Stability of the optimal schedule for perishable product processing

Abstract

In linear programming tasks, the optimal solution can remain the same even with a significant deviation of the initial data. Thus, when studying various problems in economic and mathematical analysis, the question of the optimal solution stability often arises. The problem of finding the optimal schedule for processing perishable products is solved below. For example, we could refer to sugar beet, an important strategic product that degrades during storage, losing sucrose over time according to some law, depending on time and (or) variety. Other things being equal, with an increase in incoming sucrose, the yield of the final product - sugar, also increases, therefore, by maximizing incoming sucrose, it is possible to significantly increase the production profitability. In practice, equipment often breaks down, therefore, the processing of raw materials stops for a while, but not its degradation. In this regard, the optimal schedule after the production resumption may change, or it may remain the same. Definitions of the optimal schedule stability are given. It is proved that the optimal schedules for the main special cases are absolutely stable. Examples of conditional stability and local stability for a period are given, as well as a numerical experiment showing averaged absolute and relative losses for various parameters of raw materials batches and various periods of production stoppage.