Sequence of decisions

The following decision tree shows a logical sequence of decisions (shown in the rectangular boxes) and chance outcomes (chance events are represented by circles). At each decision point, petroleum economics is applied to determine the choice, with the criterion being to achieve a positive EMV. 

In the first part of this chapter (Section 9.2), we present an uncertainty conscious scheduling approach that combines reactive scheduling and stochastic scheduling by using a moving horizon scheme with an uncertainty conscious model. In this approach, it is assumed that decisions are made sequentially and that the effect of the revealed uncertainties can be partially compensated by later decisions. The sequence of decisions and observations is modeled by a sequence of two-stage stochastic programs. 

The sequence of decisions obtained from the scheduler for all possible evolutions of the demand for the three periods is shown in Figure 9.4. The plant is started with an empty storage Mq = 0, no deficit from previous periods dp = 0, and the plant operation state on . The boxes contain the production decisions for each period while the circles contain the total objective after three periods for each scenario. The average objective value over the eight scenarios after three periods results as P = —16.05. The small figures on the right provide the evolution of the storage Mf, the deficit Bf, the late sale Mf, the sale Mi, the production x , and the objective p per period for each scenario. 

The difference between the expected demands d used in the model and the realization of an actual demand d causes a model mismatch. The scheduler corrects this error after the observation of this demand in a reactive manner by the production decisions taken at the beginning of the next period. For example, the decisions taken in period i = 1 take the expected value of the demand di into account (di = 6) while the decisions taken in period i = 2 take the true value into account. When di = 0, the large storage causes a relatively low production in the next period [xiih) = 5) whereas in case of d = 12, a deficit results and the production of the next period is larger (x2(t2) = 12). The sequence of decisions is a function of the observed demands and thus the sequence varies over the scenarios. 

The sequence of decisions obtained from the scheduler (Figure 9.4) has a tree structure. This structure results from the scenario tree of the uncertain demand parameters (Figure 9.3). Due to the moving horizon scheme, the decisions and the observations alternate at each period and the decisions are functions of the observations. Each point in time where a decision is made is called a stage. The result is a multi-stage tree where each stage corresponds to a period. 

Fig. 9.4 Deterministic scheduler sequence of decisions and results for all scenarios (average objective after three periods P = —16.05).

However, the description of the tree structure of a multi-stage model leads to complicated constraints. To simplify the original multi-stage model, it is approximated by a model with two stages. It consists of only one sequence of decisions-observation-decisions. The two-stage structure leads to considerably simpler optimization problems. It is also adequate from a practical point of view in the moving horizon scheme, only the first decision x is applied to the plant while all the remaining variables are used to compute the estimated performance only. 

This paper reflects the past activities of some of its authors in computer modeling of the chemical aspects of biological systems. This activity requires expertise in both model-building and in the relevant biology. It also involves examination of the actions of and results obtained by experts, like that routinely done in building expert systems. It also involves keeping track of and coherently explaining sequences of decisions, which expert systems are equipped to do. 

Using the criteria discussed above, we wish to select the easiest method of calculation which is both feasible to apply to the molecules of interest, and whose results are sufficiently accurate to describe the relevant experimental results. We have found it convenient to organize this selection process into a flow chart, which is given in Fig. 1. Starting at the top, one makes a sequence of decisions based upon the criteria for feasibility and accuracy. Decisions about the relative ease of different methods are not made explicitly they are implicit in the organization of the flow chart. 

Consider the optimal sequence of decisions Di, D2,. . . Du l, Du, all as yet unknown. The first (M — 1) of these optimal decisions, together with the given initial state S1, not only would determine an optimal state Su for the last stage, but also yield Y1, Y2, associated with... 

