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Warehouse Storage Configuration and Storage Policies. Bibliography Bartholdi & Hackman: Chapter 6 Francis, McGinnis, White: Chapter 5 Askin and Standridge: Sections 10.3 and 10.4. I/O. Storage Policies.

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warehouse storage configuration and storage policies

Warehouse Storage Configuration and Storage Policies

Bibliography

Bartholdi & Hackman: Chapter 6

Francis, McGinnis, White: Chapter 5

Askin and Standridge: Sections 10.3 and 10.4

storage policies

I/O

Storage Policies
  • Main Issue: Decide how to allocate the various storage locations of a uniform storage medium to a number of SKU’s.
types of storage policies
Types of Storage Policies
  • Dedicated storage: Every SKU i gets a number of storage locations, N_i, exclusively allocated to it. The number of storage locations allocated to it, N_i, reflects its maximum storage needs and it must be determined through inventory activity profiling.
  • Randomized storage: Each unit from any SKU can by stored in any available location
  • Class-based storage: SKU’s are grouped into classes. Each class is assigned a dedicated storage area, but SKU’s within a class are stored according to randomized storage logic.
location assignment under dedicated storage policy
Location Assignment under dedicated storage policy
  • Major Criterion driving the decision-making process:Enhance the throughput of your storage and retrieval operations by reducing the travel time <=> reducing the travel distance
  • How? By allocating the most “active” units to the most “convenient” locations...
convenient locations
“Convenient” Locations
  • Locations with the smallest distanced_j to the I/O point!
  • In case that the material transfer is performed through a forklift truck (or a similar type of material handling equipment), a proper distance metric is the, so-called, rectilinear or Manhattan metric (or L1 norm): d_j = |x(j)-x(I/O)| + |y(j)-y(I/O)|
  • For an AS/RS type of storage mode, where the S/R unit can move simultaneously in both axes, with uniform speed, the most appropriate distance metric is the, so-called Tchebychev metric (or L norm):

d_j = max (|x(j)-x(I/O)|,|y(j)-y(I/O)|)

active sku s
“Active” SKU’s
  • SKU’s that cause a lot of traffic!
  • In steady state, the appropriate “activity” measure for a given SKU i:

Average visits per storage location per unit time =

(number of units handled per unit of time) /

(number of allocated storage locations) =

TH_i / N_i

a fast solution algorithm
A fast solution algorithm
  • Rank all the available storage locations in increasing distance from the I/O point, d_j.
  • Rank all SKU’s in decreasing “turns”, TH_i/N_i.
  • Move down the two lists, assigning to the next most highly ranked SKU i, the next N_i locations.
example

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I/O

Example

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C: 10/2 = 5

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problem formulation
Problem Formulation
  • Decision variables: x_ij = 1 if location j is allocated to SKU i; 0 otherwise.
  • Formulation:

min S_i S_j [(TH_i/N_i) * d_j] * x_ij

s.t.

 i, S_j x_ij = N_i

 j, S_i x_ij = 1

 i, j, x_ij  {0,1} => x_ij  0

problem representation
Problem Representation

Location

SKU

N_1

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c_ij = (TH_i/N_i)*d_j

N_i

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remarks
Remarks
  • The previous problem representation corresponds to a balanced transportation problem: Implicitly it has been assumed that: L = S_iN_i
  • For the problem to be feasible, in general, it must hold that:

L  S_iN_i

  • If L - S_iN_i > 0, the previous balanced formulation is obtained by introducing a fictitious SKU 0, with

N_0 = L - S_iN_i and TH_0 = 0

locating the i o point
Locating the I/O point
  • In many cases, this location is already predetermined by the building characteristics, its location/orientation with respect to the neighboring area/roads/railway tracks, etc.
  • Also, in the case of an AS/RS, this location is specified by the AS/RS technical/operational characteristics.
  • In case that the I/O point can be placed at will, the ultimate choice should seek to enhance its “proximity” to the storage locations.
locating the i o point example 1

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Locating the I/O point: Example 1

Option A

locating the i o point example 2

I/O

Locating the I/O point: Example 2

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example 2 cont
Example 2 (cont.)
  • Option A: U-shaped or cross-docking configuration
    • amplifies the convenience/inconvenience of close/distant locations
    • appropriate for product movement with strong ABC skew
    • provides flexibility for interchanging between shipping and receiving docking capacity
    • allows for “dual command” operation of forklifts, reducing, thus, the deadhead traveling
    • minimizes truck apron and roadway
  • Option C: Flow-through configuration
    • attenuates the convenience difference among storage locations
    • conservative design: more reasonably convenient storage locations but fewer very convenient
    • more appropriate for extremely high volume
    • preferable when the building is long and narrow
    • limits the opportunity for efficiencies for “dual command” operations
storage sizing
Storage Sizing
  • Randomized Storage:
    • How many storage locations, N, should be employed for the storage of the entire SKU set?
  • Dedicated storage:
    • How many storage locations, N_i, should be dedicated to each SKU i?
    • Given a fixed number of available locations, L, how should these locations be distributed among the various SKU’s?
  • Class-based storage:
    • How should SKU’s be organized into classes?
    • How many storage locations, N_k, should be dedicated to each SKU class k?
possible approaches to storage sizing
Possible Approaches to Storage Sizing
  • Quite often, this issue is resolved/predetermined from the overall operational context: e.g., replenishment policies, contractual agreements, etc., which impose some structure on the manner in which requests for storage locations are posed by the various SKU’s
  • “Service-level” type of analysis:
    • Determine the number of storage locations, N_i to be assigned to each SKU i so that the probability that there will be no shortage of storage space in any operational period (e.g., day) is equal to or greater than a pre-specified value s.
  • Cost-based Analysis
    • Select N_i’s in a way that minimizes the total operational cost over a given horizon, taking into consideration the cost of owning and operating the storage space and equipment, and also any additional costs resulting from space shortage and/or the need to contract additional storage space.
sizing randomized storage based on service level requirements
Sizing randomized storage based on “service level” requirements
  • Q = max number of storage locations requested at any single operational period (a random variable)
  • p_k = Prob(Q=k), k=0,1,2,… (probability mass function for Q)
  • F(k) = Prob(Qk) = _{j=0,…,k} p_j (cumulative distribution function for Q)
  • Problem Formulation

Find the smallest number of locations N, that will satisfy a requested service

level s for storage availability, i.e.,

min N

s.t.

