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Exploitation of material consolidation trade-offs in multi-tier complex supply networks

Vinod Kumar Chauhan, Muhannad Alomari, James Arney, Ajith Kumar Parlikad, Alexandra Brintrup

TL;DR

The paper tackles the problem of minimising total procurement cost across a two-tier, made-to-order supply network by exploiting multi-to-multi material relationships between forgings (Tier 2) and machined parts (Tier 1). It develops a mixed-integer linear programming (MILP) formulation with linearisation and pre-computations to model the trade-off between Tier 2 forging costs and Tier 1 machining costs, while incorporating quantity discounts and inventory holding costs. The approach is validated on an aerospace case study (up to 500 parts/forgings), showing that holistic reconfiguration yields significant procurement savings, driven by forging-cost reductions and supported by reductions in inventory holding costs, albeit with modest increases in machining demand. Key insights include that larger machining option sets and higher forging fixed costs improve consolidation opportunities, and that discounting generally enhances consolidation; the model also demonstrates potential simplifications in supplier selection and inventory management. Overall, the framework provides a practical, exact optimization tool for holistically reconfiguring multi-tier supply networks, delivering measurable cost advantages in complex engineered products.

Abstract

While consolidation strategies form the backbone of many supply chain optimisation problems, exploitation of multi-tier material relationships through consolidation remains an understudied area, despite being a prominent feature of industries that produce complex made-to-order products. In this paper, we propose an optimisation framework for exploiting multi-to-multi relationship between tiers of a supply chain. The resulting formulation is flexible such that quantity discounts, inventory holding, and transport costs can be included. The framework introduces a new trade-off between tiers, leading to cost reductions in one tier but increased costs in the other, which helps to reduce the overall procurement cost in the supply chain. A mixed integer linear programming model is developed and tested with a range of small to large-scale test problems from aerospace manufacturing. Our comparison to benchmark results shows that there is indeed a cost trade-off between two tiers, and that its reduction can be achieved using a holistic approach to reconfiguration. Costs are decreased when second tier fixed ordering costs and the number of machining options increase. Consolidation results in reduced inventory holding costs in all scenarios. Several secondary effects such as simplified supplier selection may also be observed.

Exploitation of material consolidation trade-offs in multi-tier complex supply networks

TL;DR

The paper tackles the problem of minimising total procurement cost across a two-tier, made-to-order supply network by exploiting multi-to-multi material relationships between forgings (Tier 2) and machined parts (Tier 1). It develops a mixed-integer linear programming (MILP) formulation with linearisation and pre-computations to model the trade-off between Tier 2 forging costs and Tier 1 machining costs, while incorporating quantity discounts and inventory holding costs. The approach is validated on an aerospace case study (up to 500 parts/forgings), showing that holistic reconfiguration yields significant procurement savings, driven by forging-cost reductions and supported by reductions in inventory holding costs, albeit with modest increases in machining demand. Key insights include that larger machining option sets and higher forging fixed costs improve consolidation opportunities, and that discounting generally enhances consolidation; the model also demonstrates potential simplifications in supplier selection and inventory management. Overall, the framework provides a practical, exact optimization tool for holistically reconfiguring multi-tier supply networks, delivering measurable cost advantages in complex engineered products.

Abstract

While consolidation strategies form the backbone of many supply chain optimisation problems, exploitation of multi-tier material relationships through consolidation remains an understudied area, despite being a prominent feature of industries that produce complex made-to-order products. In this paper, we propose an optimisation framework for exploiting multi-to-multi relationship between tiers of a supply chain. The resulting formulation is flexible such that quantity discounts, inventory holding, and transport costs can be included. The framework introduces a new trade-off between tiers, leading to cost reductions in one tier but increased costs in the other, which helps to reduce the overall procurement cost in the supply chain. A mixed integer linear programming model is developed and tested with a range of small to large-scale test problems from aerospace manufacturing. Our comparison to benchmark results shows that there is indeed a cost trade-off between two tiers, and that its reduction can be achieved using a holistic approach to reconfiguration. Costs are decreased when second tier fixed ordering costs and the number of machining options increase. Consolidation results in reduced inventory holding costs in all scenarios. Several secondary effects such as simplified supplier selection may also be observed.
Paper Structure (22 sections, 19 equations, 9 figures, 2 tables)

This paper contains 22 sections, 19 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Purchasing consolidation
  4. Shipment, volume and order consolidation
  5. Inventory consolidation
  6. Part consolidation through product redesign
  7. Multi-tier material consolidation
  8. Problem formulation
  9. Objective function:
  10. Constraints:
  11. Optimisation problem:
  12. Solution approach
  13. Model development
  14. Linearisation:
  15. Pre-computations:
  16. ...and 7 more sections

Figures (9)

  • Figure 1: Two-tier supply chain of a manufacturing company
  • Figure 2: Illustration of the multi-tier consolidation problem: Different colours represent clusters where a square-enclosed forging is used to replace all other forgings in its cluster.
  • Figure 3: Quantity intervals for calculating discount levels for forging $k$. Quantity intervals and discounts for parts can be represented in a similar way.
  • Figure 4: Comparison of solver libraries and modelling languages.
  • Figure 5: Multi-tier material consolidation case study (500 parts/500 forgings)
  • ...and 4 more figures