# Managing mobile production-inventory systems influenced by a modulation process

## TL;DR

This paper explores the benefits of relocating production capacity in a multi-site network, demonstrating significant improvements in system performance and cost savings through heuristic solutions under uncertainty.

## Contribution

It introduces a novel model for mobile production capacity with stochastic demand influenced by macroeconomic factors, and develops heuristics for dynamic relocation and inventory control.

## Key findings

- Capacity mobility improves performance by up to 41%.
- Relocation yields 10% more savings than transshipment alone.
- Heuristics effectively solve complex stochastic decision problems.

## Abstract

We investigate the potential added value of being able to relocate production capacity, relative to fixed production capacity, in a network of multiple, geographically distributed manufacturing sites. There is a growing interest in production capacity that can be geographically relocated; e.g., modular units for pharmaceutical intermediates. It shows promise for enabling the fast fulfillment of a distributed network with a reduction in the total inventory and total production capacity of a distributed network with fixed production capacity without sacrificing customer service levels or total system resilience. Allowing also for transshipment, we model a production-inventory system with L production sites and Y units of relocatable production capacity, develop efficient and effective heuristic solution methods for dynamic relocation and multi-location inventory control, and analyze the potential added value. We describe the (L, Y) problem as a problem of sequential decision making under uncertainty to determine transshipment, mobile production capacity relocation, and replenishment decisions at each decision epoch. To enhance model realism, we use a partially observed stochastic process, the modulation process, to model the exogenous and partially observable forces (e.g., the macro-economy) that affect demand. We then model the (L, Y) problem as a partially observed Markov decision process. Due to the considerable computational challenges of solving this model exactly, we propose two efficient, high quality heuristics. We show for an instance set with five locations that production capacity mobility and transshipment, relative to the fixed production capacity case, can improve systems performance by as much as 41\% on average over the no-flexibility case and that production capacity mobility can yield as much as 10\% more savings compared to when only transshipment is permitted.