Design-planning formulation

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 material balance must be satisfied in each of the nodes that integrate the supply chain network. 

Equation (2.1) represents the material balance for each raw material r consumed at each manufacturing site s in every time period t. This equation states that the purchases of raw material r provided by suppliers e (Er) together with the initial inventory kept at the site must equal the inventory at the end of period t plus the quantity consumed by the manufacturing tasks. Note that this equation should be only applied to those products consuming raw material r and manufactured in equipment j of plant s (i e (Ij n Ir)). 

The mass balance for final products i in each manufacturing site s is enforced via Eq. (2.2). This expression states that the amount of final product manufactured at each site during a given time period t and the initial stock of the product must equal the final inventory of the product and the amount delivered from the site to the distribution centers w. 

Equation (2.3) states the material balance for distribution centers w. This equation makes the total amount of final product i coming from all sites s plus the initial inventory of the product kept at the distribution center must equal to the final inventory plus the sales in final markets m. 

---

Similarly to the Design-planning formulation, the financial formulation follows that presented in Chap. 2 (Eqs. (2.29)-(2.60)). Such formulation uses the discounted-free-cash-flow (DFCF) method in order to carry out the firm s valuation. Again, the formulation has been extended to consider the different scenarios associated with clinical trial outcomes by adding the extra index g to each variable. However, some modifications are required to incorporate the costs of development projects (RDcostirjictg, ei,c)tg) and some equations must be included so as to calculate the expected CV as well. This set of modified and new equations are described next. 

Table 3.5 2 Full Factorial Design for the Formulation of an Oral Solution (a) Experimental Design, Plan and Results (Turbidity)... 

This FOM procedure uses classical TQM techniques to brainstorm, rank, and formulate an equation that will score producibihty, assemblabUity, or any other measure that can be used in design planning. The two factors used in the producibility score are made up of the (1) the coefficient, Cx, and (2) the factor weighting, FWx. 

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. 

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. 

Thus, the SC network design-planning problem whose objeetive is to optimize a given set of objective functions can be mathematically formulated as shown below ... 

The Optimal Condition Decomposition (OCD), which is a particular case of the Lagrangian relaxation procedure, is applied to overcome the computational cost of solving the monolithic problem which integrates the design, planning, and scheduling formulations. Further details about this decomposition strategy can be found in Sect. A.7.1 of the Appendix A. 

A pesticide formulation plant should prepare and implement an emergency preparedness and response plan that takes into account neighboring land uses and the potential consequences of an emergency or accidental release of harmful substances. Measures to avoid the release of harmful substances should be incorporated in the design, operation, maintenance, and management of the plant. Pollution control equipment employed in this sector include baghouses for removal of particulate matter and carbon adsorption for removal of VOCs. 

The best way to ensure that your plan for PSM design, development, and installation will mesh with local culture is to rely heavily on local management in formulating your initial plan. In some situations, the best approach may prove to be direct importation of PSM systems developed elsewhere, while in other situations you may serve as a resource to a local team that engages in its own design process. 

The design of subsequent experiments depends on one s early findings thus, care and skepticism must be exercised at the outset. From the first result in the laboratory, the investigator begins to formulate a model and to make plans to test it. Learning how to do so is a major goal for a person doing work in kinetics. 

---