María Analía Rodríguez

Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part I: MINLP and MILP models

Abstract An optimization model is proposed to redesign the supply chain of spare part delivery under demand uncertainty from strategic and tactical perspectives in a planning horizon consisting of multiple periods. Long term decisions involve new installations, expansions and elimination of warehouses and factories handling multiple products. It is also considered which warehouses should be used as repair work-shops in order to store, repair and deliver used units to customers. Tactical planning includes deciding inventory levels (safety stock and expected inventory) for each type of spare part in distribution centers and customer plants, as well as the connection links between the supply chain nodes. Capacity constraints are also taken into account when planning inventory levels. At the tactical level it is determined how demand of failing units is satisfied, and whether to use new or used parts. The uncertain demand is addressed by defining the optimal amount of safety stock that guarantees certain service level at a customer plant. In addition, the risk-pooling effect is taken into account when defining inventory levels in distribution centers and customer zones. Due to the nonlinear nature of the original formulation, a piece-wise linearization approach is applied to obtain a tight lower bound of the optimal solution. The formulation can be adapted to several industry-critical units and the supply chain of electric motors is provided here as an example.

Inventory and delivery optimization under seasonal demand in the supply chain

Abstract This work deals with the inventory, purchase and delivery optimization problem in the supply chain. The formulation of two problems is presented involving several decision levels. The first one optimizes the company inventory and purchase tasks in a medium-term horizon planning, assuming that the total amount purchased is delivered at the beginning of each period. Then, in a more detailed formulation, the purchased amount is distributed among several deliveries giving rise to a non-linear non-convex problem. Some transformation techniques are evaluated to overcome the non-convexities in order to find a global solution in a reasonable execution time. Finally, the results obtained considering some possible scenarios are analyzed and compared.

Enterprise optimization for solving an assignment and trim-loss non-convex problem

In the present work, the planning and cutting problem for the corrugated board boxes industries is presented. This problem belongs to the category of the trim-loss problem, which is essential in the paper-converting supply chain management. Bilinear terms in demand and stock constraints, for instance, lead to a non-convex formulation. Two global convex models are formulated and tested. Results obtained in the problem solution are shown. The most efficient model is implemented by means of Java programs and GAMS, a mathematical optimization program. The system is linked to the company ERP (enterprise resource planning) system. Several issues are optimized and improved: waste generation, energy demand, environmental impact and production costs. Paper reel stock management is improved due to more accurate and statistical information obtained by the system. The planning system linked to the ERP connection allows the integration of customers and suppliers increasing the company competitiveness.

Optimal supply chain design and management over a multi- period horizon under demand uncertainty. Part II: A Lagrangean decomposition algorithm

In Part I (Rodriguez, et al., 2013 an optimization model was proposed to redesign the supply chain of spare parts industry under demand uncertainty in a specified planning horizon. To address large industrial problems, a Lagrangean scheme is proposed to decompose the MINLP of Part I according to the warehouses by dualizing the logic constraints that assign the warehouses to different customers, together with the demand constraints and factory capacity constraints. The subproblems are first approximated by an adaptive piece-wise linearization scheme that provides lower bounds, and the MILP is further relaxed to an LP to improve solution efficiency while providing a valid lower bound. An initialization scheme is designed to obtain good initial Lagrange multipliers, which are scaled to accelerate the convergence. The results from an illustrative problem and two real world industrial problems show that the method can obtain optimal or near optimal solutions in modest computational times.

A comparative assessment of linearization methods for bilinear models

Abstract In this article, optimization problems with bilinear constraints involving one discrete variable are studied. Several industrial problems present bilinear non-convex constraints which are difficult to solve to global optimality. For this purpose models must be reformulated what in general terms increases the problem size. This article proposes two disjunctive transformation techniques which are compared to other approaches presented in the literature. An analysis is made comparing qualitative and quantitative characteristics of the methods employed. In order to implement proposed transformations, three industrial cases are studied: trim-loss in a paper mill, cutting stock in the production of carton board boxes and the purchase, inventory and delivery optimization problem. All of them are reformulated and solved using the strategies included in the paper. Several instances of each problem are evaluated and their results are analyzed comparing performance of the different methods.

Mid-term planning optimization model with sales contracts under demand uncertainty

Abstract Uncertainty modeling is a challenging topic in supply chain and operation management. When planning material purchase and stock levels, demand uncertainty could have an important impact on the plan results and its feasibility. Additionally, uncertainty could greatly affect customer satisfaction, inventory costs and company profits. From a modeling perspective, problems considering uncertainty are difficult to tackle and lead to complex optimization approaches. This work proposes a mid-term planning model dealing with sales contracts to diminish the effect of uncertainty. Another interesting feature is given by the selection of different price levels. Price elasticity functions are introduced for each customer in order to jointly decide demand targets and prices. A linear generalized disjunctive programming model is developed. Short execution time shows that this model can be applied to analyze several real scenarios to decide material purchase plan, inventory levels, sales strategies, prices and demand levels in a medium term horizon planning.

Generalized disjunctive programming model for the multi-period production planning optimization: An application in a polyurethane foam manufacturing plant

Abstract A Generalized Disjunctive Programming (GDP) model for the optimal multi-period production planning and stock management is proposed in this work. The formulation is applied to a polyurethane foam manufacturing plant that comprises three stages: a first step that produces pieces with certain characteristics, a second process that involves the location of these pieces in a limited area and a third stage where pieces are stored in dedicated spaces. This article shows the GDP capabilities to provide a qualitative framework for representing the problem issues and their connections in a natural way, especially in a context where decisions integration is required. Due to the multi-period nature of the planning problem, a rolling horizon approach is suitable for solving it in reasonable computing time. It serves as a tool for analyzing the trade-offs among the different costs. Through the examples, the capabilities of the formulation and the proposed resolution method are highlighted.

Forest Supply Chain Optimization applying Generalized Disjunctive Programming

Abstract The increasing market competitiveness has put the supply chain (SC) optimization into the focus in the last years. In this context, forest SC needs new investments as well as a new business vision in order to keep profitable and satisfy customers needs and social expectations. The provision of renewable energy sources can be one strategic aspect of this supply chain. Therefore, the major objective of this work is to propose a comprehensive forest SC including investment, operational and logistic decisions. For this purpose, a mathematical formulation is developed using Generalized Disjunctive Programming as the modeling technique. The mixed integer linear programming model is solved considering a case study from the Argentinian industry.

Supply Chain Design and Inventory Management Optimization in the Motors Industry

Fil: Rodriguez, Maria Analia. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Santa Fe. Instituto de Desarrollo y Diseno (i); Argentina

Modelo matemático para la planificación de las inversiones en fuentes de energía renovables para la Argentina

En este trabajo se presenta un programa matematico mixto-entero lineal (MILP) multiperiodo para planificar las inversiones en fuentes de energia convencionales y renovables para la Argentina, poniendo el enfasis en estas ultimas. Las fuentes de energia renovables que se incluyen en el modelo son aquellas que presentan una mayor ventaja competitiva para la Argentina y cuyas tecnologias han alcanzado una cierta madurez y confiabilidad. El horizonte de tiempo propuesto es de 20 anos. La funcion objetivo del modelo matematico es minimizar los costos de inversion y operacion de las fuentes de energia. El modelo tambien permite realizar un analisis de escenarios variando fundamentalmente la disponibilidad de las reservas de petroleo. Los resultados que brinda el modelo permiten visualizar las inversiones realizadas, como afectan las mismas a la composicion de la matriz energetica y los momentos en que se deciden las inversiones asi como sus montos.