Using genetic algorithm to solve dynamic cell formation problem.

a b s t r a c t In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed using genetic algorithm (GA). Previous models presented in the literature contain some essential errors which will decline their advantageous aspects. In this paper these errors are discussed and a new improved formulation for dynamic cell formation (DCF) problem is presented. Due to the fact that CF is a NP-hard problem, solving the model using classical optimization methods needs a long computational time. Therefore the improved DCF model is solved using a proposed GA and the results are compared with the optimal solution and the efficiency of the proposed algorithm is discussed and verified

A Multiobjective Stochastic Production-Distribution Planning Problem in an Uncertain Environment Considering Risk and Workers Productivity

A multi-objective two stage stochastic programming model is proposed to deal with a multi-period multi-product multi-site production-distribution planning problem for a midterm planning horizon. The presented model involves majority of supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost. Moreover some respects as lead time, outsourcing, employment, dismissal, workers productivity and training are considered. Due to the uncertain nature of the supply chain, it is assumed that cost parameters and demand fluctuations are random variables and follow from a pre-defined probability distribution. To develop a robust stochastic model, an additional objective functions is added to the traditional production-distribution-planning problem. So, our multi-objective model includes (i) the minimization of the expected total cost of supply chain, (ii) the minimization of the variance of the total cost of supply chain and (iii) the maximization of the workers productivity through training courses that could be held during the planning horizon. Then, the proposed model is solved applying a hybrid algorithm that is a combination of Monte Carlo sampling method, modified -constraint method and L-shaped method. Finally, a numerical example is solved to demonstrate the validity of the model as well as the efficiency of the hybrid algorithm

Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey

To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making

Environmentally Conscious Design of Upstream Crude Oil Supply Chain

In the past few decades, very rapid growth in environmental legislation has resulted in an increasing will of companies to address environmental thinking through their supply chain. In this context, great strides have been made to incorporate the environmental concerns, such as “green” and “sustainable” supply chains, along with the traditional economic indicators. To assess the environmental impacts, there is no agreement on a universal environmental metric. Hence, a plethora of indicators has been developed to measure environmental impacts. The environmental indicators (e.g., Eco-indicator 99) that are founded on the Life Cycle Assessment (LCA) framework and nowadays are becoming among the popular environmental assessment methodologies. The crude oil tankers and utilities consumptions are the main origins of emissions through the crude oil supply chain. The energy required for operating upstream facilities in the crude oil supply chain represents enormous energy consumption. Whereas, ships and oil tankers are of the highest polluting combustion origins, per unit of fuel used. As a result, environmentally conscious design of upstream crude oil supply chain has created intriguing new challenges for practitioners and the managers. In this work, we introduce an environmentally conscious mathematical model to design the Upstream Oil Supply Chain (i.e., oil field development, and crude oil transportation). The model configure the supply network, select the technologies, establish the pipeline network, and plan the oil tankers with optimizing the economic objective value (i.e., the net present value) and the environmental metric value (i.e., the standard Eco-indicator 99 value)