An FPTAS for a single-item capacitated economic lot-sizing problem with monotone cost structure

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) production and backlogging cost functions. We omit concavity and convexity restrictions. Furthermore, we take advantage of a straightforward dynamic programming algorithm applied to a rounded problem

A single-item economic lot-sizing problem with a non-uniform resource: Approximation

We study a generalization of the classical single-item capacitated economic lot-sizing problem to the case of a non-uniform resource usage for production. The general problem and several special cases are shown to be non-approximable with any polynomially computable relative error in polynomial time. An optimal dynamic programming algorithm and its approximate modification are presented for the general problem. Fully polynomial time approximation schemes are developed for two NP-hard special cases: (1) cost functions of total production are separable and holding and backlogging cost functions are linear with polynomially related slopes, and (2) all holding costs are equal to zero.

Monitoring of rice agrophiocenoses in relation to their states

The aim of the research was to study the production process of rice agrophytocenoses and carry out their geoinformation monitoring to develop a methodology for automated mapping of their condition and forecasting yield. Small varietal differences in the productivity of photosynthesis of plants of intensive and extensive rice varieties on different backgrounds of mineral nutrition were noted. When a closed crop is formed, the nature of the distribution of assimilates over the organs of the plant and the shoot is the main physiological mechanism for the formation of different yields of the studied genotypes and their resistance to the effects of unfavorable environmental factors. With the onset of the flowering phase, the differences in the mass of panicle and stem of shoots in intensive and extensive rice genotypes are very significant. Research has been carried out to study the optical properties of cenoses of varieties and their relationship with the morphophysiological characteristics of plants and yield to monitor the state of their crops. It was shown that the value of the vegetation index (NDVI) has a positive relationship with signs of photosynthetic activity of plants and their nitrogen status. Linear regression equations have been obtained, which make it possible to assess the degree of relationship between yield and vegetation index NDVI