Multi‐product supply chain horizontal network integration: models, theory, and computational results

Abstract

In this paper, we develop multi-product supply chain network models with explicit capacities, before and after their horizontal integration. In addition, we propose a measure, which allows one to quantify and assess, from a supply chain network perspective, the synergy benefits associated with the integration of multi-product firms through mergers/acquisitions. We utilize a system-optimization perspective for the model development and provide the variational inequality formulations, which are then utilized to propose a computational procedure which fully exploits the underlying network structure. We illustrate the theoretical and computational framework with numerical examples. This paper is a contribution to the literatures of supply chain integration and mergers and acquisitions.

The system optimization perspective for multiproduct supply chain network

“…Modified equilibrium algorithm is defined as composition of operators for several products in the same network in comparison with prior methods that first, the multiproduct supply chain network was converted into single-product network. Therefore, this method needs a few number of iteration for converging in comparison with other methods as discussed in [8].…”

“…A flow pattern f , is called feasible, if there exists at least one feasible flow pattern x, compatible with f and following flow equation holds: (8) where δ ap = 1, if link a is contained in path P and δ ap = 0, otherwise.…”

“…Expression (8) states that the flow on a link a is equal to the sum of all the path flows on path p containing link a.…”

“…where δ is selected so that the total cost T C(f ) is minimized over the class of admissible load patternsf that are induced by the class of flow patternsx given by (8). In the case of the quadratic model, δ can be determined explicitly through the formula…”

A Physarum-inspired approach to supply chain network design

“…In the Physarum-inspired algorithm, we consider link capacities as design variables and use continuous functions to represent the costs of the links. Based on the system-optimization technique developed for supply chain network integration [51,52], we abstract the economic activities associated with a firm as a network. We make full use of two features of Physarum: a continuity of the flux during the iterative process and the protoplasmic network adaptivity, or reconfiguration.…”