Material Handling System Performance analysis

1. Material Handling SystemPerformance analysis 서울대학교 산업공학과 공장자동화연구실 1998년 3월 31일 심 억 수 (ses@ultra.snu.ac.kr)

2. Contents • Performance measure에 대한 포괄적인 내용 • Performance analysis • Conclusion

3. Performance, reliability, and performability of material handling systems B. M. Beamon (Dept. of Mechanical, Industrial, and Nuclear Engineering, Univ. of Cincinnati, Cincinnati, OH, USA) Int. J. Prod. Res., 1998, V.36, No.2, 377-393

4. Performance measures • Definition and application • Performance measure : a metric for quantifying efficiency and/or effectiveness • effectiveness : what extent the system performs the required handling tasks • efficiency : how economically (resource utilization) these tasks are performed • The categorization of the performance measures • quality, time, cost, resource utilization, operating efficiency, flexibility measures • Time-based performance measure 의 구분 • direct measures (of the activity at a particular point in time), cumulative measures, benchmarking measure (Oden 1993)

5. Performance measures for manufacturing and material handling system (1/2) • Manufacturing cycle efficiency : the ratio of the time spent in actual production operation over the total time in the production area (Fogarty 1992) • S : total setup time • R : total run time • W : total wait time • M : total material handling travel time • Value added efficiency :the ratio of time during which value is added over the total time in the production area (Fogarty 1992)

6. Performance measures for manufacturing and material handling system (2/2) • P/T ratio : the ration of the average processing time per operation divided by the average transport time per transfer (Kim and Tanchoco 1993) PAVE : average processing time TAVE : average transport time • Job throughput • Job throughput time (flowtime) refers to the total time a job spends in the system • Throughput quantity (throughput or production volume) is the number of jobs completed (or which exit the system) in a given period of time • Time required to complete a fixed number of jobs • Throughput ratio defined as the ratio of the attained throughput (parts completed) over the the total input

7. MHS performance measures (1/5) • Vehicle travel : Discrete (or travel time) (Seo and egblu, 1995) • TL : total loaded travel time • TE : total empty travel time • Vehicle travel proportions : travelling loaded, travelling empty, idle (Fogarty, 1991) • TI : total idle time • T : total time • f : traffic factor

8. MHS performance measures (2/5) • Vehicle travel : response time • define response time for a pick-up call as the time from when the pick-up request is made until the vehicle (starting from an idle and empty condition) arrives at the pick-up location • Handling time per job • the time the job spends in queues waiting for the MHD • the total travel time • the total loading and unloading time • total vehicle blocking time • Vehicle utilization • vehicle fleet size requirement 결정에 사용 • Number of loads completed : the number of loads (or deliveries) completed over a period of time by all of the MHD

9. MHS performance measures (3/5) • Station queues : Mean load waiting times (the mean time loads wait in queues for material handling transportation) • Station queues : Mean queue lengths (the mean number of loads waiting for a material handling vehicle over a specific length of time) • Material handling system cost (7) • Cin : moving cost one unit load and one unit distance within a department • Cout : moving cost one unit load and one unit distance between departments

10. MHS performance measures (4/5) • Material handling system flexibility : range and response (8) • number of equipment of type i • max unit load quantity factor, based on capacity of the equipment • equipment speed, based on the normal operating speed of the equipment • equipment loaded travel factor • relative rerouteing cost, indicates ability of equipment to reconfigure • Congestion • Vehicle Blocking Time : the time where vehicles are unable to move due to other vehicles • Track Blocking Percentages : the blocking time (as a percentage) for track segments due to vehicle interference • Track Utilization • Vehicle Waiting Time at Intersection

11. MHS performance measures (5/5) • Congestion index • TA : the actual travel time • TS : shortest travel time if there were no congestion

12. Decision-making and MHS performance analysis • Single performance measure • Travel distance와 type of flow path (시스템 비용과 vehicle travel distance 에는 tradeoff가 존재) • 만약 Vehicle utilization이 loaded vehicle travel time으로 정의된 경우 • Multiple performance measures • 여러 objective사이의 tradeoff간의 conflict가 지금까지는 무시되었다. • Economic과 시스템 performance measure는 동시에 사용 • Cost과 performance사이에는 inherent relationship이 존재 • Multiple criteria decision making • The categorical method • Weighted-point method • Modified dimensional analysis • performance index • The objective matrix • 다양한 performance score와 weight를 가진 multiple criteria를 사용

13. Performance measure selection for MHS • Characteristics of effective performance systems • Inclusiveness : MHS의 all pertinent aspect를 measure해야 함. • Universality : wide range의 operating condition에서의 comparison이 가능해야 함 • Measurability : 필요한 모든 data는 readily measurable해야 함 • Consistency : Performance Measure 는 조직 전체의 goal과 consistent해야 함 • Performance measure selection in MHS research • 개발된 모델에 따라 single performance measure를 선택 • 몇몇 multiple performance measure 사용한 경우 • 관심 시스템에 대해 계산 • 이러한 measure의 선택에 대한 justification이나 explanation이 없다. • 값들이 무엇을 나타내는 지에 대한 system-level interpretation이 없다. • No chronological trend • 조금 더 자주 사용된 performance measure • Utilization, Distance (Time), Cost

14. Reliability • Reliability : the probability that an item will perform a required function, under stated conditions, for a stated period of time • 주로 사용되는 Reliability measure : availability, unavailability, failure rate, mean time between failure (MTBF) • 1989년 연구 : Part-based reliability, System-based reliability

