Scheduling of a Paper Mill Process Considering Environment and Cost

This study presents a new decision making method for scheduling paper mill processes, especially for the paper converting process. The optimal scheduling is analyzed with the multiobjective optimization programming (MOOP) using the summation of weighed objective functions (SWOF) [Ko and Moon, 2002]. In the production planning for the paper converting mill, making the strategy for the cutting paper is the bottleneck problem. In other words, how to cut papers efficiently with the raw paper reel is critical and this is called the trim loss problem. Environment (a waste amount) and energy cost are generally conflicting objectives. To reduce the environmental waste of the trim loss requires higher energy cost by moving the cutters. The MOOP is an applicable method to satisfy both objectives simultaneously. The MOOP algorithm includes normalization, SWOF and Pareto point analysis steps. The amount of trim loss and production cost are considered objective functions under the concept of taking into account both economy and environmental impact in its scheduling. The constraints are to satisfy with order, minimum profit level, etc.. Here, the compromised solution set is identified based on Pareto points. The decision maker can select the practical solution for scheduling of paper mill process with the satisfaction of both environmental and economic requirement. KEYWORD Cost, Environment, MOOP, Scheduling, Trim loss INTRODUCTION The paper making process normally involves five units: paper machine, coater, rewinder, sheet cutter and roll ream wrapper. Paper mill process has adopted heuristic methods or database of previous cutting patterns to satisfy various demands. However, these methods may not reduce waste material efficiently. The trim loss problem is important on an aspect of environmental issue. Generally it is impossible to have schedules which maximize environmental benefit (i.e., minimize waste) and minimize the operating cost simultaneously. In a conventional scheduling optimization problem, all process variables (for instance a waste amount) are converted into cost to find the minimum overall cost or the maximum profit. However in these days, environment is a vital issue and the importance of potential environmental impact is increasing. And trims are a problem themselves as wastes in environmental aspect. Moreover, inefficient use of raw material requires large storage capacity. Then pollutant generation increases. Hence, to minimize trim loss and cost simultaneously is very important in scheduling. This problem can be formulated MOOP problem, here, we represent a novel methodology using SWOF algorithm to seek optimal schedule in biobjective optimization problem and to find the ideal compromise solution set based on the Pareto point. Multiobjective Optimization Programming (MOOP) The general description for MOOP is as follows: [ ] ) ( ),..., ( ), ( ) ( min 2 1 x f x f x f x F n x = Ω ∈ (1) subject to 0 ) ( , 0 ) ( ≤ = x g x h (2) b x a ≤ ≤ where, n ≥ 2 and Ω is the constraint set, which denotes the feasible set of equality constraints, h(x), inequality constraints, g(x), and explicit variable bounds. A vector x* Ω such that f1(x) ≤ fi(x*) for all i {1,2, ..., n}. The characteristic of a noninferior solution set is that no decrease can be made in any of the objectives without causing a simultaneous increase in one or more of the other objectives [Ko and Moon, 2002]. There are several methods for MOOP, such as Summation of Weighted Objective Function (SWOF), ε-constraint method and Parameter Space Investigation Method(PSI), etc.. Among them SWOF method is used for MOOP in this study. The SWOF method minimizes a convex combination of objectives as following equations. ∑ = Ω ∈ = n i i i i i x x f f u 1 ) ( ) , ( min α α (3)