Jianteng Xu, Qingpu Zhang and Qingguo Bai
The purpose of this paper is to find the best approximation algorithm for solving the more general case of single‐supplier multi‐retailer capacitated economic lot‐sizing (SM‐CELS…
Abstract
Purpose
The purpose of this paper is to find the best approximation algorithm for solving the more general case of single‐supplier multi‐retailer capacitated economic lot‐sizing (SM‐CELS) problem in deterministic inventory theory, which is the non‐deterministic polynomial (NP)‐hard problem.
Design/methodology/approach
Since few theoretical results have been published on polynomial time approximation algorithms for SM‐CELS problems, this paper develops a fully polynomial time approximation scheme (FPTAS) for the problem with monotone production and holding‐backlogging cost functions. First the optimal solution of a rounded problem is presented as the approximate solution and its straightforward dynamic‐programming (DP) algorithm. Then the straightforward DP algorithm is converted into an FPTAS by exploiting combinatorial properties of the recursive function.
Findings
An FPTAS is designed for the SM‐CELS problem with monotone cost functions, which is the strongest polynomial time approximation result.
Research limitations/implications
The main limitation is that the supplier only manufactures without holding any products when the model is applied.
Practical implications
The paper presents the best result for the SM‐CELS problem in deterministic inventory theory.
Originality/value
The LP‐rounding technique, an effective approach to design approximation algorithms for NP‐hard problems, is successfully applied to the SM‐CELS problem in this paper.
Details
Keywords
The purpose of this paper is to discuss some of the implications of policies, practices and new “non‐equilibrium” management approaches in mobile grassland management.
Abstract
Purpose
The purpose of this paper is to discuss some of the implications of policies, practices and new “non‐equilibrium” management approaches in mobile grassland management.
Design/methodology/approach
The author takes an actor‐oriented perspective on the narrative of land‐use practices, notional sustainable stocking rates and the problematic of state policy interventions in local context. The paper is based on two years in the field on a bilateral aid‐funded grassland management project at Xing'an League, Inner Mongolia and follow‐up among selected informants.
Findings
The constitution of grasslands “degradation” is in fact contested by resource users. Most grassland scientists, Party and Government officials in China have tended to associate ethnic “minority” mobile pastoralists with destructive cultural practices that, they argue, have led to ecological decline on the steppes. This argument is integral to the “degradation narrative” that underpins the discourse on grassland science. The conventional bio‐ecology emphasis on species dominance (growth‐form), in fact says little about the extent of anthropogenic impacts on above‐ground biomass and whether these factors have been the cause of degradation. The paper suggests that greater consideration is given to specific changes in human activity, climatic and plant productivity over time and space, based on endogenous, flexible seasonal estimates.
Research limitations/implications
Although presenting challenges to conventional grassland science based on endogenous experiences and herder practices, it may have specific geopolitical limits to more general scaling‐up in different contexts.
Practical implications
The paper discusses new modalities of non‐equilibrium grassland management, inverting normative top‐down approaches to controlling environmental degradation, livestock distribution and stocking rates.
Social implications
The paper suggests rethinking the use of customary practices, vernacular knowledge and the social organisation of herders in the design of sustainable grassland management.
Originality/value
The paper may be valuable to practitioners, rural development planners, funders and researchers interested in the use of integrated, cross‐disciplinary, new ecological knowledge in grassland management.