Chapter 18 - Lagerteori Flashcards
Hva handler lagerteori om?`
Lagerteori handler om å optimalisere hvordan vi driver lageret vårt. Dette inkluderer hvor mye varer vi har inne, og til hvilken tid. En annen måte å se det på, er “hvor mye skal vi bestille, og når skal det bestilles”. Målet er å minimere kostnader.
Vi ser som regel bort ifra inntekt, men opererer med en form for kjent etterspørsel slik at vi kan predikere hvor mye vi trenger til enhver tid.
Hvilke typer foretak ser vi på?
Vi ser spesielt på produsenter og grossister.
Dette er altså enten bedrifter som produserer varer basert på innsatsfaktorer, eller bedrifter som kjøper ferdigproduserte varer, og selger dem videre.
Begge typer foretak går under samme type lagerteori. En bedrift som produserer varer, eksempelvis TV’er, må kjøpe inn innsatsfaktorer til rett tid. Disse faktorene må lagres et sted, og dette koster penger. Samtidig må de ferdigproduserte varene også lagres ett sted før de sendes videre. Dette koster også penger. Kostnadene er knyttet til alternativkostnader, lagringskost etc.
En grossist, eksempelvis XXL, er avhengig av å ha varer på lager når kunder kommer for å kjøpe. Dermed blir det et spørsmål om hvor mye lagring skal vi ha. Hvor ofte skal vi kjøpe.
Dersom frakt og levering er gratis og momentant, hvordan ser ideel lagerteori ut?
Kun en vare på lager, kjøpes inn automatisk når en vare blir solgt. Antar at kunder kun kjøper en vare om gangen.
Prinsippet vil uansett være at det kan være gunstig å øke hyppigheten av innkjøp dersom kostnaden for innkjøp er lav, og kosntaden for å holde på varer er høy. Dersom det er motsatt, vil vi kjøpe sjeldnere.
Hva (i prosent) snakker vi i forhold til lagringskostnad sammenlignet med verdien på det som lagres?
Ofte snakker vi 25%. Altså, vi betaler 25% av verdien på lageret for å kunne lagre noe årlig.
Hvem introduserte just in time tiønærmingen?
Japanske toyota.
Hvilke steg består “scientific inventory management” av?
Det er en fire-stegs modell:
1) Formuler en matematisk modell som beskriver oppførselen på det spesifikke lageret
2) Finn en optimal “inventory policy” basert på den matematiske modellen.
3) Bruk teknologiske IT-tjenester som overvåker og kontrollerer lageret.
4) Ved å bruke IT-tjenestene, kombiner med inventory policy for å finne ut av når vi skal kjøpe og hvor mye vi skal kjøpe.
Hvilke typer matematisk lagermodell har vi?
Vi vurderer følgende:
1) Deterministisk
2) Stokastisk
Deterministiske modeller følger ganske klare mønstre på hva som er etterspørselen i hver tidsperiode.
Stokastiske modeller følges av stokastiske variabler som bestemmes av en spesiell sannsynlighetsfordeling.
Hvilke faktorer, i henhold til lagerteori, påvirker lønnsomheten på en bedrift?
Vi ser på 6 faktorer som relevante for lagerteori:
1) Ordering costs.
2) Holding costs
3) Shortage costs
4) Revenues
5) Salvage costs
6) Discount rates
Elaborate on the factor “cost of ordering”, or “ordering costs”
The cost of ordering z units (either purchasing OR producing) can be represented by a function c(z).
In a relatively simple case, we assume there are 2 main cost-components in this function:
1) The set-up cost
2) The unit cost
The set-up cost is a fixed cost, typically. Or, it acts like a fixed cost.
This set-up cost in the case of manufacturing is typically associated with readying of machines, perhaps training personnel etc.
For wholesalers, this cost can simply be costs associated with making the trade, or something similar.
The unit cost is self explanatory.
We get the following relationship:
c(z) = 0, if z=0, K+cz, if z>0
NB: It is an assumption that allows us to consider this ordering cost funciton as a composite of 2 parts. This is not necessarily always the case.
In regards to wholesalers vs manufacturers, the parts of the ordering cost function will typically be very different. Wholesellers usually have much smaller set-up costs, but they will have larger unit cost than manufacturers.
This alone would indicate that manufacturers would likely benefit from producing vast amounts at a time, while wholesellers benefit from more frequent purchases.
Elaborate on the holding cost
The holding cost is often called “storage cost”. The holding cost represent ALL COSTS associated with storing the items after they have been bought/produced and until they are sold and removed from the storage.
Very important factors that will contribute to the costs of holding inventory includes:
- Cost of capital tied up
- Space
- Insurance
- Protection
- Taxes
It seems like we generally would to keep the inventory as low as possible, but extend it as far as it is beneficial in regards to other gains.
The holding cost can be assessed either continuously or period-by-period. If period-by-period, the holding cost may be a function of maximum quantity held during the period, average quantity held during the period, or the quantity held at the end of the period.
