meet demand P=1 -- you are meeting all demand I THINK

intuition of single period inventory models

we have some historical demand distribution, with a mean and a standard deviation we want to know how much to order today, based on the costs of being over and being under the order quantity with be some combo of the mean and standard dev the more we order, the less likelihood of stocking out for example a 99.9% chance of not stocking out would be the mean plus 3 standard devs in both directions

three important terms used to find the optimal level

cost of having too much inventory the cost of having too little inventory the probability of stocking out

key mathematical

critical ratio

inventory hides problems

decrease inventory reveals productivity problems like rocks under water

how do we know how much to oder for a general case

optimal stocking level in a single period inventory model occurs where expected benefits from carrying the next unit (marginal benefit) are less than the expected costs for that unit the optimal level is solved using probabilities

negative z score

order below mean

if overage costs are high in relation to underage costs

order less

if overage costs are low in relation to underage costs

order more

how are the costs related to each other when we order exactly the mean

p <= Cu / (Co + Cu)

TO DO

practice probs in notes

inventory includes

raw materials, finished products, component parts, supplies, and work-in-process

manufacturing inventory

refers to items that contribute to or become part of a firm's product

inventory models 3

single period model fixed order quantity model (multi period) fixed time period model (multi period)

fixed time period model

the item is ordered at certain intervals of time

inventory system

the set of policies and controls that monitor levels of inventory determines what levels should be maintained, when stock should be replenished, and how large orders should be WE NEED TO KNOW WHAT THE RIGHT AMOUNT OF INVENTORY IS BECAUSE INVENTORY IS WASTE BC IT HIDES PROBLEMS AND DOES NOT MAKE MONEY BUT COMPANIES NEED IT

inventory definition

the stock of any item or resource used in an organization

purposes of inventory

to maintain independence of operations to meet variation in product demand to allow flexibility in production scheduling to provide a safeguard for variation in raw material delivery time to take advantage of economic purchase order size

single period inventory model - consider the problem of deciding how many newspapers to put in a hotel lobby

too few papers and some customers will not beable to purchase a paper and profits associated with these potential sales are lost too many papers and the price paid for papers that were not sold during the day will be wasted, lowering profit need to find the balance between overstocking and understocking

single period model

used when we are making a one time purchase of an item like newspaper boy because the newspaper is only good for one day and useless other days or vendor selling t shirts at a football game seeks to balance the costs of inventory overstock and under stock