Abstract
In a container terminal management, we are often confronted with the following problem: how to assign a reasonable depositing position for an arriving container, so that the efficiency of searching for and loading of a container later can be increased. In this paper, the problem is modeled as a transportation problem with nonlinear side constraints (TPNSC). The reason of nonlinear side constraints arising is that some kinds of containers cannot be stacked in the same row (the space of storage yard is properly divided into several rows). A branch and bound algorithm is designed to solve this problem. The algorithm is based on the idea of using disjunctive arcs (branches) for resolving conflicts that are created whenever some conflicting kinds of containers are deposited in the same row. During the branch and bound, the candidate problems are transformed into classical transportation problems, so that the efficient transportation algorithm can be applied, at the same time the reoptimization technique is employed during the branch and bound. Further, we design a heuristic to obtain a feasible initial solution for TPNSC in order to prune some candidates as early and/or as much as possible. We report computational results on randomly generated problems.
Similar content being viewed by others
References
Ali AI, Allen EP, Barr RS, Kennington JL (1986) Reoptimization procedure for bounded variable primal simplex network algorithm. Eur J Oper Res 23:256–263
Christofides N, Alvarez-Valdes R, Thamrit JM (1987) Project scheduling with resource constraints: A branch and bound approach. Eur J Oper Res 29:262–273
Ford LR, Fulkerson DR (1962) Flows on Networks. Princeton University Press, Princeton, N.J.
Glover F, Karney D, Klingman D, Russel R (1978) Solving singly constrained transshipment problems. Transp Sci 12:277–297
Klingman D, Phillips NV (1988) Equitable demand adjustment for infeasible transportation problems. J Operat Res Soc 39:737–742
Klingman D, Russel R (1975) Solving constrained transportation problems. Operat Res 23:91–106
Murty K (1976) Linear and Combinatorial Programming. Wiley
Thompson GL, Sethi AP (1986) Solution of constrained generalized transportation problems using the pivot and probe algorithm. Computer and Operat Res 13:1–9
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cao, B. Transportation problem with nonlinear side constraints a branch and bound approach. ZOR - Methods and Models of Operations Research 36, 185–197 (1992). https://doi.org/10.1007/BF01417216
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01417216