Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 73

Equivalently to the beginning of this chapter, we first consider the uncertainty‐free case. Then, the overall transportation cost per case is determined by

(2.15)

where is the loading cost, is the distance related cost, and is the distance between plant and market according to Table 2.1. Thus, the amount of product shipped for all combinations needs to be determined. As there are two plants and two markets, this results in four variables, and a total cost given by:

(2.16)

where the coefficients are calculated according to Eq. (2.15). The next step is to formulate the constraints. The constraints are that (i) there cannot be more supply than amount in stock and (ii) the market demands needs to be satisfied. Mathematically, this can be written as

(2.17a)

(2.17b)

Additionally, note that transport can only be positive. This results in the LP problem of the form:

(2.18)

the solution of which features the minimal cost of , and the corresponding transport amounts as

(2.19)