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Several studies have found methods of optimizing order allocation and trim loss in paper industry. However, the resulting solution may not be adoptable due to some widths of stocked rolls exceed or less than those required for acceptable scheduling. To meet actual customer demand and better suitability of results, a new decision model has been presented which can be used for simultaneous cutting of master reels and stocked rolls with limitation on cutting blades at winder. The objective is to fulfill customer need using minimum possible number of master reels and stocked rolls. The problem is solved by simplex method which generally leads to non-integer optimal solution. Phase-II is solved by a new method to make the final solution integer using binary programming. Mathematical and decision models are given and a numerical example has been solved to illustrate the applicability of proposed method.

One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

Network design and optimization problems for product flow appear widely in shipping and production applications. We present a new variation to such class of problems in which the shipping cost linked with a route depends not only on the product flow moving across that route but on the product flow on other routes in the supply chain network as well. Selecting a route with fewer hurdles increases the product flow effectiveness. We consider the entire supply chain network i.e., from raw material supply to production, finished products to warehouses and then to the demand points. We formulate an integer mathematical model and present computational results for a set of test problems arising from shipping and production applications to analyze how the model performs with the varying network characteristics.

Network design and optimization problems for product distribution appear widely in shipping applications with the main objective to minimize the shipping cost, as the product distribution accounts for a significant portion of the logistical costs. The impact of various factors (traffic factor, cross route costs, production time constraints and demand time for product) on the total cost are analyzed in this paper. The procedure developed leads to considerable improvement in terms of supply route selection, allocation of customers to production facilities, location of production facilities and minimizing the total cost. An integer LP mathematical model for multi-product flow is formulated and test problems are solved to analyze the performance of the model when the network characteristics are changed. The results obtained show that the performance of the model is efficient for all test problems.