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A Primal‐dual Steepest‐edge Method for Even‐flow Harvest Scheduling Problems
Author(s) -
Liu ChiunMing
Publication year - 2002
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/1475-3995.00339
Subject(s) - mathematical optimization , time horizon , minimum cost flow problem , flow network , scheduling (production processes) , computer science , linear programming , flow shop scheduling , job shop scheduling , operations research , mathematics , schedule , operating system
The even‐flow harvest scheduling problem arises when the forestry agency has evolved into a rigid non‐declining even‐flow policy. In this paper, we investigate model formulation and solution strategies for the even‐flow harvest scheduling problem. A multiple‐objective linear programming problem is formulated for even‐flow harvest scheduling problems with multiple‐site classes and multiple periods. The aim of this problem is to simultaneously maximize a desired harvest‐volume per hectare for each period of planning horizon and the total economic return. A block diagonal constraint structure, with many sets of network sub‐problems and a set of coupling constraints, is identified in this linear programming problem. A longest path method for each of network sub‐problems and a primal‐dual steepest‐edge algorithm for the entire problem are developed. The developed algorithm has been coded in Borland C++ and implemented on a personal computer. An illustrative example is used to display the detailed procedure for the developed algorithm and a real‐world case study is used to show the trade‐off between desired even‐flow harvest volume policy and total economic return. Results show the potential benefits of this approach.