CPLEX Code of PhD thesis (Multi Objective Robust Aggregate Production Planning in a Supply Chain under Uncertainty)



Department of Industrial Engineering


Multi Objective Robust Aggregate Production Planning in a Supply Chain under Uncertainty



A Thesis Submitted in Partial Fulfillment of the Requirement for the Degree of Doctor of Philosophy in Industrial Engineering


Aggregate production planning in a supply chain is one of the most important activities in the field of planning in leading companies. In this research, several novel aggregate planning models in a supply chain are proposed under uncertainty by the help of multi-objective mathematical programming approach. The proposed models are including two main steps: at first step; some critical decisions about pre-production phase are made such as determining quantity and method of supply and associated logistics and transportation planning, and determining production rate and human resource planning. In the next step, after the realization of first step decisions, we decide about quantity and method of holding inventory, distribution of the end product to the customers and associated transportation planning. The first step decisions are made based on the value of the predicted parameter while the second step decisions are made based on the revealed values of parameters.

The objective functions of the proposed models are as follows:

  • Minimizing total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost
  • Considering customer satisfaction through minimizing the sum of the maximum amount of shortages among the customers’ zones in all periods.
  • Maximizing the worker’s productivity through training courses that could be held during the planning horizon.
  • Minimizing the risk and variability of the plans due to the uncertain nature of the supply chain.

the proposed models have the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow from a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint functions, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated in to the models.

Finally, the proposed models are solved using the exact methods (standard packages CPLEX, LINGO, AUGMECON), simulation method, heuristic method (combination of augmented epsilon-constraint, L-shaped and extended Monte Carlo sampling methods) and metaheuristic method (combination of augmented epsilon-constraint method and Genetic algorithm). By applying the proposed models on a real case study from CHOUKA company also on the numerous randomly generated problems, and comparing the solutions of the proposed methods with the results obtained from the standard packages, the applicability, practicability and efficiency of the proposed methods and mathematical models are demonstrated.

Keywords: Aggregate production planning, supply chain planning, uncertainty, multi-objective optimization, robust stochastic programming

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