Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

Dick den Hertog,Aharon Ben-Tal,Ruud C. M. Brekelmans,Frans J. C. T. de Ruiter

doi:10.1007/s10287-016-0253-6

Abstract

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.

Highlights

With the uprise of Big Data, most of the currently available methods for controlling a multi-stage production-inventory system, are using a “datadriven” approach
In this paper we extend the AARC method to a method named adjustable robust counterpart with decision rules based on inexact data (ARCID) that incorporate past data uncertainty while keeping the resulting robust counterpart tractable
If the information set is equal to It = {1, . . . , t − 1}, in period t we can base our production decision rule on the exact values of the demand realizations in periods 1, . . . , t − 1, and use no information on the demand in periods after t − 1. We extend these experiments to include inexact data in some periods to show the benefits of the ARCID model over the ARC model

Summary

Introduction

With the uprise of Big Data, most of the currently available (theoretical or practical) methods for controlling a multi-stage production-inventory system, are using a “datadriven” approach. In this paper we extend the AARC method to a method named adjustable robust counterpart with decision rules based on inexact data (ARCID) that incorporate past data uncertainty while keeping the resulting (deterministic) robust counterpart tractable. This is our main contribution, and it is achieved using results and techniques from the current robust optimization arsenal. We illustrate the benefits of the ARCID model by revisiting the inventory problem that was used in the first paper on ARO (Ben-Tal et al 2004) Numerical results for this production-inventory problem show that if one neglects the inexact nature of the revealed data, the resulting solution might violate the constraints in many scenarios. Throughout this paper we use bold lower-case and upper-case letters for vectors and matrices, respectively, while scalars are printed in regular font

Adjustable robust models

The new adjustable robust model based on inexact data

Production-inventory problem

The nominal model

The affinely adjustable robust model based on inexact data

Numerical results

Experiments with decision rules using inexact data on demand

Comparison with affinely adjustable robust model based on exact data

Findings

Conclusions