A literature survey on planning and control of warehousing systems by JEROEN P. van den BERG Part II

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A literature survey on planning and control of
warehousing systemsby JEROEN P. van den
BERGPart II

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• ??????
• 2005/4/25

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Unit-load retrieval systems

• AuthorGoetschalckx, Ratliff19 introduce
  duration of stay for individual load as
  alternative of COI(cube-per-order index ??????
  ,???????????????)

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Unit-load retrieval systems

• Hausman et al.3 introduce the cumulative demand
  function G(i)is 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 s0.139 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

• ??????(Closest Open Location)???????????????????
  ???
• Referhttp//www.materialflow.org.tw/abstract/book
  4/chap3.html

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Chebyshev(????) travel

• 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/no
  tes/mams14.html

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Unit-load retrieval systems

• Guenov Raeside20 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 Lee21 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 orders

• Two 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 orders

• For static approach
• select a seed order for batch
• 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 operations

• Ratliff Rosenthal56 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(??) of minimum cost

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Order-picking operations

• Petersen57 evaluates the performance of 5
  routing heuristics in comparison with the
  algorithm of Ratliff Rosenthal56
• 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 operations

• Goetschalckx Ratliff58 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 operations

• Goetschalckx Ratliff59 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 operations

• Gudehus1 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 operations

• Golden Stewart60
• 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(??)

• ???????(convex polygon,?????)???????????????
• Refer http//www.geocities.com/kfzhouy/Hull.html

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Convex hull(??)

• Akl Toussaint61 present a fast algorithm for
  finding the convex hull

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Order-picking operations

• Bozer 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 Song65 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 operations

• Daniels et al.66 consider the situation where
  products are stored at multiple location and
  picked freely. Its not acceptable because
• Propagates aging of the inventory (not FIFO)
• Increases storage space requirements (multiple
  incomplete pallets)

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Carousel operations

• Bartholdi and Platzman67 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

• ???? Euler ???????????????????????,??????????????
  ,???????Hamiltonian path? ,????????vertex?,???????
  ?????????vertex?degree??
• Referhttp//episte.math.ntu.edu.tw/java/jav_knigh
  t/

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Carousel operations

• Wen and Chang68 present 3 heuristics
• Sequencing picks in single order
• Time to move between bins may not be neglected
• Based upon the algorithm in Bartholdi and
  Platzman67

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Carousel operations

• Ghosh and Wells69, van den Berg70 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 operations

• Bartholdi and Platzman67 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 operations

• Van den Berg70 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 Platzman67 for their
  heuristic is incorrect

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Relocation of storage

• Jaikumar and Solomon71 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 storage

• Muralidharan 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 Park73 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

• Egbelu74 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 Wu75 use simulation to evaluate the
  performance of several strategies

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Dwell point positioning

• Hwang and Lim76 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 White78

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Question Discussion