IE 252 Operational Research Case Study # 2 Flexible Manufacturing Systems (FMS) are integrated systems of computer numerically controlled (CNC) machines connected with automated material handling mechanisms. The capital intensive nature of these systems renders eftective use of available tme and tool magazine capacity crucial for long term survival. Consider a machine time and tool magazine capacity allocation problem faced in FMS environments There are n operations to be processed by a set of m identical parallel CNC machines. An operation can be processed on at most one machine without preemption. The profit brought by operation i on any machine is w money units. P is the total processing requirement of operation i and C, is the time capacity of machine j. P and C, are expressed in the same time units. All CNC machines can accommodate all the tool types. Machine j has a tool magazine capacity of Sj tool slots. There are t tool types in the system and each tool type k uses sk tool slots. Due to the technological restrictions and/or budget limitations, a maximum of na tools of type k are available in the system. To process operation i, a set of tools l(k) should be available on the tool magazine of the machine it is assigned on. The problem is to assign the operations together with their associated tools to the machines so as to maximize the total profit a) Give Integer Programming formulation of the problem. Consider the following instance with 6 operations, 3 machines and 10 tool types where n 1 f ?1,6, 7, 10 and n-2 for k-23.4.5.8.9, s-2 for all k, S-8 for all j, and C,-302; C2-451; C3-381. T profits, processing times and required tools of the operations are given in the following tables. Table 1. The profits and the processing requirements of the operations W 133 71 42 83 91 63 P 60 252 302 79 500 440 IE 252 Operational Research Case Study # 2 Flexible Manufacturing Systems (FMS) are integrated systems of computer numerically controlled (CNC) machines connected with automated material handling mechanisms. The capital intensive nature of these systems renders eftective use of available tme and tool magazine capacity crucial for long term survival. Consider a machine time and tool magazine capacity allocation problem faced in FMS environments There are n operations to be processed by a set of m identical parallel CNC machines. An operation can be processed on at most one machine without preemption. The profit brought by operation i on any machine is w money units. P is the total processing requirement of operation i and C, is the time capacity of machine j. P and C, are expressed in the same time units. All CNC machines can accommodate all the tool types. Machine j has a tool magazine capacity of Sj tool slots. There are t tool types in the system and each tool type k uses sk tool slots. Due to the technological restrictions and/or budget limitations, a maximum of na tools of type k are available in the system. To process operation i, a set of tools l(k) should be available on the tool magazine of the machine it is assigned on. The problem is to assign the operations together with their associated tools to the machines so as to maximize the total profit a) Give Integer Programming formulation of the problem. Consider the following instance with 6 operations, 3 machines and 10 tool types where n 1 f ?1,6, 7, 10 and n-2 for k-23.4.5.8.9, s-2 for all k, S-8 for all j, and C,-302; C2-451; C3-381. T profits, processing times and required tools of the operations are given in the following tables. Table 1. The profits and the processing requirements of the operations W 133 71 42 83 91 63 P 60 252 302 79 500 440