Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems

Chen, Haoxun

doi:10.1016/j.omega.2015.03.002

Cited by 63 publications

(36 citation statements)

References 30 publications

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“…Constraints (29) are similar to constraints (25). Models (21) and (28) are both deterministic models; hence these models can be tractably solved by our next proposed algorithms.…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the following, we first define the so-called " -degree-connection" to combine the decision of resources, products, demands, and time periods. Then the subproblems of the fix-and-optimize approach can be redefined based on the concept " -degree-connection" (as we have discussed before, our models have "many-to-one" demand structure; we need to state that, in the work of [25], a similar concept "Interrelatedness" is defined; however, his concept is for one-to-one demand structure and cannot be applied to our models). Finally, we present our FO approach for both the S-MICLSP and S-MICLSP-L models.…”

Section: New Fix-and-optimize (Fo) Approachmentioning

confidence: 99%

“…The change of may also cause the change of , , , whereby D = D = , due to constraints (23). Similarly, the change of may also cause the change of , , , whereby , ∈ P , ∈ R, due to constraints (25).…”

Section: Definition Of " -Degree-connection"mentioning

confidence: 99%

“…Newly, Chen [25] proposed an excellent integrative framework combining FO and VNS for deterministic lotsizing problems. Since our models have "many-to-one" demand structure, his framework cannot be applied to our models.…”

Section: Introductionmentioning

confidence: 99%

“…However, motivated from his work, we propose our FO and integrative FO-VNS for our stochastic lot-sizing problems. Compared with the work of [25], our proposed FO allows capacity-infeasible (overtime cost is not zero) solutions and can be applied to "many-to-one" demand structure, while he prohibited capacity-infeasible solutions and his framework was only valid for one-to-one demand structure. Thus, we apply the integrative framework to models without setup carryovers, S-MICLSP, and successfully extend it to our setup carryovers version, S-MICLSP-L, while Chen [25] only applied his framework to models without setup carryovers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fix‐and‐Optimize and Variable Neighborhood Search Approaches for Stochastic Multi‐Item Capacitated Lot‐Sizing Problems

Song

et al. 2017

Mathematical Problems in Engineering

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We discuss stochastic multi-item capacitated lot-sizing problems with and without setup carryovers (also known as link lot size), S-MICLSP and S-MICLSP-L. The two models are motivated from a real-world steel enterprise. To overcome the nonlinearity of the models, a piecewise linear approximation method is proposed. We develop a new fix-and-optimize (FO) approach to solve the approximated models. Compared with the existing FO approach(es), our FO is based on the concept of " -degreeconnection" for decomposing the problems. Furthermore, we also propose an integrative approach combining our FO and variable neighborhood search (FO-VNS), which can improve the solution quality of our FO approach by diversifying the search space. Numerical experiments are performed on the instances following the nature of realistic steel products. Our approximation method is shown to be efficient. The results also show that the proposed FO and FO-VNS approaches significantly outperform the recent FO approaches, and the FO-VNS approaches can be more outstanding on the solution quality with moderate computational effort.

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“…Constraints (29) are similar to constraints (25). Models (21) and (28) are both deterministic models; hence these models can be tractably solved by our next proposed algorithms.…”

Section: Model Descriptionmentioning

confidence: 99%

Section: New Fix-and-optimize (Fo) Approachmentioning

confidence: 99%