Pareschi, G. Santarelli

Transcription

1 University of Bologna (Italy) Department of Industrial Mechanical Plants (DIEM) Optimal dwell point policies for new automated Storage/Retrieval systems A. Regattieri, R. Accorsi, M. Bortolini, M. Gamberi(*), R. Manzini, A. Pareschi, G. Santarelli DIEM, University of Bologna, viale Risorgimento 2, 40136, Bologna Italy *DTG, University of Padova, Stradella San Nicola 3, 36100, Vicenza Italy XVI Summer School Francesco Turco Impianti Industriali Meccanici Abano Terme, Padova 14-16/09/2011

2 INTRODUCTION An Automated Storage and Retrieval System (AS/RS) consists of a variety of computer-controlled devices and methods for automatically placing and retrieving loads from specific storage locations

3 INTRODUCTION Advantages (Rosemblatt et al., 1993) Disadvantages Rosenblatt M.J., Roll Y., Zyser V. (1993). A combined optimization and simulation approach for designing Automated Storage/Retrieval Systems. IIE Transactions, vol. N. 25(1), pagg

4 SP-AS/RS A Split Storage/Retrieval (SP-S/R) mechanism carries out loads with separate devices: the first moving in the vertical direction and the second moving in the horizontal one. Both the vertical and the horizontal drivers work independently. (Hu et al., 2005)

5 Conventional AS/RS vs SP-AS/RS Comparing the structure of the traditional mechanism with the innovative S/R mechanism of an AS/RS system, it is possible to remark the main advantages about the new mechanism: Traditional mechanism S/R SP - S/R The two drives work The two drives work Movement of the vertical simultaneously and belong at independently and belong at two and horizontal drives the same machine separate devices Lifting capacity Low High Concurrency Low High Performance Low High Rack configuration Not flexible Flexible Fault tolerance Low High Hu Y.H., Huang S.Y., Chen C.Y., Hsu W.J., Toh A.C., Loh C.K., Song T. (2005). Travel time analysis of a new automated storage and retrieval system. Computers & Operations Reasearch,vol. l N. 32,pagg

6 NEW PROPOSED MODEL THE GOAL To find the optimal Dwell Point Policy (DPP), in order to minimize the travel time and the distance traveled for SP-AS/RS system. Dwell Point: the location where the stacker crane lies when it is inactive

7 NEW PROPOSED MODEL Hypothesis: Unit loads are allocated in a random way Single command missions Storage (S) or Retrieval (R) mission The rack is a single depth type The acceleration and deceleration of stacker crane are not considered The pdf of mission inter-arrivals time is a normal distribution with a mean value µ and a standard deviation σ Consideration of the dwell point policies defined by Bozer and White, 1984: INPUT (IN) MIDPOINT (MID) INPUT/OUTPUT (I/O) LAST LOCATION (LL) Bozer Y.A. and White J.A. (1984). Travel time models for Automated Storage/Retrieval Systems. IIE Transactions, vol. N. 16, pagg

8 NEW PROPOSED MODEL Hypothesis: Unit loads are allocated in a random way Single command missions Storage (S) or Retrieval (R) mission The rack is a single depth type The acceleration and deceleration of stacker crane are not considered The pdf of mission inter-arrivals time is a normal distribution with a mean value µ and a standard deviation σ Consideration of the dwell point policies defined by Bozer and White, 1984: INPUT (IN) MIDPOINT (MID) INPUT/OUTPUT (I/O) LAST LOCATION (LL) At the end of each cycle relative to a request, the stacker crane comes back at the input point Bozer Y.A. and White J.A. (1984). Travel time models for Automated Storage/Retrieval Systems. IIE Transactions, vol. N. 16, pagg

9 NEW PROPOSED MODEL Hypothesis: Unit loads are allocated in a random way Single command missions Storage (S) or Retrieval (R) mission The rack is a single depth type The acceleration and deceleration of stacker crane are not considered The pdf of mission inter-arrivals time is a normal distribution with a mean value µ and a standard deviation σ Consideration of the dwell point policies defined by Bozer and White, 1984: INPUT (IN) MIDPOINT (MID) INPUT/OUTPUT (I/O) LAST LOCATION (LL) At the end of each cycle relative to a request,the stacker crane comes back in the middle of each shelf Bozer Y.A. and White J.A. (1984). Travel time models for Automated Storage/Retrieval Systems. IIE Transactions, vol. N. 16, pagg

10 NEW PROPOSED MODEL Hypothesis: Unit loads are allocated in a random way Single command missions Storage (S) or Retrieval (R) mission The rack is a single depth type The acceleration and deceleration of stacker crane are not considered The pdf of mission inter-arrivals time is a normal distribution with a mean value µ and a standard deviation σ Consideration of the dwell point policies defined by Bozer and White, 1984: INPUT (IN) MIDPOINT (MID) INPUT/OUTPUT (I/O) If the last request is a storage, the stacker crane must stop at the position of the last mission; if the request is a retrieval, the stacker crane must LAST LOCATION (LL) be placed at the outputpoint Bozer Y.A. and White J.A. (1984). Travel time models for Automated Storage/Retrieval Systems. IIE Transactions, vol. N. 16, pagg

