Design a bi-objective mathematical model for cellular manufacturing systems considering variable failure rate of machines
针对单元制造系统中机器故障率随加工次数和时间变化的问题，建立了一个双目标数学模型，同时最小化设备购买和物料移动成本以及机器维修总时间，并通过数值算例验证了模型的有效性。
Current business environment compels manufacturers to produce high-quality products at low cost with the shortest possible delivery time. Cellular Manufacturing Systems (CMSs), utilised to equip the producers to deal with this predicament, have been a point of attraction to both researchers and practitioners. Machine reliability is one of key performance measures of a CMS and the reason is that high machine failure rates lead to due date collision and loss of customers. Therefore, this paper presents a bi-objective mathematical model for a CMS considering the sequence data, alternative process plans, candidate locations for machines, maximum capacity for each machine and variable failure rate of each machine. In the proposed model, the variable failure rate is considered as a dependent variable of ‘number of setups’ and ‘total processing time’ in a regression equation. The first objective of this model is minimising the purchase cost of machines, intra-cellular movements (forward and backward) and the inter-cellular movement costs of materials while the second one is to minimise the total repair time for failed machines. To illustrate the performance of the proposed model, a numerical example is solved in the Generalized Algebraic Modeling Systems software using augmented ε-constraint method. The results of the numerical examples show that the proposed approach is promising.