More than half a century later, in the middle of the Second Industrial Revolution, it was a generation focused on building the future. Optimization of the (Q,R) model if the stockout costs depend on the size of the stockout.
Managing multiechelon chains: Installation us
Decisions on price: double marginalization .1 The first best solution: the vertically
The vertically disintegrated case
A way out: designing incentives and Decision on eflort to produce and sell the product
Concluding remarks
Final remarks 8.6 For further reading
Continuous random variables
Some continuous distributions A.5 Jointly distributed random variables
Independent random variables A.6.2 Covariance and correlation
Distributions obtained from the normal and the central limit theorem
Conditional expectation
Stochastic processes A.8 Parameter estimation
Sample covariance and correlation A.8.2 Confidence intervals
Hypothesis testing .1
Best fitting by least squares
Verification of the underlying assumptions A.lU.6 Using linear regression to estimate
B.2 Optimization models B.3 Convex sets and functions
Linear programming
- Branch and bound methods B. 6.2
For further reading
- WHAT DO WE MEAN BY LOGISTICS?
- Plan of the chapter
- STRUCTURE OF PRODUCTION/DISTRIBUTION NETWORKS From a physical point of view. a supply chain consists of possibly several stages
- C O M P E T I T I O N FACTORS, COST DRIVERS, A N D STRATEGY IVhen managing a supply chain, the natural aim is providing thc customer
- Competition factors
- T H E ROLE OF INVENTORIES
- DEALING WITH U N C E R T A I N T Y
- A two-stage decision process: Production planning in an assemble-to-order environment
- PHYSICAL FLOWS A N D T R A N S P O R T A T I O N
- INFORMATION FLOWS A N D DECISION RIGHTS
- T I M E H O R I Z O N S A N D HIERARCHICAL LEVELS
- DECISION APPROACHES
- QUANTITATIVE MODELS A N D M E T H O D S
- FOR FURTHER READING
- T H E ROLE OF INTERMEDIATE NODES IN A DISTRIBUTION NETWORK
- LOCATION A N D FLOW O P T I M I Z A T I O N MODELS
- The transportation problem
- MODELS INVOLVING NONLINEAR COSTS
- C 0 N T I N U 0 US- S PAC E LO CAT1 0 N M 0 D E LS
- RETAIL-STORE LOCATION MODELS
- FOR F U R T H E R READING
- INTRODUCTION
Lye believes it's actually a borderline case as it defines the "last mile" (i.e. %last echelon) of the consumer goods supply chain. To start with. the inventory manager in the distribution center sees a collection value for each item: this question also depends on it, in a potentially complicated way. on the transport pattern from distribution center to store i.. we have the additional problem of synchronization between inbound and outbound transport from the distribution center. in terms of 1) other fatigue and quantity.
- The forecasting process
For example, let's assume that we need to forecast demand for each of the next 52 weeks. You have introduced the five dimensions that identify the object of prediction.. ie. the variable we want to predict; but we still need to answer a key question: .. hat is the right choice for these five dimensions?. This simplistic analysis can lead us to believe that we should always try to collect dc.mand about product. time and locations to indeed reduce the prediction error. since the object of prediction is more total. the demand pattern tends to be more stable.
To properly set the parameters of the forecasting process, we should first understand the decision problem) we want. Thus, the retailer asks the manufacturer to temporarily cut the wholesale price (ie the price the manufacturer charges the retailer).
- The Mean Error
- Mean Absolute Deviation
- Theil's U statistic
Thus, the U statistic compares the error of the method we applied with the error that a simplistic model would generate. In the event that our model generates an n error greater than the naive's error, the U statistic is greater than 1. MAD% and RAlSE%) of the prediction model adopted by the company - and the performance of the nai' five method (Ft+l = Y,).
The idea behind this is to use a precision metric that is a good proxy for the company's cost function. In this case, we compare the performance of both forecasting methods over several periods.
These methods can therefore only be deployed when the relevance of the issue and the game justifies the use of such precious resources. The higher the demand forecast. the higher the stock level; this in turn implies more available products and easier sales. The company decided to reward them only based on the accuracy of the +3 meeks forecast (ie the forecast three weeks into the future), to make the incentive scheme simple.
Note that the role of the quantitative method is to (i) provide a point of reference so that the expert can focus only on the net effect of the new product launch on the demand for the existing one and (ii) take into account with the this is one of the fundamental problems with neural networks. Market research can also be one of the most important inputs to estimate the market potential of a new product.
MOVING AVERAGE
- The algorithm
- Setting the parameter
The moving average algorithm estimates the level demand (called baseline demand) Bt for the future as the average of the last k demand observations. A small k thus makes the moving average very responsive, but at the same time very serious. Figures 3.6 and 3.7 show how the moving average responds to an odd demand observation that differs significantly from the average.
This means that the time period is the single day and the forecast horizon is two days (h = 2). The store manager tries to predict future demand with the moving average algorithm. 0 If k = 5, the forecast generated in period 5 is the average of the demand in the first 5 periods.