11 NEW PROPOSED MODEL Assumptions: Rack dimensions Lp 1.500(h) mm Number of spans 72, 81, 108, 144 Number of levels 36, 32, 24, 18 Input/output point Level 0 Crane horizontal speed Crane vertical speed Aisle s dimension Load/unload fixed time 2,0 m/sec 1,0 m/sec 1,5 m 20 sec The position of a generic unit load is defined by the couple (x,y) x number of span y number of level

12 INSTANCES AND SIMULATION RUNS 8 configurations are considered varing the number of span and the number of levels. Variable Conf. 1 Conf. 2 Conf. 3 Conf. 4 Conf. 5 Conf. 6 Conf. 7 Conf. 8 Number of span Number of level I/O point Level 0 µ 1 = 330 sec Mean value of interarrival time (µ) 2 = 210 sec µ µ 3 = 150 sec Std deviation of inter-arrival time (σ) σ = 60 sec 3 different mission inter-arrival times are considered 36 different instances and, for each of them, simulative runs are developed (ANALYSIS SUPPORTED BY MS-EXCEL & VISUAL BASIC SOFTWARE PLATFORM)

13 NEW PROPOSED MODEL The model is articulated in three travel time sub-models, one for each dwell point strategy. Hio = input/output point P 1 = position of the load to storage/to retrieve P n-1 = position of the last load stored or retrieved L/2 = middle of length of the warehouse H/2 = middle of height of the warehouse T l/u = load/unload time Tc = travel time Dtot = distance traveled for the mission Tm (Hio_P 1 ) = time spent from Hio and the point P 1 D (Hio_P 1 ) = distance between Hio and the point P 1 Tm (P n-1 _P 1 ) = time spent from the point P n-1 to P 1 D (P n-1 _P 1 ) = distance between the points P n-1 and P 1 Dwell Point Policy Mission n n-1 IN (I/O) S/R - MID S/R - LL S/R S R Tc Tm(Hio_P 1 ) = Tc = T l/u + Tm(Hio_P 1 ) Tm(Hio_P 1 ) = Tc = T l/u + Tm(Hio_P 1 ) Tm(P n-1 _P 1 ) = Tc = T l/u + Tm(P n-1 _P 1 ) Tm(Hio_P 1 ) = Tc = T l/u +Tm(Hio Tm(Hio_P 1 ) Dtot D(Hio_P 1 ) = Dtot = 2 Hio-y1 + 2 x1-0 D(Hio_P 1 ) = Dtot = 2 L/2-x1 +2 H/2-y1 D(P n-1 _P 1 ) = Dtot = y(n-1)-y1 + x(n-1)-x1 D(Hio_P 1 ) =Dtot = 2 Hio-y1 + 2 x1-0

14 AD DPPTT [min] RESULTS AND DISCUSSION_1 An Average Dwell Point Policy Travel Time (ADPPTT) is obtained considering the average value of travel time for all tested instances using the average behaviour betweeneen the different pdf distribution of inter-arrivals als time. 3,4 3,2 3,0 2,8 2,6 2,4 2,2 2,0 IN MID LL 1, Level Span

15 RESULTS AND DISCUSSION_2 ADPPTT trends according to several configurations in terms of span and levels, using dfferent swell point strategies. 3,4 32 3,2 3 ADPPTT [min n] 2,8 2,6 2,4 IN MID LL 2,2 2 1,8 72;18 81;24 72;36 81;32 108;24 144;18 108;32 144;36 Span; Level

16 RESULTS AND DISCUSSION_3 Average travel time (ADPPTT), normalized to one obtained with LL policy. 1,3 1,3 1,2 1,2 ADPPTT [%] 1,1 1,1 1,0 1,0 0,9 0,9 IN MID LL 0,8 72;36 81;32 108;24 144;18 72;18 81;24 108;32 144;36 Span; Level

17 CONCLUSION The aim of the model is to find the optimal dwell point policy, able to minimize the travel time and the distance traveled for this kind of AS/RS system. A new model and a simulation software are defined 3,4 ADPPTT T [min] 3,2 3,0 2,8 2,6 2,4 2,2 2,0 IN MID LL 1, Best policy: LAST LOCATION (S, L, HI/O, µ, σ, N)

18 FURTHER RESEARCH A parametric model considering a very high number of different configurations is under construction. The optimal dwell point evaluation considering the effect of the class-based storage assignment and the effect of dual command missions (DC).

19 Giulia Santarelli University of Bologna (Italy) Department of Industrial Mechanical Plants (DIEM) Thank you.