There are few works that adopt the total planning concept considering the areas
mentioned above. In a collaboration with a copper component manufacturer,
Hendry et al. (1996) have combined scheduling and cutting stock problems for
melting scrap metal and casting it as logs, and then for cutting logs into billets. A
two-stage solution procedure is proposed to minimize costs whilst meeting the
demand for billets at the bottleneck. Tachibana (1997) has dealt with the cutting
stock problem for the manufacturing process of the paper industry. The goals are
decreasing the paper loss, levelling of the weight of paper lots and decreasing the
number of lots. Savsar and Cogun (1994) have demonstrated that corrugated box
production plans must also consider the bottleneck bu er area between corrugater
and converting machines. They have formulated a linear programming model to
minimize trim loss, while considering the capacity limits of converting machines
and storage area. The model by Savsar and Cogun (1994), MSC, is applied in a
box factory located in Riyadh.
Although the MSC model is the ® rst to combine several aspects of corrugated
box production and has introduced a lot of new ideas, it has some shortcomings. The
purpose of this work is to remove some of its simplifying assumptions, and develop a
procedure to produce more implementable solutions e ciently. The rest of the paper
is organized as follows. In sections 2 and 3 we demonstrate the weaknesses of the
previous model and propose an alternative one. Following this is the solution
approaches to the new model. In section 5, we present experimental results.
Finally, section 6 contains concluding remarks.
2. Critique of the previous model
The objective of the previous model MSC is to minimize the total amount of trim
loss in one shift. An optimum solution may require the combination of several
cutting patterns, resulting in the production of several products with di erent
widths. Obviously, introducing a new product will require a set-up and will decrease
the operating time of converting machine. However, the constraints related to the
converting machine capacities in MSC assume that there will be only one type of
product to be produced at each machine group (one set-up) during one shift.
Furthermore, a trade-o study may be required between the total trim loss and
the number of set-ups in one shift.
Secondly, the MSC assumes that the bu er is one big area rather than being
made up of several conveyors and the storage area can be utilized continuously in
both directions. This means that, for example, three piles of paper each of 0.42 m
width can be stored side by side on two neighbouring conveyors each of 0.64 m
width. In reality, because of its dimensions, there is only one way to lay a carton
board on the conveyor, and that is lengthwise, i.e. its longer sides will be parallel to
the moving direction of the conveyor. Furthermore, the conveyors are loaded one by
one on the basis of `® rst available’ and unloaded to feed the related converting
machine group on the basis of `longest waited’ . Finally, the converting machines
are jointly operated, i.e. all converting machines in one group process the same
product until all the papers of this product are depleted on the conveyors.
The following example, taken from Savsar and Cogun (1994), clearly illustrates
both points. For the next 12 h production period, ® ve products V,W,X,Yand Zare
considered with di erent demands to be cut from ® ve paper rolls with di erent
widths. The total number of allowed cutting patterns is 73. The data for the products
and the results of the proposed solution are given in table 1. There are two AP-type
1582 A. Bolat
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