Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

Dieter Fiems,Eline De Cuypere,Dieter Claeys,Koen De Turck

doi:10.3390/math8111925

Dieter Fiems, Eline De Cuypere + Show 2 more

Open Access

https://doi.org/10.3390/math8111925

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Abstract

We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished products are produced up front and stored in a decoupling inventory. When an order arrives, the products are completed and possibly customised. We study this system in a stochastic setting: demand and production are modelled by random processes. In particular, our model includes two coupled Markovian queues: one queue represents the decoupling inventory and the other the order backlog. These queues are coupled as order processing can only occur when both queues are non-empty. We rely on matrix analytic techniques to study the performance of the MTO/MTS system under non-restrictive stochastic assumptions. In particular, we allow for arrival correlation and non-exponential setup and MTS and MTO processing times, while the hybrid MTS/MTO system is managed by an (s,S)-type threshold policy that governs switching from MTO to MTS and back. By some numerical examples, we assess the impact of inventory control, irregular order arrivals, setup and order processing times on inventory levels and lead times.

Highlights

The boundary between forecast-driven and demand-driven activities is a key strategic decision in supply chain management
The present study differs from previous work on stochastic hybrid MTS/MTO systems by its inclusion of an order backlog
We summarise the description of the inventory system at hand, by listing the possible transition rates from a fixed state (n, m, i, j) ∈ X :

Summary

Introduction

The boundary between forecast-driven and demand-driven activities is a key strategic decision in supply chain management. The present study differs from previous work on stochastic hybrid MTS/MTO systems by its inclusion of an order backlog This modification considerably complicates performance assessments, as the corresponding stochastic model consists of two coupled ‘queues’: a decoupling inventory and an order backlog. For Markovian systems that include both queueing and inventory management The performance of this hybrid MTS/MTO system is assessed when the same production capacity is used for MTS and MTO. It is possible that MTO production temporarily stops, without switching to MTS This happens when there are more than s semi-finished products in the inventory and there are no outstanding orders.

Balance Equations

Quasi-Birth-Death Process

Performance Measures

Overload Analysis

Numerical Results

Conclusions