An Integrated Inventory-Production-Distribution Model for Crisis Relief Supply Chain Optimization: A Systematic Review and Mixed Integer Programming Formulation - Berbiche, Nawfal; Chakir, Mouna; Hlyal, Mustapha; Jamila El Alami (Journal Europeen des Systemes Automatises, 2024)
Confronted with budgetary constraints and complex sustainment systems in challenging environments, optimization of supply chains has become a necessity. The paper investigates a large body of literature related to integrated and decomposed supply chain problems’ modeling, optimization software and mathematical programming, including analytical and heuristic solution methods. The main purpose of this study is to contribute with a review of global optimization models of forward/reverse crisis relief supply chains within tactical and operational levels before developing an Integrated Three-Echelon Multi-Period Multi-Commodity Inventory-Production-Distribution Problem formulation. It aims to minimize the total cost of inventory, production, transportation and shortage penalties from support facilities to satisfy deterministic non-stationary demand of finished and recovered repaired commodities over T periods. Besides functions integration and constraints, no such elaborated decision model has also considered before, simultaneously direct shipments in heterogeneous vehicles with non-stationary demand, hostility attrition, and the loading and safety constraints of heterogeneous commodities clustering and vehicle-commodity compatibility. This work shows how existing modeling approaches are valuable and inspiring to understand and adapt to complex new real-world supply chains with the unique proposed formulation and anticipated upgrades. It receives growing attention worldwide from business, humanitarian and military decision-makers, as well as from automotive industries, to build efficient supply chain strategies, how vital economically, socially and environmentally. This mathematical model leads to an NP-hard mixed integer linear programming (MILP) problem with too many variables and constraints where some promising solution methods are discussed. What we have investigated and modeled so far appeal to a further contribution of a sophisticated solution approach, decomposing it into sub-problems, more tractable through Lagrangian relaxation for lower bounds, or branch-and-price based column generation method.