15. Performability • Failure나 repair를 고려하지 않음으로 해서 system ability를 overestimate했다. • MHS : degradable (degrading) system • Failure를 완충하기 위한 충분한 redundancy를 구축하는 것이 항상 가능한 것은 아니고 현실적이지 못함 • 대부분의 시스템에서 component failure detection이 immediate 하지 못함 • Performance와 reliability를 동시에 설명하는 measure필요 • Performability는 위의 두개를 incorporate한다. • Performability의 정의 : the probability distribution function of the cumulative performance during a specified period of time

16. Conclusion • Numerous performance measures - not effective or appropriate • Multiple performance measures provide more comprehensive information about system behavior • Reliability of MHS has been ignored • Performability measures which simultaneously measure performance and reliability, emerge as appropriate measures for use in the design and analysis of MHS

17. Performance Analysis of FMS with a Single Discrete Material-Handling Device Rajan Suri (Dept. of Industrial Engineering, Univ. of Wisconsin-Madison) Ramakarishna Desiraju (Industrial Dynamics Group, Philips Research, Briarcliff Manor) Int. J. FMS, 9 (1997): 223-249

18. Introduction • The signification of FMSs with a single material-handling resource • This configuration is common in the industry • This configuration simplifies material-handling control • This configuration is potentially amenable to analysis using simple analytical tools • This configuration forms a building block for more complex systems • Motivation for analytical modeling • 시스템 투자가 막대하다. Front-end design과 ongoing analysis effort에 상당한 노력이 필요 • 여러 가지 대안의 FMS configuration을 비교, analytical model이 빠른 response time과 reasonable degree of accuracy로 효율적으로 performance measure가능 • 이 연구에서는 accuracy와 computing speed에서 good trade-off를 제공하는 Queueing Network Analysis Method를 사용한다. • 이 연구의 목적 : Configuration상태에서 performance analysis에 있어서 speed와 accuracy 사이의 good trade-off 를 제공하는 analytical model을 개발하는 것

21. 분석하는 시스템의 특징들 • A closed network • 시스템내의 pallet 의 수는 고정 • 많은 방법들은 MVA에 기반하여 CQN을 분석했다. • MHD interference of blocking • Processing 완료 후 MHD가 available 하고 station에 도착해야만 offload 가능 • Material handling • State-dependent routing • Pallet 의 목적지는 MHD 가 도착하는 다음 station의 상태에 의존한다. • Central buffer

22. The configuration we model • Performance measure • X : the steady-state throughput of the system • rm : m번째 station의 utilization • Wm : m번째 station에서의 job에 대한 기대 response time • L : Job 의 모든 processing 을 끝내기 위해 필요한 기대 response time • 여러 가지 상황들 • M : processing stations (loading, unloading 포함) • N : pallets • Single discrete MHD • Central buffer (개별 station은 buffer를 가지지 못함) • 모든 part는 같은 routing을 가짐 • K : steps in routing • Ni : i번째 step에서 방문되는 station의 index • qj : j번째 step에서의 평균 processing time • dij : station I에서 station j로의 이동 시간, dio, doi

24. Analytical modeling for state-dependent routing (1/3) • Throughput, utilization, response time과 같은 steady-state performance measure를 estimate하려고 한다. • MVA : Bernoulli routing과 exponential processing time을 가진 CQN configuration을 정확히 분석 • Visit count vi : 한 process plan동안 station i 로의 pallet의 visit 수 • 여러 station으로 K visit를 한다. Ni에서 qi의 시간을 보낸다. Inputs Number of pallets Number of stations Service times Visit counts Mean Value Analysis Outputs Utilization of stations Throughput Response times

25. Analytical modeling for state-dependent routing (2/3)

26. Analytical modeling for state-dependent routing (3/3) • Algorithm1. Performance evaluation of a system with state-dependent routing • Inputs : K, N, M, (qi, Ni), dij • Outputs : X, {(rm , Wm ), m=1,….., M+1} • Detailed simulation 결과와 비교

27. Conclusion • The significance of FMS that have a single MH resource and a central buffer • Queuing network based analytical models • Analyze larger mfg. Systems

28. Conclusion and future research • Performance measure of the MHS • The algorithm of the performance of the single discrete MHD • More nice performance measure proposal • Heuristic algorithm which can estimate the performance of the MHS more effectively

29. Performability & CQN(Addendum) 1998. 4. 14. 심억수 (ses@ultra.snu.ac.kr)

30. Why model the effect of Reliability on Performance? • Performability model 의 구성 • reliability model (structure-state process) • performance (reward) model

31. Modeling reliability vs performance • Choose metrics • Formulate separate reliability and performance models • Analyze performance and reliability models separately • Combine results • Refine model • Use results to guide system design • Structure of Performability Models • structure-state process • performance or reward model tells how well the system works with each possible set of operational components • mean interval availability (cumulative-occupancy time) • Computation availability - a single measure that describe perf. and reli. • mean performance level at a given time and is the weighted sum of state probabilities

32. State Diagram for the 2-Processor System 1-bDt 2a 1-2aDt 2aDt a 2 1 2 1 0 b bDt

33. The response-time distribution for the system is the mixture of the fully operational system response-time distribution and the degraded system response time

34. Specification of Queueing Models • Stochastic models for the arrival and service process • Structural parameters of the system • Operating policies SERVER QUEUE B(t) A(t) Customer arrivals Customer departures

35. Limited number of resources • total arrival rate (free constant) • normalization constant

36. Closed queueing network l2 m2 p l1 m1 1-p l3 m3

37. Mean Value Analysis • MVA는 network node에서의 avg. customer system time과 그 node에서의 avg. queue length와의 관계를 이용 • 위의 식들로 평균 queue length, avg. system time at node i, throughput 들 여러 N값에 따라 평가할 수 있다.