Mathematical Modelling for the Supply Chain System

In this chapter, the DSC and ISC will be represented by mathematical modelling, with the uncertainties noted in Chapter 5. There are four sub-models including a customer order model, a production model, a raw material ordering and transportation model and a finished goods satisfying customer demand and transportation model. 

After formulating four sub-models, the SCP including the SC total cost and CSL will be defined mathematically. Finally, parameterised and non-parameterised strategies that will be used to manage the SCM issues are introduced. 

In this section, the notation in the models is introduced, classified into several categories including static input variables, decision variables, state variables, time uncertainty related variables, quantity uncertainty related variables, dynamic input or derived variables, cost coefficients and performances indicators. 

T the maximum number of periods placing domestic customer orders in advance  

Uo(t) the planned production quantity for finished goods at period 

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Markov chain and process model (Augutis Uspuras 2006), where transition probabihties depend only on the current system state, were selected as the basic mathematical apparatus for development of mathematical model of energy supply disturbances in network system. 

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