Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities
In inventory management, storage capacity constraints complicate multi-item lot-sizing decisions. As the number of items increases, deciding how much of each item to order without exceeding capacity becomes more difficult. Dynamic programming works efficiently for a single item, but when capacity co...
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MDPI AG
2025-06-01
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| author | Warut Boonphakdee Duangrat Hirunyasiri Peerayuth Charnsethikul |
| author_facet | Warut Boonphakdee Duangrat Hirunyasiri Peerayuth Charnsethikul |
| author_sort | Warut Boonphakdee |
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| description | In inventory management, storage capacity constraints complicate multi-item lot-sizing decisions. As the number of items increases, deciding how much of each item to order without exceeding capacity becomes more difficult. Dynamic programming works efficiently for a single item, but when capacity constraints are nearly minimal across multiple items, novel heuristics are required. However, previous heuristics have mainly focused on inventory bound constraints. Therefore, this paper introduces push and pull heuristics to solve the multi-item uncapacitated lot-sizing problem under near-minimal capacities. First, a dynamic programming approach based on a network flow model was used to generate the initial replenishment plan for the single-item lot-sizing problem. Next, under storage capacity constraints, the push operation moved the selected replenishment quantities from the current period to subsequent periods to meet all demand requirements. Finally, the pull operation shifted the selected replenishment quantities from the current period into earlier periods, ensuring that all demand requirements were satisfied. The results of the random experiment showed that the proposed heuristic generated solutions whose performance compared well with the optimal solution. This heuristic effectively solves all randomly generated instances representing worst-case conditions, ensuring robust operation under near-minimal storage. For large-scale problems under near-minimal storage capacity constraints, the proposed heuristic achieved only small optimality gaps while requiring less running time. However, small- and medium-scale problems can be solved optimally by a Mixed-Integer Programming (MIP) solver with minimal running time. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-058c32ae84f242998804ecddcb2ed2312025-08-20T03:26:11ZengMDPI AGComputation2079-31972025-06-0113614810.3390/computation13060148Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage CapacitiesWarut Boonphakdee0Duangrat Hirunyasiri1Peerayuth Charnsethikul2Department of Industrial Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, Nakhon Pathom 73140, ThailandDepartment of Textile Science, Faculty of Agro-Industry, Kasetsart University, Bangkok 10900, ThailandDepartment of Industrial Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, Nakhon Pathom 73140, ThailandIn inventory management, storage capacity constraints complicate multi-item lot-sizing decisions. As the number of items increases, deciding how much of each item to order without exceeding capacity becomes more difficult. Dynamic programming works efficiently for a single item, but when capacity constraints are nearly minimal across multiple items, novel heuristics are required. However, previous heuristics have mainly focused on inventory bound constraints. Therefore, this paper introduces push and pull heuristics to solve the multi-item uncapacitated lot-sizing problem under near-minimal capacities. First, a dynamic programming approach based on a network flow model was used to generate the initial replenishment plan for the single-item lot-sizing problem. Next, under storage capacity constraints, the push operation moved the selected replenishment quantities from the current period to subsequent periods to meet all demand requirements. Finally, the pull operation shifted the selected replenishment quantities from the current period into earlier periods, ensuring that all demand requirements were satisfied. The results of the random experiment showed that the proposed heuristic generated solutions whose performance compared well with the optimal solution. This heuristic effectively solves all randomly generated instances representing worst-case conditions, ensuring robust operation under near-minimal storage. For large-scale problems under near-minimal storage capacity constraints, the proposed heuristic achieved only small optimality gaps while requiring less running time. However, small- and medium-scale problems can be solved optimally by a Mixed-Integer Programming (MIP) solver with minimal running time.https://www.mdpi.com/2079-3197/13/6/148multi-itemlot sizenear-minimal storage capacityreplenishment plan |
| spellingShingle | Warut Boonphakdee Duangrat Hirunyasiri Peerayuth Charnsethikul Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities Computation multi-item lot size near-minimal storage capacity replenishment plan |
| title | Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities |
| title_full | Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities |
| title_fullStr | Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities |
| title_full_unstemmed | Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities |
| title_short | Effective Heuristics for Solving the Multi-Item Uncapacitated Lot-Sizing Problem Under Near-Minimal Storage Capacities |
| title_sort | effective heuristics for solving the multi item uncapacitated lot sizing problem under near minimal storage capacities |
| topic | multi-item lot size near-minimal storage capacity replenishment plan |
| url | https://www.mdpi.com/2079-3197/13/6/148 |
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