describes the assignment of every log assortment a to an ejection box
e and storage box s.(3)
(4)
(5)
(6)
(7)
(8) Objective function (3) minimizes the total transportation time, which in turn is calculated with the first constraints (4). The next constraints (5) ensure a feasible solution of the assignment for every assortment a and storage box s.
Constraints (6), (7) and (8) make sure that every assortment is assigned to exactly one ejection box and storage box and that on the other hand at most one ejection box and one storage box is used for an assortment.
Excel optimization process
The systematic used to solve this logistic problem is based on the transportation problem which is specified in VAHRENKAMP AND MATTFELD (2007). The aim of this study was to generate a system which offers an industry applicable solution to the problem of a logistic optimization. Both linear programming models (double-stage and single-stage) are two-layered. This means that parallel to the minimum transportation time a constraint, reflecting the box placement possibilities per assortment, is taken into account and is finally prioritized over the minimum transportation time. The combination with the lowest number is privileged.
Xpress optimization
To get the optimal material flow the problem is solved with Xpress, first with the double-stage approach and second, with a three indexed binary variable linear optimization model described earlier. After due consideration, it occurred that when looking at the whole assignment at once, a better solution could be gained. Therefore, when solving the single-stage approach the solution can be minimized compared to the double-stage approach.
The 5th Conference on Hardwood Research and Utilisation in Europe 2012
RESULTS AND DISCUSSION
To evaluate the quality of the test results, the generated data is compared with a solution which is obtained by classic manual planning. The former way of assortment allocation worked on an ad-hoc basis. The storage boxes were filled, depending whether they were empty or not, the factor of transportation time was not implemented here. The yard throughput is assumed to be equal over all dimensions.
Table 1: Comparable solutions of the log yard and box assignment problem
Assortment Original Excel Excel Xpress Xpress
Assortment Original Excel Excel Xpress Xpress
double-stage single-stage double-stage single-stage
1 1/- 1/- 1/- 1/- 1/- optimized log yard is the single-stage model, even though the double-stage model shows values, nearby. In the columns the ejector box and the storage box are given in dependence of the assortment. Ejector boxes 1, 2 and 3 contain oversize, undersize and metal infected logs. The single-stage models both perform the 10% time reduction if compared to the manual planning model. The two-stage models performed quite well. Anyway, only the Xpress version meets in this case the threshold of a 10% time reduction in comparison to the manual planning. Assuming this the Excel model meets the preconditioned target value of a deflection of less than 3%.
CONCLUSION
The Log Yard and Box Assignment Problem has been modeled in a new way which guarantees a production optimized and time transparent solution. The model is flexible enough to deal with variations of the production volume and intermittent blocked boxes. The solution methods of the problem are adapted to the variations, corresponding to the changes. From the test results it is evident, that the model facilitates with both, double- and single-stage algorithm, a solution superior than those achieved by annual planning. Even more the deviation of the optimization models of Excel and Xpress show low numbers, confirming the Excel model. Future work should be performed analyzing the gained data in comparison with real data. In practical application it is possible to confirm the exact generation of the optimization models. In this paper the model is based on feeding data and log storage yard spacing regulations meeting direct production data in contrast to theoretical approaches, which do not take advantage of structures in the problem data.
Nevertheless, the model presented in this paper shows a valuable way of solving logistic problems in wood products industry.
Further work should be done on the optimization of the lumber yard. The lumber yard shows a high variety of different species, grades and even more important, a high variation in turnover frequency.
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The 5th Conference on Hardwood Research and Utilisation in Europe 2012
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