To appreciate the effectiveness of this method, consider the case where the decision d( at each stage must be chosen from among k possibilities. Then there are in all kM different sequences of decisions possible for the M stage problem. For every possible state su at the last stage, all but one of the k possibilities is eliminated by analysis of the last stage. Thus the number of sequences to be considered is reduced by a factor of 1/fc. In, fact, the number of nonoptimal sequences eliminated is kM — kM/k = (fc — l)fcaf 1. When k is 10, for example, the analysis of the last stage of a five-stage decision process eliminates 90,000 sequences out of the 100,000 possible. 

For TV stages a suitable sequence of decisions would be as follows. 

Sequence of decisions leading to final choice of welding diagram. 

Both test and inspection are from Latin roots, with the former defined by Websters as to view closely in critical appraisal look over, and the latter implying a critical examination, observation, or evaluation or a procedure, reaction, or reagent used to identify or characterize a substance or constituent. Precision, depth, and validity are key elements in these definitions, wMle reliability appears of necessity in a manufacturing context where a sequence of decisions is required. To differentiate between test and inspection, test typically requires a determination of functional suitability for use, while inspection is more usually confined to indications of fitness for purpose short of actud use testing. For example, each new aircraft produced will be flight tested before delivery to determine whether it fulfils its functional requirements. Prior to this flight test, considerable inspection of components and subassemblies will have taken place to ensure that they are free from manufacturing or assembly defects. 

Dynamic decision problems often have as objective to maximize the sum of the rewards obtained in each time period, or equivalently, to minimize the sum of the costs incurred in each time period. Other types of objectives sometimes encountered are to maximize or minimize the product of a sequence of numbers resulting from a sequence of decisions, or to maximize or minimize the maximum or minimum of a sequence of resulting numbers. 

Decision-making processes do not determine individual optimal decisions but an optimal sequence of decisions (policy) with regard to the target system (Bamberg et al. 2008). In order to reduce the overall computing time, one attempts to decompose the simultaneous optimization of a sequence of decisions into a sequence of individual decisions, which can be optimized a lot easier (Bamberg et al. 2008). For this purpose, the method of dynamic optimization is used (Bellman 1957 Sniedovich 2011). 

From this hst, it wdl be clear that depending on the circumstance the content and order of the steps will be different in general also quite some iterations wdl occur. Moreover, next to this sequence of steps dedicated to the direct engendering of the product, there is also a clear need for market research and marketing analysis. In any case, the product development cycle has to be accompanied by an adequate requirement specification. Often, the product development fife cycle is seen as a sequence of decision-making processes. 

The sequence of decisions for the design of a countercurrent washing train... 

The stochastic problem is characterised by two essential features the uncertainty in the problem data and the sequence of decisions. In our case, the demand is considered as a random variable with a certain probability distribution. The binary variables associated to the opening of a plant/warehouse as well as the continuous variables that represent the capacity of plants/warehouses are considered as first stage decisions. The fluxes of materials and the sales of products are taken as second stage or recourse variables. The objective hinctions are therefore the expected net present value and the expected consumer satisfaction. 

The sequence of decisions is as follows. For a given w, the retailer determines her reaction function by maximizing her expected profit in Q. The manufacturer s reaction function is then obtained by maximizing his expected profit in w, subject to... 

The sequence of decisions to be made covers several fundamental points. The first is the need to be clear about service conditions, based on experience or plant data. This is the key to material selection. The second decision is the choice of application process for the material. This involves the question of compatibility with the coating material that is, not all materials can be applied by all processes. A further question of compatibility arises between both material and process with the substrate, for example, whether distortion from high-temperature processes be tolerated. All these issues are covered in subsequent chapters in this book (see, in particular. Chapters 7 and 8). 

Figure 2. Flowchart showing the sequence of decision steps to be taken in the tackling of a particular analytical problem.

Blake, the sole survivor of the Wilberg fire, was inby the fire when the fire started. His handwritten report describes the sequence of decisions that saved his life as he moved from a position inby the fire to a safe position outby the disaster. 

For the given reorder time t, the decision process involves choosing Qi, observing x and then determining the inventory position I for the remainder of the season to minimize total backorder, understock and overstock costs. This sequence of decisions is shown in Fig. 1. 

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