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2.3 Influence between configuration selection and production process design
The operation of product has the great influence on manufacturing device in production line, and one specific operation usually has the most suitable configuration of machine tool. Meanwhile, reconfiguration of RMT will lead to the substantial cost, and it will also affect production time and cost. Moreover, different configurations even have some impact on machining precision. Each station of the reconfigurable production line has several configurations, whose relations with reconfiguration cost, production time, production cost and machining precision of OP are analyzed as follows.
Due to changes of configurations, the production time and cost for the same OP is also changed. For example, for a series of straight holes in cylinder head, if by changing main axis and clamping components they are processed from fine boring way of horizontal machining centre to grinding way, the production time will increase, but production cost will reduce to some extent. Generally, different configurations of machine tools inevitably lead to the fluctuation of precision. Thus, it is needed to select the appropriate processing accuracy according to different OP requirements which can ensure the quality of product and save the reconfiguration and production cost. Summarize of above that the process plan according to product features should consider the selection and configurations of machine tool including production line balance, smoothness, and so on; meanwhile, the reconfiguration ability and design of machine tool have great impact on product process, machining precision as well as cost.
3 Problem Formulation
3.1 Performance measures
The performance measures are classified into monetary and nonmonetary. The monetary measures are mainly cost related such as reconfiguration and production costs. On the other hand, the nonmonetary measures are mainly related with line balance and machining precision which should be treated differently. The details are explained as follows. (1) Monetary measures. Important cost components relate to reconfiguration of machine tool and production. The amount of cost is given as (1) where is the amount of cost of monetary measure. is the production related cost. is the total reconfiguration cost of machine tools of the production line, and (2) where is the number of stations, is the number of different configurations, is configuration selection variable, and is the configuration cost of the jth configuration of station m. The total production cost is expressed as: (3) where is the production cost determined by the production volume and the selected configurations of machine tools, which is (4) , CO CRCPCO CP CR 1 1 , M J mj mj m j CR u CR m 1, 2,, ; mMj 1, 2,, . j Jmj u1, if the th configuration of station is selected, 0, otherwise, mj j m u mj CR, CP CV CICV 1 1 1 , I M J imj imj i m j CV V x CO where V is the number of operations to be dealt with, and is the cost that the ith operation is produced when it is allocated to the jth configuration of the mth station, and is the selection variable. is the idle cost due to unbalanced station workloads, which is (5) where Tc is the cycle time, and is the processing time of operation i, which is dependent on the associated configuration of machine tool, and is the cost of unit idle time, M is the number of stations. (2) Nonmonetary product performance measure. The nonmonetary performance measures include line balance and machining precision, which is (6) where is the nonmonetary product performance measure of production line. is the degree that the workload is distributed as evenly as possible, which can be measured by the smoothness index: (7) whereis the maximum station workload and is the workload of station j, which is defined as (8) where is the operation-station assignment variable, and is to index the machining precision which is determined by the configuration of machine tool, and defined as (9) where represents the precision value for the jth configuration of the mth station. 0 means the precision is high, and 1, otherwise. is the unit value for precision. imj COimj xCI c 1 1 , I i i CI V MT T L i T1 L, NO LBMP NO LB 2 max 1 1 ( ) , J j j LB TS TS J max TSj TS 1 , I j i ij i TS T Z ij Z1, if the operation is assigned to the station , 0, otherwise, ij i j z MP 2 1 1 , M J mj mj m j MP u p L mj pmj p2 L