Search Problem of the Reels Cutting Optimal Sequence

The primary production of pulp and paper industry factories is paper making. In accordance with process flowsheet, paper web, the length of which is limited from above and below, is wound around iron spools. Further, that paper web (is called also reel) is cut on winder (machine which is used to cut the paper/board on a reel) into great number of rolls with certain lengths of generatrixes are called formats. The number of rolls, which are born at the same time as the result of unwinding and cutting paper web, is called set of rolls. The important characteristic of all rolls in one set is its radius (length). Reel length should correspond to the all sets, which are forming its cutting. Such reels are so called standart reels. If sets are identical inside one reel, then reel length is multiple of set length.

Not all produced reels could be considered as standart reels, because paper web break could happen during production process, otherwise paper could have bad quality or damages. Such reels are called non-standart reels, after cutting which some paper is left on the spool. For the purpose of paper waste minimization and increasing the efficiency of production that paper web remainders are spliced together in such a way that obtained paper web could be used in the production.

The initial data for the task are information about sets to produce, as well as about available standart and non-standart reels. Let us to consider that sequence of spliced reels is one logical reel. After cutting such long logical reel it is necessary to take into account locations of splicing points that are formed as the result of paper web splices. Ideally it would coincide with the points of sets superpositions. For some sets, splices are allowed at the beginning, in the middle and at the end of roll.

The problem is concluded into synchronization of two flows, reels and products (sets), with taking into account the limitations for splices locations. The complexity of synchronization with minimum waste formation is that during generation of permutations, it is necessary to consider specific characteristics of the production line and equipment, including well-defined sequence of paper processing machines for one separately taken reel, limitations for possible reel dimensions, which can be processed on that machines, handling of parallel machines and others.