| 1. |
- Aardal, Karen, et al.
(författare)
-
Decomposition principles applied to the dynamic production and work-force scheduling problem
- 1987
-
Ingår i: Engineering Costs and Production Economics. - 0167-188X .- 1878-4011. ; 12:1-4, s. 39-49
-
Tidskriftsartikel (refereegranskat)abstract
- One of the most important problems in the production and inventory planning field, is the scheduling of production and work force in a dynamic environment. Although this problem can be formulated as a linear program, it is often quite difficult to solve directly, due to its large scale. Instead, it might be fruitful to use a decomposition approach. Decomposition, in general, means decomposing a difficult problem into several easier, or a sequence of easier problems which are later coordinated to reconstruct the original problem.In this report we discuss several possibilities of applying the most common decomposition principles, namely Benders (primal) and Datnzig-Wolfe (dual), as well as a relatively new decomposition method, called cross decomposition, to the dynamic, multiproduct production and employment planning problem. A number of special cases are also presented.
|
|
| 2. |
- Aardal, Karen, et al.
(författare)
-
On the resemblance between the Kornai-Liptak and cross decomposition techniques for block-angular linear programs
- 1990
-
Ingår i: European Journal of Operational Research. - : Elsevier BV. - 0377-2217 .- 1872-6860. ; 46:3, s. 393-398
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper the resemblance is demonstrated between the master- and subproblems generated by the Kornai-Liptak algorithm and the subproblems obtained by using the cross decomposition method on linear optimization problems with block-angular structure. The significance of the similarity between these two algorithms becomes apparent considering the main disadvantage attributed to cross decomposition. In cross decomposition a master problem has to be solved from time to time since the subproblems alone do not always give a converging sequence of primal and dual solutions. But if the cross decomposition algorithm is modified in such a way that the successive primal and dual subproblem solutions are taken into consideration with equal weights, this results in the Kornai-Liptak algorithm for which convergence is guaranteed
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
- Ari, E. Aysen, et al.
(författare)
-
Disaggregation under uncertainty in hierarchical production planning
- 1988
-
Ingår i: European Journal of Operational Research. - : Elsevier BV. - 0377-2217 .- 1872-6860. ; 35:2, s. 182-186
-
Tidskriftsartikel (refereegranskat)abstract
- This study deals with a hierarchical planning system that is used for planning of a single-stage manufacturing system. We consider two decision levels, aggregate and detailed planning, and formulate a model for evaluation of aggregate plans and optimal disaggregation in case of independent stochastic demand. It is shown how the optimal solution can be obtained with the aid of a dynamic programming algorithm. Furthermore, we give conditions that will guarantee optimality of a simple intuitive disaggregation rule
|
|
| 6. |
- Aysen, Ari
(författare)
-
Approximate solutions to the disaggregation problem under uncertainty
- 1989
-
Ingår i: Engineering Costs and Production Economics. - 0167-188X .- 1878-4011. ; 15, s. 299-306
-
Tidskriftsartikel (refereegranskat)abstract
- This paper studies the disaggregation problem within a hierarchical production planning framework for the case when demands are random variables with known probability density functions. Three different heuristic allocation rules have been proposed in order to provide approximate solutions to the problem. The numerical study shows that it is possible to obtain fairly good results by using heuristic rules instead of the optimizing routine. The additional decision rule for choosing one plan among the set of plans suggested by the heuristic, seems to play an important role as far as the first two heuristics are concerned. The third heuristic is less sensitive' with respect to the additional decision rule and also performs slightly better than the other two heuristics
|
|
