Using Lagrangean Techniques to Solve Hierarchical Production Planning Problems

1982 ◽  
Vol 28 (3) ◽  
pp. 260-275 ◽  
Author(s):  
Stephen C. Graves
Keyword(s):  
Production Planning ◽  
Hierarchical Production Planning ◽  
Planning Problems

Hierarchical production planning in forestry using price-directed decomposition

2007 ◽  
Vol 37 (10) ◽  
pp. 2010-2021 ◽  
Author(s):  
Samuel D. Pittman ◽  
B. Bruce Bare ◽  
David G. Briggs
Keyword(s):  
Production Planning ◽  
Net Present Value ◽  
Forest Planning ◽  
Planning Model ◽  
Data Set ◽  
Decomposition Approach ◽  
Hierarchical Production Planning ◽  
Production Models ◽  
Planning Models ◽  
Land Inventory

Forest planning models have increased in size and complexity as planners address a growing array of economic, ecological, and societal issues. Hierarchical production models offer a means of better managing these large and complex models. Hierarchical production planning models decompose large models into a set of smaller linked models. For example, in this paper, a Lagrangian relaxation formulation and a modified Dantzig–Wolfe decomposition – column generation routine are used to solve a hierarchical forest planning model that maximizes the net present value of harvest incomes while recognizing specific geographical units that are subject to harvest flow and green-up constraints. This allows the planning model to consider forest-wide constraints such as harvest flow, as well as address separate subproblems for each contiguous management zone for which detailed spatial plans are computed. The approach taken in this paper is different from past approaches in forest hierarchical planning because we start with a single model and derive a hierarchical model that addresses integer subproblems using Dantzig–Wolfe decomposition. The decomposition approach is demonstrated by analyzing a set of randomly generated planning problems constructed from a large forest and land inventory data set.

MINIMUM AVERAGE COST PRODUCTION PLANNING IN STOCHASTIC MANUFACTURING SYSTEMS

1998 ◽  
Vol 08 (07) ◽  
pp. 1251-1276 ◽  
Author(s):  
SURESH P. SETHI ◽  
HANQIN ZHANG ◽  
QING ZHANG
Keyword(s):  
Control Problem ◽  
Production Planning ◽  
Average Cost ◽  
Production Cost ◽  
Manufacturing Systems ◽  
Production Control ◽  
Production Capacity ◽  
Production Rates ◽  
Planning Problems

Recently, the production control problem in stochastic manufacturing systems has generated a great deal of interest. The goal is to obtain production rates to minimize total expected surplus and production cost. This paper reviews the research devoted to minimum average cost production planning problems in stochastic manufacturing systems. Manufacturing systems involve a single or parallel failure-prone machines producing a number of different products, random production capacity, and constant demands.

A new project scheduling approach for improving multi-product multi-period production planning problems

2008 ◽  
Vol 222 (11) ◽  
pp. 1517-1527 ◽  
Author(s):  
S Noori ◽  
M Bagherpour ◽  
F Zorriassatine ◽  
A Makui ◽  
R Parkin
Keyword(s):  
Production Planning ◽  
Project Scheduling ◽  
Resource Constraints ◽  
Simulation Analysis ◽  
Analytical Models ◽  
Hybrid Solutions ◽  
Demand Fluctuations ◽  
Feasible Solutions ◽  
Operational Criteria ◽  
Planning Problems

The problem of matching production levels for individual products to demand fluctuations during multiple periods is known in the production planning literature as the multi-product multi-period (MPMP) problem. Linear programming (LP)-based solutions have been extensively reported in this respect. MPMP problems are commonly solved by using either analytic or simulation methods. More recently, hybrid solutions consisting of both analytical models and simulation analysis have been proposed where some operational criteria, e.g. the order of visit to machining centres, are taken into account. In this paper, results related to some of the literature based on hybrid solutions are used as the initial feasible solutions and then examined in the context of project scheduling by considering the influences of resource constraints. After converting the MPMP to a project network problem and assigning resources to activities and consequently levelling the resource profiles, it is discovered that machine utilization can be further improved by applying unused machine capacities. A LP model is therefore developed in order to maximize feasible production rates over all the production planning periods. The proposed approach results in improvements on the results of earlier hybrid solutions reported in the literature. Finally, three different planning problems are suggested for further applications of the proposed approach in the context of manufacturing environments.

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