An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation

Effective allocation of scarce resources across supply chain environments is an emerging issue, as enterprises face shortfalls in raw materials, human labour, budgetary resources, equipment, energy and capacity. We consider these related objectives in designing efficient and sustainable supply networks using a multi-objective mixed-integer non-linear programming (MINLP) model for efficient and sustainable supplier selection and order allocation with stochastic demand. Our approach considers sustainability dimensions including economic, environmental and social responsibility, but also seeks to design the most efficient supply network given constraints of the supply market. Enterprise efficiency is assessed using a bi-objective data envelopment analysis (DEA) whose inputs include raw materials, current expenses and labour force capacity. The resulting model is non-convex because of the presence of bilinear terms in DEA-related constraints, so we introduce a multi-stage solution procedure that first uses piecewise McCormick envelopes (PCM) to linearise the bilinear terms. Next, we introduce a set of valid inequalities in order to improve solution time of the problem whose dimension significantly increases after being linearised. We then exploit chance constrained programming approaches to deal with stochastic demand. Finally, a single aggregated objective function is derived using a fuzzy multi-objective programming approach. A manufacturing case study demonstrates the validity of the proposed approach, and its effectiveness in designing a supply network that addresses the 'triple bottom line' of people, profit and planet that comprises many sustainability initiatives in an efficient manner.