The SC Design-Planning Model

The SC design-planning approach follows the model developed in Chap. 2. In this formulation (Eqs. (2.1H2.28)), a four echelon SC is considered as shown in Fig.4.2. In this chapter, the equation expressing that part of the demand can be left unsatisfied because of limited production capacity (Eq.(2.4)) becomes one of the integrating equations as stated in Sect.4.3.4. 

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The value of ifijff a is Axed and constant, provided that all environmental impacts are directly proportional to the activity performed in that node (i.e variable of the SC design-planning model). This issue is common practice in LCA, where all direct environmental impacts are considered linear with respect to the functional unit... 

The stochastic SC design— planning model is presented next. This section has been divided in two parts (i) the scenario tree representation of uncertainty and (ii) the corresponding deterministic equivalent model. 

Here, the flexible design-planning approach presented in Chap. 5 is utilized. This model is suitable to collect all SC nodes information through a single variable, which facilitates the environmental formulation. This way SC nodes characteristics are modeled with a single equation set, since manufacturing nodes and distribution centers are treated in the same manner as well as production and distribution activities. The model s details are in Chap. 5. 

This chapter starts from the general framework for the SC design and planning presented in Chap. 2. Recall that such a framework is based on the development of a holistic model that covers two areas of the company process operations and finances. The model explicitly considers shareholder value as a design objective. The corporate value (CV) of the firm is calculated by means of the discounted-free-cash-fiow (DFCF) method and is adopted as the objective to be maximized. 

Equations (9.10)-(9.15) can be easily unplugged from the design-planning model in case the SC manager decides not to consider scheduling issues. 

A novel stochastic multi-period design/planning/scheduling MILP model of a multiechelon SC with financial considerations is used as a predictive model in this work. The model assumes that different technological equipment is available to be installed in potential sites and assists in their selection. Furthermore, the model allows the expansion of plant equipment capacities, not only in the first planning period. Regarding the financial area, the mathematical program endeavors to evaluate the shareholder value. 

The structure of the SC that is taken as reference to develop the mathematical model is illustrated in Fig. 2.3. The design/planning mathematical formulation is based on the work of Hugo and Pistikopoulos (2005) in which the authors presented a mathematical methodology that included life cycle assessment criteria as an additional objective to be optimized at the strategic level of the SCM. The model has been enhanced to allow the storage of products, and to include distribution center nodes in the supply chain network. The model equations are described in detail in the next sections. 

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 ... 

Next, the SC network design and planning is formulated as an ( L + l)-stage stochastic MILP, where L denotes the number of events that unfold throughout the planning horizon. The structure of the SC taken as reference to develop the mathematical model is illustrated in Fig. 7.4. The model is the stochastic extension of that presented in Chap. 2. The reader is referred to the aforementioned chapter for the detailed problem formulation, but for completeness and understanding, a brief description is provided here. 

The major regulatory factors that can influence strategic decisions in the design and operation of chemical SCs are introduced and classified by Oh and Karimi (2004). They model and highlight the effects of two important regulatory factors corporate tax and import duty on the capacity-planning decisions. 

Additionally, as indicated by Varma et al. (2007) there is a need to model financial planning decisions, R D resource allocation, as well as capacity expansion decisions within an integrated model, so that capital and capacity allocation can be performed simultaneously with R D projects selection and prioritization in order to enhance value generation. Certainly, R D decisions necessarily impact the design and the regular activities of the entire SC. Thus, such operational impact should be considered and assessed at the time R D and SC decisions are taken. 

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