Citation: Berk, E.; Ayas, O.; Ülkü, M.A. Optimizing Process-Improvement Efforts for Supply Chain Operations under Disruptions: New Structural Results. Sustainability 2023, 15, 13117. https://doi.org/10.3390/su151713117 Academic Editor: Giada La Scalia Received: 5 July 2023 Revised: 22 August 2023 Accepted: 24 August 2023 Published: 31 August 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). sustainability Article Optimizing Process-Improvement Efforts for Supply Chain Operations under Disruptions: New Structural Results Emre Berk 1,2, * , Onurcan Ayas 1 and M. Ali Ülkü 2,3, * 1 Faculty of Business Administration, Bilkent University, Ankara 06800, Türkiye; onurcan@bilkent.edu.tr 2 CRSSCA-Centre for Research in Sustainable Supply Chain Analytics, Dalhousie University, Halifax, NS B3H 4R2, Canada 3 Department of Management Science & Information Systems, Faculty of Management, Dalhousie University, Halifax, NS B3H 4R2, Canada * Correspondence: eberk@bilkent.edu.tr (E.B.); ulku@dal.ca (M.A.Ü.) Abstract: Rampant disruptions have probed the fragility of supply chains: Renewed perspectives and comprehensive operational models are needed to enhance resiliency and sustainability in business. This paper proposes a new inventory management model that explicitly integrates process improve- ment efforts to improve supply chain sustainability through the better use of capital (materials, assets, and technology) and labor (workforce and know-how). Under a desired service-level constraint, we study reducing setup (fixed) costs when they are expressed in terms of economic production functions of two (input) decision variables: the level of capital (e.g., process change, and technology investments) and the level of labor required. This research is motivated by lean manufacturing practices, which rely on shaping the operating environment and operating optimally within that business environment. Based on mathematical modeling and analysis, we provide closed-form optimality expressions and structural results that lend themselves to decision insights. In particular, we provide, along with illustrative numerical examples, results on the sensitivity of setup-reduction efforts to demand rates, variability, and explicit expressions for determining the required labor and capital resources. A generalization of the model for carbon emissions is also presented. Keywords: process improvement; supply chain; economic production functions; disruptions; sustainability 1. Background and Brief Literature Review To enhance efficiency and effectiveness, streamlining supply chain (SC) operations is a formidable but necessary task. From improving product quality to flawless shipment deliv- ery to precise data-sharing for coordination and environmental compliance, SC members need to invest in process-improvement efforts continuously to be viable in a competitive marketplace [1–3]. SCs incur fixed costs in their operations in various forms, such as overhead in management, setup in manufacturing, ordering costs in retailing logistics, data acquisition for accurate forecasting, or process improvement for cost and carbon savings. For instance, a buyer may commit to a fixed transport capacity, the utilization of which may be wavering due to uncertainties in demand and supply. Often, fixed costs dictate operational decisions (e.g., inventory management). Investments in reducing fixed costs (e.g., choosing a more reliable and less costly third-party logistics provider) may reduce overall costs and decrease environmental damage because of increased capacity utilization [4]. Therefore, it is plausible to state that investments in process improvements (fixed costs) impact the sustainability of SCs. Although the literature is well-established in “economies of scale” (whereby, for instance, given the fixed dispatch cost of a truck, a lower per unit transportation cost could be attained if the truck’s carrying capacity is better utilized), more research is needed in understanding the operational factors of and investing in reducing fixed costs. In this Sustainability 2023, 15, 13117. https://doi.org/10.3390/su151713117 https://www.mdpi.com/journal/sustainability