In this paper, a type II robotic mixed-model two-sided assembly line Balancing problem is considered. This paper presents a new mixed-integer programming model for type II robotic mixed-model two-sided assembly line Balancing to minimize the cycle time, energy consumption, and purchased cost of robots for a given number of workstations. We provided an effective framework for optimizing the multi-objective robotic mixed-model two-sided assembly line Balancing problem considering energy consumption and smoothing Workload in the make to order environment to help the decision-makers make the right decisions under stochastic demand. An augmented epsilon constraint and Lp-metric methods were applied to solve the problem, and then, with the help of defining two vertical and horizontal criteria, we attempt to help the decision-maker to choose a more efficient solution to make the production line more smooth Workload. We demonstrate the efficiency of the proposed method by designing the numerical experiments.

Assembly Line production is one of the widely used basic principles in production system. The problem of Assembly Line Balancing deals with the distribution of activities among the workstations so that there will be maximum utilization of human resources and facilities without disturbing the work sequence. Research works reported in the literature mainly deals with minimization of idle time i.e. Balancing, subject to precedence constraints. Lack of uniqueness in their optimum solutions has led to the present work where minimization of both Balancing loss and system loss has been envisaged under the usual precedence constraints. The researchers suggest a generic approach for designing of an assembly line where, with a given number of workstations, one can efficiently arrive at the desired solution under different methods of search like simulation, heuristic etc. Thus, the main aim of this paper is to redefine the objective of the Assembly Line Balancing Problem and sequentially handle Balancing Loss and System Loss. A numerical example has been added to demonstrate the generic nature of the researcher's approach and improvement in the solution set when compared with different standard line Balancing methods available so far in the literature.

The main goal of this paper is to develop a new generalization of Balancing and Lucas-Balancing sequences namely Balancing and Lucas-Balancing p-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.