Profit maximization via capacity control for distribution logistics problems

TL;DR

This paper addresses profit maximization in distribution logistics by developing a dynamic decision-making model for accepting requests, proposing a mixed-integer linear programming approximation, and analyzing its computational performance.

Contribution

It introduces a novel dynamic formulation for capacity control in logistics and proposes an MILP approximation to aid real-time revenue management decisions.

Findings

The MILP approximation effectively guides request acceptance decisions.

The proposed methods perform well on academic test problems.

The approach balances immediate revenue with future capacity considerations.

Abstract

We consider a distribution logistics scenario where a shipping operator, managing a limited amount of resources, receives a stream of collection requests, issued by a set of customers along a booking time-horizon, that are referred to a future operational period. The shipping operator must then decide about accepting or rejecting each incoming request at the time it is issued, accounting for revenues, but also considering resource consumptions. In this context, the decision process is based on dynamically finding the best trade-off between the immediate return of accepting the request and the convenience of preserving capacity to possibly exploit more valuable future requests. We give a dynamic formulation of the problem aimed at maximizing the operator revenues, accounting also for the operational distribution costs. Due to the "curse of dimensionality", the dynamic program cannot be solved optimally. For this reason, we propose a mixed-integer linear programming approximation, whose exact or approximate solutions provide the relevant information to apply some commonplace revenue management policies in the real-time decision-making. Adopting a capacitated vehicle routing problem as an underlying distribution application, we analyze the computational behaviour of the proposed techniques on a set of academic test problems.