We usually use the average inventory quantity during a cycle when dealing with holding cost.
Elaborate on shortage cost
Shortage cost is often called “the cost of unsatisfied demand”.
It is basically the cost of what happens when the demand exceeds inventory levels. In some cases, clients are willing to wait for the service or product. However, in other cases they are not willing to wait.
In some cases, clients will change buyer and never turn back if presented with such a case.
Shortage cost is very close to goodwill.
Shortage cost depends heavily on whether we assume backlogging or not. Backlogging allows us to store an order, and treat it when the merchandise arrives. This means that excess demand is not necessarily lost. Shortage, especially for wholesalers, will reduce goodwill. It will severely impact the client-store relationship.
In the case of no backlogging, we loose the demand. Consider the case where we need to buy a product for immediate use. IF the store does not have it, we will go somewhere else.
Elaborate on revenue as one of the factors of inventory theory
Revenue may or may not be included in the model.
If the demand and price is determined by the market and is far outside our control (the firm’s control), then the revenue will be independent of the inventory policy. Then we may neglect it.
However, if we neglect revenue, we must include “loss of revenue” in the shortage cost.
Elaborate on salvage
Can be either a cost or value. It is the value or cost that is leftover from products.
We typically assume that salvage value is somehow added into holding cost.
Elaborate on discount rate
This is essentially the time value of money.
We use a discount factor, alpha, to calculate the net present value of the costs or profits from some inventory policy.
What do we use as discount factor in short time frames?
1
What is the goal of an inventory policy?
Minimizing costs. Under the assumption that the firm has no control over price and demand, minimizing costs is basically the same as maximizing profit.
What is “lead time”?
Lead time is the time between placing an order to replenish the inventory, and when the goods are actually placed into the inventory.
Elaborate on different types of reviews
This is about how we monitor the inventory levels. is it continuous or periodic? If we use continuous, we can place new order as soon as some good reach a certain low-point. The same principle applies for periodic reviews, but of course at only these intervals.
In practice, it is common to use periodic with a low timeframe so that we approximate continuous review.
Name a common “inventory situation” that many organizations face
The most typical case goes like this: We have an inventory that have levels which will deplete over time, kind of smoothly in many cases, and then the inventory is replenished with what we call a “batch”. The batch brings the inventory level back up to some threshold we operate with.
What is EOQ?
Economic Order Quantity.
economic order quantity is the quantity that gives the minimized costs.
It is a model for representing inventory scenarios where stock levels are depleted smoothly over time, and then brought back up with a batch of new units.
Elaborate on the EOQ model
The model assumes that the stock levels are being depleted at a constant, known rate. We use the letter “d” to represent the rate at which stock levels deplete. Stands for demand. Therefore, “d” is “demand per unit of time”.
it is also assumed that the inventory levels are replenished when needed by ordering a batch of products, or ordering a batch of production. The important part is that the batch is assumed to be of fixed size, and we use the letter “Q” to represent the fixed batch size. The batch arrive alltogether at the same time.
For the very basic EOQ model, only 3 costs are of interest:
1) Set up cost, K
2) Unit cost, c
3) Holding cost, h.
The goal of inventory analysis using this model is to figure out how much to produce and when, so that we minimize these costs.
We also assume continuous reviews
What is the goal of EOQ model?
Understand how much inventory to replenish, and when, so that we minimize the 3 costs.
What are the assumptions of the basic EOQ model?
1) we assume a known, constant rate of demand per unit of time.
2) The order quantity Q arrives exactly when desired, and all together.
3) Planned shortages are not allowed.
The amount of time between placing an order, and to when the delivery is actually in the inventory, is called lead time.
The inventory level at which the order is placed is called the “reorder point”. To satisfy assumption 2, we do this:
ReorderPoint = demandRatePerTime x LeadTime
Reorder point refers to a level of inventory stock level when we should place the replenishment order. This is simple. DemandRatePerTime tells us how much we loose of our levels per time, and the leadTime tells us how much time the order requires. Thus, by placing the order at the point as given, we will replenish inventory levels exactly when it would have otherwise hit 0.
Elaborate on “reorder point”
ReorderPoint = demandRatePerTime x LeadTime
Reorder point refers to a level of inventory stock level when we should place the replenishment order. This is simple. DemandRatePerTime tells us how much we loose of our levels per time, and the leadTime tells us how much time the order requires. Thus, by placing the order at the point as given, we will replenish inventory levels exactly when it would have otherwise hit 0.
The reorder point is something we use in the context of the EOQ model. EOQ assumes constant lead time. this is important. If we do not have constant lead time, we will not be able to calculate the reorder point like this.
What is a “cycle” in this context?
A cycle is the time between replenishments.
The cycle length will be = BatchSizeUnits/demandRate = Q/d
This is universal, as long as d is constant.
