Mathematical Optimization Model

Some models also include transportation mode selection (e.g., air freight, ship or truck transport, full container load or less than container load) either solely based on cost comparisons or also considering the trade-off between transportation costs and pipeline inventory or lead time (cf. Zeng 2002 Vidal and Goetschalckx 2000, pp. 106-107 Jayaraman 1998, pp. 474-476). Due to the limited importance of transport costs in specialty chemicals and the fact that products are typically transported between plants and markets in full container loads this level of detail does not provide additional insights. 

While raw material supply is usually taken for granted, some models also include vendor selection, vendor capacity constraints or vendor delivery reliability (e.g., Martel et al. 2005 Vidal and Goetschalckx 2000 Vidal and Goetschalckx 1996). 

In this chapter the MILP model that incorporates the aspects discussed in the previous chapter is presented. Chapter 3.4.1 introduces the notation used and Chapter 3.4.2 presents and discusses the model formulation. Extensions to the basic model are presented in Chapter 3.4.3. 

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Mathematical optimization models that explicitly consider such a multi-stage structure belong to the class of multi-stage stochastic programs. A deterministic optimization model with uncertain parameters is extended to a multi-stage model by three measures ... 

Assumptions on temporal allocation of cash flows and discounting period need to be consistent (e.g., beginning, middle or end of period) which is sometimes not the case in mathematical optimization models (cf. Erlenkotter 1981, p. 134). Generally, it is assumed that cash flows are realized at the end of a period. Alternatively, continuous payments can be assumed but the error caused by the year-end assumption is limited (cf. Brealey et al. 2006, pp. 46-48). 

The objective of using a mathematical optimization model is to identify network design alternatives that best exploit structural cost differences between various locations and resolve trade-offs between different cost elements such as production cost advantages and additional transporta-tion/tariff costs. Therefore, relationships expressing the costs that will be incurred as a function of cost drivers (decision variables of the model) have to be established. A proper creation of these cost functions is a critical success factor of the overall analysis (cf. Shapiro 2001, p. 234 Vidal and Goetschalckx 1996, p. 13). 

Gas supply system is defined by graph of 89 main pipelines. The natural gas is supplied to the system from two sources the debit of import from neighbor country is 31.2 MmVday and the other source is terminal of liquid natural gas, the debit is 11 MmVday. The mathematical optimization model (optimization of maximum flow with goal programing) is used to simulate gas supply system. 

Duffuaa, S.O., El-Ga aly, A. (2013). A multi-objective mathematical optimization model for process targeting using 100% inspection policy Applied Mathematical Modelling yi 1545-1552. 

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