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A literature survey on planning and control of warehousing systems by JEROEN P. van den BERG P art II. 指導老師:林燦煌 博士 報告者:梁士明 200 5/4/25. Unit-load retrieval systems. - PowerPoint PPT Presentation
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A literature survey on planning and control
of warehousing systems
by JEROEN P. van den BERG
Part II
指導老師:林燦煌 博士報告者:梁士明
2005/4/25
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Unit-load retrieval systems
• Author:Goetschalckx, Ratliff[19] introduce duration of stay for individual load as alternative of COI(cube-per-order index 訂單體積指標 ,計算物品空間需求與暢銷性的關係 )
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Unit-load retrieval systems
Hausman et al.[3] introduce the cumulative demand function G(i)=i^s
and show that a class-based policy with relatively few classes yields mean travel times that are close to those obtained by dedicated policy
• i denotes a fraction of the products which contains the products with highest COI
• s is a suitably chosen parameter, and s=0.139 if 20% products generates 80% of all demand
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Unit-load retrieval systems
Graves et al.[2] observe furture travel time reductions when aloowing dual command cycles
• Extended from Hausman et al.[3]• Analytic computations using a continuous
rack and discrete computations using a rack with 30x10 locations
• Determine the expected cycle time for combination of storage policies 、 sequencing strategies 、 queue length of S/R requests
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Unit-load retrieval systems
Schwarz et al. verify the analytic results in [2],[3] with simulation
• Closest Open Location rule is applied to select a location under randomize storage policy
• Mean travel times with COL rule are comparable to analytic results which baes on arbitrary location selection
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Closest Open Location
靠近出口法則 (Closest Open Location) :將剛到達的商品指派到離出入口最近的空儲位上。
Refer:http://www.materialflow.org.tw/abstract/book4/chap3.html
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• S/R machines can often move simultaneously along horizontal and vertical paths at speeds vx and vz. To reach a location (x,z) from (0,0) requires the Chebyshev measure travel time max(x/vx,z/vz). If rl is the rack length and rh the rack height Chebyshev travel require
rl vx = rh vz
• Rectangular building designs with I/O points at the eand of each aisle are often optimal for Chebyshev travel
Refer : http://www.rh.edu/~ernesto/C_S2001/mams/notes/mams14.html
Chebyshev( 柴比雪夫 ) travel
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Unit-load retrieval systems
Guenov & Raeside[20] in experiments, an optimum tour with respect to Chebyshev travel may be up to 3% above the optimum for travel time with acceleration/deceleration
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Unit-load retrieval systems
Hwang & Lee[21] provide a travel time measure that include acceleration/deceleration
Chang et al.[22] consider various travel speeds
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Order-picking systems
Organ pipe arrangement• Aisles closest to the center should
carry the highest COI
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Control of warehousing operations
• Batching of orders• Routing and sequencing• Dwell point positioning
Focus on AS/RS
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Batching of orders• To reduce mean travel time per order• Orders in batch may not exceed the
storage capacity of vehicle• Large batches give rise to response
times• Orders at the far end of WH delayed• Trade-off between efficiency and
urgency
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Batching of ordersTwo trade-offs• Static approach: select a block with
most urgent orders and find a batching to minimize travel time
• Dynamic approach: assign due date to orders and release orders immediately, then establish a schedule that satisfies these due date
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Batching of ordersFor static approach1. select a seed order for batch2. Expand the batch with orders that
have proximity to seed order• Capacity can not be exceeded• Distinctive factor is the measure for
the proximity of orders/batches
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Routing and sequencing
• Unit-load retrieval operations• Order-picking operations• Carousel operations• Relocation of storage
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Unit-load retrieval operations
Hausman et al.[3] only consider single command cycles
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Unit-load retrieval operations
Graves et al.[2] study the effects of dual command cycles and observe travel time reductions of up to 30%
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Order-picking operationsRatliff & Rosenthal[56] present dynamic
programming algorithm that solves TSP• In a parallel aisle warehouse with
crossover aisles at both ends of ech aisle
• Computation time is linear in the number of stops
• Problem remains tractable if there are 3 crossovers per aisle
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Traveling salesman problem(TSP)
• The salesman have to visit the cities in his territory exactly once and return to the start point
• find the itinerary( 行程 ) of minimum cost
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Order-picking operationsPetersen[57] evaluates the
performance of 5 routing heuristics in comparison with the algorithm of Ratliff & Rosenthal[56]
• Best heuristics are on average 10% over optimal for various wh shapes, locations of I/O station and pick list sizes
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Order-picking operationsGoetschalckx & Ratliff[58] give
algorithm for order-picking in WH with non-negligible aisle width
• Savings of up to 30% are possible by picking both sides of the aisle
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Order-picking operationsGoetschalckx & Ratliff[59] propose a
