Planning deterministic models

Melo et al. (2005) propose a multi-period, deterministic, multiple-product MILP model for strategic supply chain planning. The model does not impose any restrictions on the number and type of facilities and the transportation links between facilities. The basic model explicitly covers relocation of capacity to new facilities. It can be extended to include capacity expansions and reductions. To this end, two fictitious, non-selectable facilities are introduced that provide additional or absorb excessive capacities. Capacity is assumed to be adjustable on a continuous scale but an extension to modular capacity is also provided. The model is very... 

The multi-period deterministic model that is developed next provides a flexible connectivity framework for the design of SCs. The model assumes that equipment is available for eventual installation at potential locations and assists in its selection. The model also allows the expansion of the capacities of the plant equipment, not only in the first planning period but also during any other period in which managers believe that opportunities to invest in facilities may result in a more favorable performance. The problem can be stated as follows ... 

Up to this point, it is assumed that prices are deterministic, which is true for contract demand and procurement but is not necessarily true for spot demand and procurement prices. Therefore, an important value chain planning requirement is the consideration of uncertain prices and price scenarios. Now, uncertain spot demand prices are under consideration and it is illustrated how price uncertainty can be integrated into the model in order to reach robust planning solutions. 

Air quality control r ions (aqcr s), 128 Air quality prediction models, 195, 678-79 airshed photodiemical, 218 balance-equation, 205 box, 213-15, 219 classification of, 200-205 criteria for selecting, 219-20 deterministic, 203 dispersion, 205 explanation of, 1% for episode control, 202 for land-use planning, 201-2 for physiochemical transformations, 208-10... 

The realization of the need and importance of petrochemical planning has inspired a great deal of research in order to devise different models to account for the overall system optimization. Optimization models include continuous and mixed-integer programming under deterministic or parameter uncertainty considerations. Related literature is reviewed at a later stage in this book, based on the chapter topic. 

The deterministic LP model was set upon GAM S and solved using C P LEX. Table 2.15 illustrates the computational results for the refinery Model. The planning model suggested producing 2000 t/day of gasoline, 625 t/day of naphtha, 1875 t/day of jet... 

The above discussion shows the importance of petrochemical network planning in process system engineering studies. In this chapter we develop a deterministic strategic planning model of a network of petrochemical processes. The problem is formulated as a mixed-integer linear programming model with the objective of maximizing the added value of the overall petrochemical network. 

In this chapter we presented an MILP deterministic planning model for the optimization of a petrochemical network. The optimization model presents a tool... 

We demonstrate the implementation of the proposed stochastic model formulations on the refinery planning linear programming (LP) model explained in Chapter 2. The original single-objective LP model is first solved deterministically and is then reformulated with the addition of the stochastic dimension according to the four proposed formulations. The complete scenario representation of the prices, demands, and yields is provided in Table 6.2. 

In Chapter 3 of this book we discussed the problem of multisite refinery integration under deterministic conditions. In this chapter, we extend the analysis to account for different parameter uncertainty. Robustness is quantified based on both model robustness and solution robustness, where each measure is assigned a scaling factor to analyze the sensitivity of the refinery plan and integration network due to variations. We make use of the sample average approximation (SAA) method with statistical bounding techniques to generate different scenarios. 

The analysis plan should specify not only how the analysis will be conducted, but also how the results will be presented. Indeed, the way results will be communicated will usually influence the choice of both model structure and analysis method and is ultimately driven by the information needs of risk managers and other stakeholders and their management goals (see Figure 2.2). Careful advance planning for the communication of results is especially important for probabilistic assessments because they are more complex than deterministic assessments and less familiar to most audiences. It may be beneficial to present probabilistic and deterministic assessments together, to facilitate familiarization with the newer approaches. 

The model proposed by Bhutta et al. (2003) is a multi-period, deterministic multiple-product MILP model integrating plant location, production, distribution and investment planning in a global environment. It is relatively simple both mathematically (no binary decision variables but integer production quantities) and with respect to the assumptions made for key modeling parameters. Capacity can be modified continuously without lower or upper bounds. International features are limited to exchange rates and tariffs. 

In a deterministic planning environment the most likely scenario, here scenario 2, would be considered the base case and the optimization model would be solved based on this scenario. The optimal decision would be to open facility 1 in period 1 and facility 3 in period 2 leading to a total profit of 2,590. To assess the robustness of this network to alternative demand scenarios the profit achievable with this configuration in case of the alternative demand scenarios can be assessed. In the example, for scenario 1 the overall profit would be 1,640 and for scenario 3, 2,765 respectively. Considered individually, the optimal decision for scenario 1 would be to open only facility 1 with a total profit of 1,880 and for scenario 3 to open both facilities 1 and 2 in period 1 with a total profit of 2,931. In order to explicitly incorporate the uncertainties caused by the different realization probabilities of the three demand scenarios, the optimization model can be extended into a two-stage decision with recourse ... 

None of preventive maintenance planning models considers constraints on resources available in process plants, which include labor and materials (spare parts). For example, the maintenance work force, which is usually limited, cannot perform scheduled PM tasks for some equipments at scheduled PM time because of the need to repair other failed equipments. Such dynamic situations can not be handled by deterministic maintenance planning models or are not considered in published maintenance planning models that use Monte Carlo simulation tools. 

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