Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem
Rakhawy, M., Mohamed, M., Ibrahim, M., Ellaimony, E. (2024). Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem. EKB Journal Management System, 183(3), 36-51. doi: 10.21608/erj.2024.377125
Mohamed Rakhawy; Mostafa Mohamed; Mohamed Ibrahim; Elsayed Ellaimony. "Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem". EKB Journal Management System, 183, 3, 2024, 36-51. doi: 10.21608/erj.2024.377125
Rakhawy, M., Mohamed, M., Ibrahim, M., Ellaimony, E. (2024). 'Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem', EKB Journal Management System, 183(3), pp. 36-51. doi: 10.21608/erj.2024.377125
Rakhawy, M., Mohamed, M., Ibrahim, M., Ellaimony, E. Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem. EKB Journal Management System, 2024; 183(3): 36-51. doi: 10.21608/erj.2024.377125

Proposed an Algorithm for Solving a Special Case of Multi-Index Multistage Transportation Problem

Engineering Research Journal
Article 3, Volume 183, Issue 3, September 2024, Page 36-51  XML PDF (322.57 K)
Document Type: Original Article
DOI: 10.21608/erj.2024.377125
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Authors
Mohamed Rakhawy email 1; Mostafa Mohamed2; Mohamed Ibrahim3; Elsayed Ellaimony3
1Administrator, Automotive and Tractor Eng. Dept., Mataria, Helwan university, Cairo, Egypt
2Lecturer, Automotive and Tractor Eng. Dept., Mataria, Helwan university, Cairo, Egypt
3Prof., Automotive and Tractor Eng. Dept., Mataria, Helwan university, Cairo, Egypt
Abstract
The transportation problem is a special case from applications of linear programming and plays a vital role in the logistics supply chain. Its primary objective is to minimize the total cost of transportation for a network that spans multiple sources and destinations while ensuring that the sources are available, and the destinations are fulfilled. This paper presents the mathematical formulations for four types of multi-index multistage transportation problems (MMTP1, MMTP2, MMTP3, and MMTP4), which cover the various conditions that apply to operating trucks fleets in real transportation networks. The algorithm introduced here is designed to solve MMTP1, a multi-index multistage transportation problem without any restrictions on transportation in the intermediate stages. The algorithm transforms the problem into a multi-index single-stage problem using dynamic programming to find the minimum transportation cost for each means of transport between the first stage's sources and the last stage's destinations. The LINGO software is then used to validate the optimal solution. An illustrative example is provided to demonstrate the effectiveness of the proposed algorithm.
Keywords
Transportation Problems; Multi-Index Transportation Problem; Multistage Transportation Prob-lem; Dynamic programming
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