dynamic programming algorithm that the travel time of the order-picker is measured with the rectilinear metric
• Determine the optimal stop position of vehicle when performing multiple picks per stop is allowed
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Order-picking operationsGudehus[1] describes band heuristic• Rack is devides into 2 horizontal
bands• Vehicle visit the locations of lower
band on increasing x-coordinate• Subsequentlt, visit upper band on
decreasing x-coordinate
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Order-picking operationsGolden & Stewart[60]• TSP for which travel times are
measured by Euclidean metric has an optimal solution
• Nodes on the boundary of the convex hull are visited in the same sequence
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Convex hull( 凸包 )
• 求最小凸多邊形 (convex polygon, 沒有凹陷位 ) 將平面上給定的所有點包含在裡面
Refer :http://www.geocities.com/kfzhouy/Hull.html
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Convex hull( 凸包 )• Akl & Toussaint[61] present a fast
algorithm for finding the convex hull
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Order-picking operationsBozer et al.[64] present that use convex hull
of the rack locations as an initial subtour• Locations in the interior of hull are inserted• For Chebyshev & rectilinear metric some
locations can be inserted without increasing the travel time
• also present an improved version of the band heuristic that blocks out a central portion of the rack
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Order-picking operations
Hwang & Song[65] present a heuristic that considers the convex hull for Chebyshev travel and rectilinear hull for rectilinear travel to ensure safety of pickers
• Below a predetermined height Chebyshev travel is performed
• Above this height , rectilinear travel is performed
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Order-picking operationsDaniels et al.[66] consider the situation
where products are stored at multiple location and picked freely. It’s not acceptable because
• Propagates aging of the inventory (not FIFO)
• Increases storage space requirements (multiple incomplete pallets)
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Carousel operationsBartholdi and Platzman[67] present a
linear time algorithm• Sequencing picks in single order• Assume time needed by robot to
move between bins within the same carrier is negligible compared to the time rotating carousel to next carrier
• Reduce the problem of finding shortest Hamiltonian path on a circle
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Hamiltonian path由數學家 Euler 提出的:西洋棋的騎士能否
走完一個空棋盤的六十四格,而且每格只走過一次。這條路徑,在圖論上稱為「 Hamiltonian path 」 ,而每個格子稱為「 vertex 」,每個格子能向外走出的步數稱為「該 vertex 的 degree 」。
• Refer:http://episte.math.ntu.edu.tw/java/jav_knight/
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Carousel operationsWen and Chang[68] present 3
heuristics• Sequencing picks in single order• Time to move between bins may not
be neglected• Based upon the algorithm in Bartholdi
and Platzman[67]
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Carousel operationsGhosh and Wells[69], van den Berg[70]
present optimal pick sequence• Multiple orders• Dynamic programming algorithm• Sequence of orders is fixed• Sequence of picks in orders is free
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Carousel operationsBartholdi and Platzman[67] present a
heuristic for the problem with extra constraint
• Order sequence is free• Picks within same order must be
performed consecutively• Extra constraint: each order is picked
along its shortest spanning interval
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Carousel operationsVan den Berg[70] presents a polynomial
time algorithm that solve the problem with extra constraint to optimality
• At most 1.5 revolutions of the carousel above a lower bound for the problem without extra constraint
• Reveal that the upper bound of one revolution presented by Bartholdi and Platzman[67] for their heuristic is incorrect
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Relocation of storageJaikumar and Solomon[71] address the
problem of relocating pallets with a high expectancy of retrieval to locations closer I/O station during off-peak hours
• Assume there is sufficient time (travel time is omitted)
• Present a algorithm to minimize the number of relocations
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Relocation of storageMuralidharan et al.[72] suggest
randomized location assignment• Combines benefits of randomized
storage (less storage space) and class-based storage (less travel time)
• Respect to their turnover rate during idle periods
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Dwell point positioning
Dwell point : the position the S/R machine resides when system is idle
• Minimize the travel time from the dwell point to position of 1st transaction
• If 1st operation is advanced, all operations within the sequence are completed earlier
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Dwell point positioning
Graves et al.[2] select the point at the I/O station and Park[73] shows the optimality
• If the probability of the 1st operation after idle period being a storage is at least 0.5
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Dwell point positioning
Egbelu[74] presents LP-model that• Minimize the expected travel time• Minimize the maximum travel time to
the 1st transaction
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Dwell point positioning
Egbelu and Wu[75] use simulation to evaluate the performance of several strategies
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Dwell point positioning
Hwang and Lim[76] treats this problem as a Facility Location Problem
• Computational complexity is equivalent to sorting a set of numbers
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Dwell point positioning
Peters et al.[77] presents an analytic model based on expressios found by Bozerand White[78]
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