Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model.

An Analysis of Research Trends in the Sustainability of Production Palnning

Sustainability has become of great interest in many fields, especially in production systems due to the continual increase in the scarcity of raw materials and environmental awareness. Recent literature has given significant attention to considering the three sustainability pillars (i.e., environmental, economic, and social sustainability) in solving production planning problems. Therefore, the present study conducts a review of the literature on sustainable production planning to analyze the relationships among different production planning problems (e.g., scheduling, lot sizing, aggregate planning, etc.) and the three sustainability pillars. In addition, we analyze the identified studies based on the indicators that define each pillar. The results show that the literature most frequently addresses production scheduling problems while it lacks studies on aggregate production planning problems that consider the sustainability pillars. In addition, there is a growing trend towards obtaining integrated solutions of different planning problems, e.g., combining production planning problems with maintenance planning or energy planning. Additionally, around 45% of the identified studies considered the integration of the economic and the environmental pillars in different production planning problems. In addition, energy consumption and greenhouse gas emissions are the most frequent sustainability indicators considered in the literature, while less attention has been given to social indicators. Another issue is the low number of studies that have considered all three sustainability pillars simultaneously. The finidings highlight the need for more future research towards holistic sustainable production planning approaches.

Production Scheduling of Personalized Fashion Goods in a Mass Customization Environment

The COVID-19 pandemic has put fashion manufacturers’ needs for optimization in the spotlight. This study argues that mass customization is becoming increasingly instrumental for offering consumers individualized solutions and that suppliers of fashion have to look for more sophisticated solutions in order to face the increasing demand for more sustainable products. With the deduction of a mathematical model derived from production sequencing it became evident that sustainability can be associated with a level production schedule and that cost-based production optimization is useful in achieving holistic sustainability in the fashion industry. The flexibility in the conceived mathematical model specifications allows for a generalizable approach, not limited to a single branch of the fashion industry. This paper additionally delivers a cost-based optimization approach which fashion companies, operating in a mass customization production layout, can easily implement without extensive know-how. The proposed two-stage algorithm is based on the concept of level scheduling. In a first stage, the algorithm determines a feasible production sequence in a time-efficient way while, in the second stage, it further advances the efficiency of the solution. Thus, it offers a framework to optimize a production in a mass customization environment and can contribute to a company taking major steps towards a holistic sustainable orientation as available resources are used more (cost) efficiently.