- The algorithm
- Initialization
- Drawbacks and limitations
In the simple exponential smoothing technique. the current demand level is estimated by means of a weighted average of the last demand observation yt and the previous estimate of the demand level Bt-1. Note that as in the case of moving average, we continue to update the estimate of the demand level Bt. If Q changes, we indeed change the weight of the most recent demand observation yt and of the earlier demand forecast Bt-1.
On the contrary, for high values of a, the weight of observation Yt-1 is significantly lower than that of the most recent observation V,. The choice of the appropriate values of Q (and more generally the parameters of the smoothing algorithms) is a key to controlling and improving the forecasting progress.
- The algorithm
- Initialization
- Drawbacks and limitations
As for the trend factor, we will update the last period estimate with the last observation of demand growth (decrease). These two parameters can then be used to initialize the baseline and trend factors at time 0: Bo = a and TO = b. Once we have created a trend factor estimate, we can use it to make the demand 1 observations directly comparable and use them to initialize the underlying demand Bo.
As the forecast horizon h increases, the model is increasingly sensitive to possible errors in the estimation of the trend factor Tt. For example, when the base demand is Bt 100 units and the trend factor Tt is -40.
EXPONENTIAL SMOOTHING WITH SEASONALITY
- The algorithm
- Setting the parameters
- Initialization
- Drawbacks and limitations
So when we want to update the previous estimate of average Bt-1 demand with the June observation, we will calculate the seasonality of the specific month. If the seasonality factor is 2, we expect demand in December to be twice the average monthly demand. To update previous estimates, we will compare the last observation of demand Yt with the most recent estimate of average demand Bt.
The seasonal factors represent the difference between the demand in each specific month and the average month of the year. With this figure, we can now initialize the seasonal factors for the seven days of the week.
- The algorithm
- Initialization
In this case, the seasonality of April 6 does not depend on the specific weather conditions of April 6, but on the average condition of the week of April 6. Bt + hTt is the level of demand we would expect in period t + h. if there was no seasonality or the seasonality factor of that period was 1. Of course, if the seasonality index of these two periods is close to 1, this is a minor issue and has no practical effects.
On the contrary, in the event that the seasonality index is significantly above or below 1, it is a major concern and it is more appropriate to use at least 2s of demand observations, that is, two whole seasons. We can now use the above estimate of trend TO to tell the effect of trend of seasonality and thus estimate both the s seasonality factors and the baseline demand Bo.
SIMPLE LINEAR REGRESSION
Also. the selection of the parameters will follow the same process (they can be accurately predicted). Indeed, a perfect estimate of the parameters leads to a perfect estimate of the expected level ( a + P.0) of the demand YO. Therefore, any error is due to misestimation of the parameters, rather than the randomness of the query process.
The definition of a shows that the estimated line passes through the centroid of the demand observations (z; Y. Thus, the errors in the slope estimation (Seeb) have no effect on the imprecision of the demand when xo = Z.
- FORECASTING D E M A N D FOR N E W PRODUCTS
One of the authors simulated the committee process with a group of managers from different companies. So, in the basic Delphi method, panelists interact only through the administrator of the Delphi process. 0 Analysis of the responses in the second round (Steps 5 to 7 are repeated as long as desired or necessary to achieve stability in the results).
After each round of the questionnaire, the responses are analyzed and the panelists are given a summary of the responses (eg, the mean response, the standard deviation, and where he/she is in the distribution). When the first round is completed, the panelist gets the distribution of the answers and he/she finds out that other experts do not share his/her vision of the future.
Concept 3.5 The Delphi method relies on experts' knowledge to forecast, and it is designed to control social interaction in such a way that the signal about
The early sales model
To do this, one must estimate the ratio between the demand in March and the demand for the entire season. One can study the past relationship between these two variables to see if actual demand in March is a good predictor of total seasonal sales and, if so, estimate the relationship. More formally, let Y,t be the demand for item i at time t within the season, T be the length of the marketing year, C,t be the cumulative demand for item z at time t, and P,.t be the percentage of the total . seasonal sales of item where I took place.
We simply note that over time we tend to sell a certain percentage of the season's total sales. 33. We can then use this percentage carried curve to estimate the season's total sales for the new product j as.
THE BASS MODEL
Therefore, the probability that a potential user adopts a product at time t depends on the rate of innovative adoption and the rate of imitation multiplied by the percentage of current users. There are essentially two adoption probabilities, and the second is fully distributed only when the number of actual adopters reaches a maximum level m: p+q is the "last party" adoption probability. This probability of acceptance is multiplied by the number of potential new customers who have not yet accepted the product: 3.51).
In the case of q = 0 there is no imitation and thus the percentage of customers who adopt the product is stable (see figure 3.30). This means that the adoption pattern follows a logarithmic curve (see figure 3.31) and demand is decreasing since we have a constant probability of adoption but a decreasing number of potential adopters.
