The lateral transhipment problem with a-priori routes, and a lot sizing application

TL;DR

This paper develops exact solution methods for a lateral transhipment problem with a pre-defined customer sequence, considering costs, profits, and constraints, with applications in lot sizing and inventory redistribution.

Contribution

It introduces a novel combination of dynamic programming and branch-and-bound methods tailored for the problem, enhancing solution efficiency.

Findings

Branch-and-bound solves instances with up to 50 locations in under ten seconds.

The proposed methods outperform existing approaches in computational efficiency.

Different problem sizes and constraints influence the choice of the most suitable solution approach.

Abstract

We propose exact solution approaches for a lateral transhipment problem which, given a pre-specified sequence of customers, seeks an optimal inventory redistribution plan considering travel costs and profits dependent on inventory levels. Trip-duration and vehicle-capacity constraints are also imposed. The same problem arises in some lot sizing applications, in the presence of setup costs and equipment re-qualifications. We introduce a pure dynamic programming approach and a branch-and-bound framework that combines dynamic programming with Lagrangian relaxation. Computational experiments are conducted to determine the most suitable solution approach for different instances, depending on their size, vehicle capacities and duration constraints. The branch-and-bound approach, in particular, solves problems with up to 50 delivery locations in less than ten seconds on a modern computer.