Production and distribution planning, scheduling, and routing optimization in a yogurt supply chain under demand uncertainty: A case study

TL;DR

This paper presents a comprehensive optimization model for yogurt supply chain planning under demand uncertainty, integrating production, scheduling, and routing with a robust fuzzy programming approach and a genetic algorithm for solution.

Contribution

It introduces a mixed-integer non-linear programming model combined with a fuzzy programming approach to handle demand uncertainty in yogurt supply chains, along with a tailored genetic algorithm for solving large instances.

Findings

The genetic algorithm outperforms exact methods in large problems.

Shift to smaller batches improves demand fulfillment under uncertainty.

Company policies adapt to demand fluctuations but increase inventory costs.

Abstract

Considering the evolution of the food industry and its challenges, like high perishability, managing the food industry supply chain is a key focus for researchers and decision-makers. Uncertainty in decision-making has gained importance, particularly in the yogurt industry, known for its complexity. This study addresses production and distribution planning, scheduling, and routing in the yogurt supply chain. The problem is characterized by multiple products, a single plant, multiple distribution centers, multiple periods, and various transportation methods. A mixed-integer non-linear programming (MINLP) model is used to minimize total costs, including production, setup, overtime, unmet demand, and transportation. Additionally, a robust fuzzy programming approach is applied under uncertainty, with linearization procedures proposed to convert it into a linearized mixed-integer programming formulation. The problem is tested with two data types: a sample problem in three sizes (small, medium, and large) and real data from Kalle Dairy Company, Iran. A Genetic Algorithm (GA) is developed to solve the problem, with necessary modifications made for its application. The GA's performance is compared to an exact algorithm (Branch & Cut), showing that the company's production policy adapts daily to meet demand precisely. The shift to smaller batch production and longer shelf life allows better stock allocation and avoids shortages in uncertain conditions. The company's policies adapt to severe fluctuations in the business environment, though this requires high costs, such as inventory maintenance.