The usual Transshipment Problem is to minimize the total cost for shipping the various capacities of the goods on the requirement of destinations from the available sources, well known N.P-Hard problem. Generally, the transshipment problem consist a unit cost on supplied goods to destinations from the sources. But in bulk transshipment the cost is independent of number of goods supplied to destinations, it is practical. In this paper we investigated a “variant of constrained bulk transshipment problem”. Let there are m-sources and n-destinations. The destinations can get its complete requirement from a source directly or through some destination. The practical constraint is considered as only fewer destinations will act as transshipment nodes i.e. a destination can get its complete requirement from a source through a permitted destination; this transshipment node can be utilized with the specified finite number of times in the optimal schedule. The cost of transportation of products from the sources to destination and destinations to destination is given. The total availability of the product at the sources is greater than or equal to the total requirement of the product at the destinations. Generally movement of a product from source to source or destinations to source is not natural, hence these possibilities are avoided and movement from destinations to destination is only considered. This is more generalized problem and comes under combinatorial programming problem. Often, the model is expressed as a zero-one programming problem. The objective of the problem is to minimize the total bulk cost of supplying the required products to the destinations with the restriction that any destination should get its supply from one source only, even when it gets from a destination. In the sequel, we have developed a Lexi Search Algorithm using Pattern Reorganization Technique to obtain the optimal solution. The concepts and algorithms developed are explained with a suitable example. The algorithm is tested and the experimental results indicate that the hard instance problems also solved in reasonable time. © Research India Publications.