Novel Scenario-Based Policies for Dynamic Multi-Period Inventory Routing Problems

• Applicant: Professor Dr. Marlin Ulmer
• Subject Area: Operations Management and Computer Science for Business Administration
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554437526

The project focuses on effective decision support for stochastic dynamic multi-period inventory routing problems where over a set of periods, a fleet of vehicles is used to control inventory at different geographical locations in the presence of demand uncertainty. This problem class spans several relevant practical applications such as the supply of stores or production facilities, the collection of groceries, waste or recycling material, and the distribution of resources in shared mobility. Effective decision making for such problems requires a thorough optimization of inventory routing in every period as well as an anticipation of demand and decisions in future periods. For such problems, anticipation is usually done via demand scenarios as they allow for a detailed depiction of future uncertainty. However, when integrating scenarios in optimization, existing research usually treats them as static and deterministic. This may lead to inflexible and ineffective decisions. Instead, we propose to apply and unify two concepts of the stochastic dynamic optimization literature, progressive hedging for capturing stochasticity and information relaxation for capturing dynamism. The first allows for finding integrated decisions while considering all scenarios. The latter penalizes usage of information in the static solutions of the scenarios. Both concepts did receive very limited attention in the dynamic routing literature yet. We will adapt the two concepts to a set of specific stochastic dynamic inventory routing problems. We will then analyze their theory to distill one unified methodology. The research objectives of the project are therefore two-fold. First, the project will investigate the problem class of stochastic dynamic multi-period inventory routing problems. The project will provide effective decision support for a selected number of specific problems differing in the components of the problem class: objective, stochasticity, dynamism, inventory management, and vehicle routing. It will also investigate the structure of the obtained policies to derive general insights in the effective practical decision making. Second, for this problem class, the project will provide two specific and new solution concepts leveraging scenarios and considering stochasticity and dynamism explicitly in the search of effective decisions. We compare their functionality and provide insights in when and how they work. Our proposed methodology unites the work on solving static deterministic mixed programs with creating anticipatory dynamic policies. The proposed solution methodology will be applicable for a large range of stochastic dynamic problems, where detailed information must be considered (via scenarios) while anticipation is required to avoid inflexible and myopic decisions. The unification of the two ideas to one common concept can go beyond decision making for transportation and logistics but may provide general theory in operations research.

• DFG Programme: Research Grants
• International Connection: USA
• Co-Investigator: Shohre Zehtabian, Ph.D.
• Cooperation Partner: Professor Justin Goodson, Ph.D.