Expected Cost Model

This model estimates the expected cost per unit time of maintaining the equipment on an inspection regime of period T. The probability of a defect arising as a breakdown failure is given in Equation (8.1) as b(T). As an inspection repair cost applies to all components even if the component is in good condition, the probability of fault arising as an inspection repair is 1 -b(T). 

There are three cost elements which need to be considered in this modelling phase. These three elements are (Pillay (2001), Pillay et al. (2001a, b))  

Using the same assumptions and notations described in Section 8.5.1, Equation (8.4) is modified to include the various costs involved in an inspection maintenance regime to give  

C(T) = the expected cost per unit time of maintaining the equipment on an inspection system of period T. 

---

The Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Management (BMLFUW) commissioned various studies, showing that almost 4000 Austrian companies would basically qualify for the application of Chemical Leasing models, cutting today s annual use of 150,000 tons of chemicals by one third. On average, the user of such new business models can expect cost savings of approximately 15%. 

Monte Carlo techniques were used to account for uncertainty and variability in individual cost elements—a facet of the nascent nature of this technology. Figure 2 shows the model results for expected cost. Levelized hydrogen costs are estimated at around 3.70/kg. Further work will be undertaken during the design phase to review these cost factors and revise the model. 

Can we predict these costs beforehand If a conrpany is considering committing capital to a new project, then in order to determine if that capital investment would be a vise one, that is, one that would meet expected rates of return and would be superior to placing the capital in other investments or projects, modeling of the new process must be done to calculate the expected costs of production. This modeling must begin with kinetics. 

Performing a steady-state simulation experiment implies that the analyst is interested in long-run performance of the model that is independent of the initial conditions of the simulation replication or run. In the inventory simulation the parameter of interest is the long-run expected cost per period of inventory policy which does not depend on the inventory position in period 1. 

Industrial engineers frequently use simulation experiments to compare the performance of alternative systems and, ideally, to optimize system performance. When a system is modeled as a stochastic process, the objective is often to optimize expected performance, where expected means the mathematical expectation of a random variable. This section describes methods for optimization via simulation, using the problem of selecting the inventory policy that minimizes long-run expected cost per period as an illustration. 

More critictilly, the point estimate derived without CRN is positive, indicating that policy 2 yields the smallest expected cost, while the point estimate derived with CRN is negative, indicating that policy 1 is superior. For this simple model it can be shown that policy 1 does have the smellier expected cost, so the use of CRN leads to the correct decision. However, in both experiments the 95% confidence interveil for the difference contains 0, so it cannot be stated conclusively that policy 1 is best based on the data. Additional batches are needed to reduce the error even further. 

However, if all plants and warehouse capacities remain, then the model can be optimized with the new cost parameters. The new optimal solution is to operate only PI and Wl and thus have a cost of 895,000. If there was an 80% chance of such a cost change, then the expected cost with all plants open would be (0.2 X 1,370,000) + (0.8 X 895,000) = 990,000. Thus, the slack capacity offers the flexibility to respond to such cost-reducing opportunities and decreases expected cost. 

Intuitively, the supply chain manager chooses a capacity level that sets the expected revenue associated with increasing capacity equal to the expected cost associated with increasing capacity. Thus, following the newsvendor model, the optimal capacity has to satisfy... 

As we have seen, minimization of the total expected costs in the models by Van Dantzig and Eijgenraam leads to optimal investment strategies, but leaves a large uncertainty for the actual costs of future floodings. Therefore it can be desirable to choose an investment strategy which is less optimal, but of which the outcome is less uncertain. To take this uncertainty into account the variance of the total costs is included in the... 

One of the main results of this analysis is the fact that the assumption of a non-homogeneous Poisson process to describe the occurrence of floodings over time leads to elegant equations for both the expectation and the variance of the discounted costs (Eqns. 12 and 13). These formnlas were nsed to (analytically) calculate the standard deviation of the costs in the cost-benefit models by Van Dantzig and by Eijgenraam. As e q)ected, the variance of the costs in the strategy with the lowest expected costs, turns ont to be qnite large. 

A traditional approach for solving this problem is to apply availability and cost modelling as described by e.g NORSOK (1998), Wang Pham (2006) and Aven Jensen (1999). An optimal maintenance poHcy is determined minimi zing some optimisation criterion, for example the expected long run cost per unit of time or the total expected discounted cost. Constrained optimisation criteria have also been suggested, for example the minimisation of expected costs while some system reliability requirement(s) are satisfied, or the maximisation of system reliability when some cost require-ment(s) are satisfied see e.g., Wang and Pham (2006). 

This paper focuses on the difference between relevant maintenance scenarios in terms of system production. Another important aspect in many cases could be safety and environmental issues. This is more difficult to quantify than production but if it is applicable to the system of interest the optimal solution can not be found without taking it into account. If this is to be integrated into one large cost model, more input is necessary, namely the expected (discounted) cost of e.g. production loss, environmental spill and accidents of various severities. 

Figure 17.10 depicts a black-box view to the optimization procedure for complex products. The inputs for the optimization procedure are a product model, a cost model and sales figures. The product model represents the product data and the cost model assigns certain cost values to the product model. The sales figure is a list of product variants that are expected to be sold or were sold in a defined time period. 

Zhou et al. [61] described production planning of multi-location plant and distributors on condition that unit production cost, production capacity and demand are fuzzy parameters. They built up a fuzzy expected value model and fuzzy related chance-constrained programming model in consideration of different decision criteria and discussed a clear equivalent form of the fuzzy programming model when... 

In this section, we formulate the model for disaster preparedness decision making, with consideration of the expected outcomes of the response stage. The decisions that are made before a disaster hits are usually made with consideration of all possible scenarios, while decisions that are made afterward must depend on the actual scenario. To allow for this uncertainty, we calculate the expected costs for each of several scenarios. Stochastic programming allows for several different decisions to be integrated. 

In the MOO (multiobjective optimization) method expected cost and robustness measure are simultaneously optimised. The robust model is based on the stochastic model (Eq. 10, with a = 0) having an additional objective of controlling the variability of performances of individual scenarios. The worst-case scenario is taken as the objective variable for the robustness measure and a decision-making procedure is applied to choose the best robust design alternative for the case study. 

To provide a comprehensive optimization of time period T, the analytical model was developed (for the case of perfect inspection). Taking into account the additional assumption, that inspection action performance begins the new maintenance cycle for the analyzed system, the expected costs of n-element system maintenance in one inspection cycle are defined (Jodejko-Pietruczuk and Werbihska-Wojciechowska, in press) ... 

---