Does the basic EOQ model include shortage?
no
What cost components are considered in the basic EOQ model?
Set up the EOQ formula
The ordering cost: K+cQ
The holding cost: hQ^2 /2d
On the holding cost:
The average inventory level during a cycle is: (Q+0)/2. we can do it this simple because we assume that the rate of demand is constant, linear.
Thus, the average inventory level during a cycle is Q/2 number of units.
NB: If we are just given a function of demand, we need to be careful when calculating the average number of units in the inventory during a cycle. The general procedure is to integrate the function over the cycle-interval, and divide by the length of that interval. This will give the average value.
Since the holding cost h, is per unit, we get this = hQ/2. This is per units. We need per cycle, so we multiple with the cycle size, which is the number of time units included in a single cycle. Since the cycle is Q/d, we get that the total holding cost is:
= hQ^2/2d
Then we get the total cost per cycle:
TC = K + cQ + hQ^2/2d
To convert this into total cost per unit of time, we divide by the cycle length, which gives us:
TC per unit = Kd/Q + dc + hQ/2
To find Q-star, the optimal level of Q, we differentiate and set equal to 0 (first order conditions). Doing this gives us:
Q-star = sqrt(2dK/h)
This is a known result.
We can also find the optimal cycle time, t-star: Q-star / d = sqrt(2K/dh)
When can planned shortages be used?
Only when customers are willing to accept the delay. In such cases, the firm is given the advantage of not having to pay that much holding cost, and the client is given what they want/expect.
We say that we have backlogging whenever this is the case. Backlogging allows us to create a sort of queue of orders that we immediatly perform when we order/receive the new batch.
Planned shortage can be utilized well whenever the firm has significant leverage in the deal. For instance, if we want to buy a MAC, would be forced to wait the time because nobody else satisfies these needs.
Note that there will always be some level of shortage costs, but they will be damn low in some cases.
In general, when does it make sense to consider planned shortage?
Whenever the holding cost is high relative to the shortage cost, it can be a good thing. Low shortage costs have of course baked in the fact that clients must not be bothered that much by the increased delivery time.
What changes do we make to the basic EOQ model so that it allows shortages?
We change the third assumption from “no shortage allowed” to “Planned shortage is now allowed. Customers will wait, the backorders will be filled immediately when the inventory is replenished”.
Graphically, what is the difference between the basic EOQ model that does not allow shortages, and the one that do allow shortages?
The model that doesnt allow shortages does not use a backlog, which means that it will never achieve negative inventory levels.
The EOQ model that actually allows shortage using backlogging, looks like the one in the image.
The key is to understand where the “top” is now. It is not Q anymore. it is S. “S” indicates the level of inventory just after the new batch of size Q arrives. Because we still assume constant, known demand, the only effect is a shift downward.
What components are included in the EOQ model that allows shortages?
Set up the functions and expressions
We have the following variables/constants:
Q: Batch size
p: shortage cost per unit of time short
d: demand, constant, known
S: inventory level just after a new batch arrives
Q - S: The negative inventory level just before the new batch arrives.
The production/ordering costs remains the same: K+cQ
The holding cost is now more complicated, because we have two cases to treat: The one where inventory levels are positive, and the one where inventory levels are negative.
During each cycle, the inventory level is positive for S/d time units.
The average inventory level during this time, is (S+0)/2 = S/2 units. Therefore, the holding cost per time unit is hS/2.
thus, the total holding cost per cycle is = hS/2 x S/d = hS^2/(2d)
BUT: Shortages occur as well. They occur for a time equal to (Q-S)/d
The average inventory level during this negative time period, is: (0-(S-Q))/2 = (Q-S)/2 units. The corresponding cost is p(Q-S)/2 per unit time.
this gives us shortage cost per cycle of p(Q-S)^2 /(2d)
Therefore, the total cost per unit time is:
= (K+cQ+hS^2 /(2d) + p(Q-S)^2/(2d)) / (Q/d)
= dK/Q + dc + hS^2 /(2Q) + p(Q-S)^2/(2Q)
In this model, there are two decision variables:
1) S
2) Q
We find these by finding first order conditions of the result above, and solving the system of equations that we get.
Elaborate on what’s happening on this image
The image shows 3 different total cost per unit time, at different unit prices. The solid lines represent where the curve is “active”. This is actually the only parts we care about.
We essentially want to find the lowest part of the solid line. In the case of the image, it is the curve corresponding to t2.
What happens is that we compare total cost. If we want the t3 unit cost to kick in/activate, we need to buy more than 80’000 units. t2 activates at 10’000 units. For less than 10k t1 applies. Therefore, we are evaluating the tradeoff between the different costs: holding vs ordering. More units equal more holding cost, while more units also gives the opportunity to gain discounts.
By looking at the lowest point of the solid line, we can find the point that minimize total cost overall, which gives us the number we need to aim for.
Recall that demand is baked into the curves.
