A New Method of Fms Scheduling Using Optimization and Simulation

Nowadays, in modern manufacturing the trend is the development of Computer Integrated Manufacturing, CIM technologies which is a computerized integration of manufacturing activities (Design, Planning, Scheduling and Control) that to produce right products right at right time to react quickly to the global competitive market demands. The productivity of CIM is highly depending upon the scheduling of Flexible Manufacturing System (FMS). Shorting the makespan leads to decreasing machines idle time which results improvement CIM productivity. Conventional methods of solving scheduling problems such as heuristic methods based on priority rules still result schedules, sometimes, with significant idle times. To reduce these, the present paper proposes a new high quality scheduling method. This method uses multi-objective optimization and simulation. The method is called “Break and Build Method”, BBM. The BBM procedure has three stages, in the first Building stage; the steps are to build up some schedules using any scheduling methods for example: heuristic ones which are tested by simulation. In the second Breaking stage, optimum sizes of batches are determined. In the final Rebuilding stage, the most proper schedule is selected using simulation. The goal of use of simulation within manufacturing scheduling is to achieve the two following objectives: first is the visual representation of manufacturing process behavior of a chosen schedule. The second is testing and validation of schedules to select the most proper schedule what can be successfully implemented. There are two-objectives achieved by BBM to the given simple example, one is improved productivity by 31.92% and the other is meeting delivery dates. The method produces a new direction of manufacturing scheduling using differential calculus, gives a new results and new information for solving simple manufacturing scheduling problem. INTRODUCTION Flexible Manufacturing System (FMS) is an automated manufacturing system which consists of group of automated machine tools, interconnected with an automated material handling and storage system and controlled by computer to produce products according to the right schedule. Manufacturing scheduling theory is concerned with the right allocation of machines to operations over time. FMS scheduling is an activity to select the right future operational program and/or diagram of an actual time plan for allocating competitive different demands of different products, delivery dates, and/or sequencing through different machines, operations, and routings that for combination the high flexibility of job shop type with high productivity of flow-shop type and meeting delivery dates. FMS Scheduling system is one of the most important information-processing subsystems of CIM system. The productivity of CIM is highly depending upon the quality of FMS scheduling. The basic work of scheduler is to design an optimal FMS schedule according to a certain measure of performance, or scheduling criterion. This paper focuses on productivity oriented-makespan criteria. Makespan is the time length from the starting of the first operation of the first demand to the finishing of the last operation of the last demand. Conventional methods of solving scheduling problems such as heuristic methods based on priority rules (FIFO, SPT, SLACK...) determined the corresponding schedule but usually, still having idle times. To reduce these and improving CIM productivity, this paper presents a new method so called “Break and Build Method”, BBM. The paper can be classified into forth parts as follow:-First Part: Scheduling using BBM. Second Part: Application of BBM to the simple scheduling problems. Third Part: Conclusion, and References. SCHEDULING USING BBM BBM is a multi-criteria optimization and simulation approach in which the optimum schedule of tasks of High Number of Parts (HNP) are divided into optimum subseries (batches), then rebuild the schedule again and overlapping production can be realized at certain condition and tested using one of simulation methods (e.g.: Taylor ED). BBM has two-objectives for this situation, one is a higher productivity and the second is meeting delivery dates. Heuristic Scheduling Methods A heuristic is a rule of thumb procedure that determines a “good-enough” , satisfactory and feasible solution within certain constraints, but not necessarily guarantees the best or optimal, solution to a problem. A good heuristic is generally within 10% of optimality, the amount of error is not known and degree of optimality is not known. Heuristic methods based on priority rules for job-shop scheduling problem are not a convenience but a necessity for selecting which job is started first on certain machine. Some of the rules used to scheduling problems are FIFO (First In First Out), SPT (Shortest Processing Time) and SLACK.... rules. in this paper the number of schedules to be evaluated is s Π = n!=2 schedule, where, n: number of demands = 2 . The priority rules used in the present paper are FIFO and SPT as following:BBM Procedure The BBM procedure is consists of the following three stages:1. Building Stage In the building stage, the steps are to built up an optimum schedule using any scheduling methods such as heuristic method and tested by simulation Scheduling Problem The shop considered in this paper consist of 2-different independent machines M1, M2 of load, L1, L2 respectively will process 2 demands, d1, d2 of units, X1, X2 .Each demand processed by 2 operations O1,O2 each operation consists of run time t and set up time δ with precedence relationship O1 precedes O2 and the processing times are P1, P2 respectively, The due date of d1 and d2 is D. Data is summarized at demand table in fig.1. The Objective is to determine the best schedule using productivity criteria. a) SPT rule Table (2) SPT Table M1 M2 s O f s O f 0 22 2 O f1 11 2 O L1 L1 T1 11 2 O 11 2 O 11 2 O 11 1 O 22 1 t Table (1) Demand Table. b) FIFO rule d O1 O2 P d1 11 1 O 22 1 O P1 d2 11 2 O 22 2 O P2 L L1 L2 t S Table (3) FIFO Table M1 M2 s O f s O f 0 2 11 1 O L1 L1 T2 22 1 O f 11 1 O 11 1 O 11 1 O 11 2 O 22 2 t Notations om i O :O (Operation time), o (operation number) , Mathematical Model The mathematical model for the formulated problem is m (machine number),i (demand number) , om i t : run time, Objective Function: Minimize r: ready time, s: start time, f: flow time, t S : Schedule time, s Π :Number of schedules, T: Makespan Lmax:bottleneck machine load, η :Schedule Productivity Index, ηR :Schedule Productivity Rate T = t + 11 1 22 1 t + 11 2 t + 22 2 t + 4δ ....(1) Subject to 11 1 t 22 1 t , 11 2 t 22 2 t ≥ 11 1 t 22 1 t ≥ 11 2 t ≥ 22 2 t , L1 ≤ T ≤ D ≤ t S Assumptions T1 = Lmax + 22 1 t , where Lmax= max (L1, L2) = L1 1. No Cancellation. No Breakdown. No Preemption. T2 = Lmax + 22 2 t 2. Operating cost is constant. Since 22 2 t ≤ 22 1 t , Lmax = constant 3. δ is constant , r =0 Demand chart as in fig. (1), shows how much time required to processing each demand P1, P2 , . Load chart as in fig. (2) Shows how much time to be loading each machine L1, L2 required to produce the two demands. T2 ≤ T1 T2 = ∗ T = Lmax + 22 2 t , Lmax = 11 1 O + 11 2 O om i O = om i t +