F(N)  s

N  0

  • Solution:

N = min{k: _{j=0,…,k} p_j s}

sizing dedicated storage based on service level requirements
Sizing dedicated storage based on “service level” requirements
  • Q_i = max number of storage locations requested at any single operational period for the storage of SKU i (random variable)
  • F_i(k) = Prob{Q_i  k} (cumulative distribution function of Q_i)
  • If a distinct service level s_i is defined for each SKU i, then the determination of N_i is addressed independently for each SKU, according to the logic presented for the randomized storage policy.
  • Next we address the problem of satisfying a single service level requirement, s, defined for the operation of the entire system, i.e.,

Prob{no storage shortages in a single day}  s

under the additional assumption that the storage requirements posed by various SKU’s are independent from each other.

  • Then, for an assignment of N_i locations to each SKU i,

Prob{no storage shortages in a single day} = _i F_i(N_i)

and

Prob{1 or more storage shortages} = 1 - _i F_i(N_i)

sizing dedicated storage based on service level requirements cont
Sizing dedicated storage based on “service level” requirements (cont.)
  • Formulation I: Fixed service level, s

min _i N_i

s.t.

_i F_i(N_i)  s

N_i  0  i

  • Formulation II: Fixed number of locations, L

max _i F_i(N_i)

s.t.

_i N_i  L

N_i  0  i

class based storage sizing and location assignment
Class-Based Storage Sizing and Location Assignment
  • Divide SKU’s into classes, using ABC (Pareto) analysis, based on their number of turns TH_i/N_i.
  • Determine the required number of storage locations for each class C_k
    • ad-hoc adjustment of the total storage requirement of the class SKU’s

N_k = p * _{iC_k } N_i, where 0 < p < 1

    • Class-based “service-level” type of analysis:

Q_k = storage space requirements per period for class k = _{iC_k} Q_i

For independent Q_i:

p_k(m) = Prob(Q_k=m) = _{m_i: _i m_i = m}[_ip_i(m_i)]

where p_i( ) : probability mass function for Q_i.

  • Assign to each class the requested storage locations, prioritizing them according to their number of turns,

TH_k/N_k where TH_k = _{iC_k } TH_i

a simple cost based model for dedicated storage sizing
A simple cost-based model for (dedicated) storage sizing
  • Model-defining logic:Assuming that you know your storage needs d_ti, for each SKU i, over a planning horizon T, determine the optimal storage locations N_i for each SKU i, by establishing a trade-off between the
    • fixed and variable costs for developing this set of locations, and operating them over the planning horizon T, and
    • the costs resulting from any experienced storage shortage.
a simple cost based model for dedicated storage sizing cont
A simple cost-based model for (dedicated) storage sizing (cont.)
  • Model Parameters:
    • T = length of planning horizon in time periods
    • d_ti = storage space required for SKU i during period t
    • C_0 = discounted present worth cost per unit storage capacity owned during the planning horizon T
    • C_1 = discounted present worth cost per unit stored in owned space per period
    • C_2 = discounted present worth cost per unit of space shortage (e.g., per unit stored in leased space) per period
  • Model Decision Variables:
    • N_i = “owned” storage capacity for SKU i
  • Model Objective:
    • min TC (N_1,N_2,…,N_n) =

S_i [C_0 N_i + S_t {C_1 [min(d_ti, N_i)] + C_2 [max(d_ti - N_i, 0)]}]

a fast solution algorithm for the case of time invariant costs
A fast solution algorithm for the case of time-invariant costs
  • For each SKU i:
    • Sequence the storage demands appearing in the d_ti, t=1,…T, sequence in decreasing order.
    • Determine the frequency of the various values in the ordered sequence obtained in Step 1.
    • Sum the demand frequencies over the sequence.
    • When the obtained partial sum is first equal to or greater than

C’ = C_0/ (C_2-C_1)

stop; the optimum capacity for SKU i, N_i, equals the corresponding demand level.

example1
Example
  • Problem Data:

N=1; T=6; d = < 2, 3, 2, 3, 3, 4,>; C_0 = 10, C_1 = 3, C_2 = 5

  • Solution:

C’ = C_0/(C_2-C-1) = 10/(5-3) = 5

=> N = 2

storage configuration and policies for unit load warehouses topics covered
Storage Configuration and Policiesfor “Unit Load” warehouses: Topics covered
  • Storage Policies: Assigning storage locations of a uniform storage medium to the various SKU’s stored in that medium
    • Dedicated
    • Randomized
    • Class-based

Criterion: Maximize productivity by reducing the traveling effort / cost

  • The placement of the I/O point(s)

Criterion: Maximize productivity by reducing the traveling effort / cost

storage configuration and policies for unit load warehouses topics covered cont
Storage Configuration and Policiesfor “Unit Load” warehouses: Topics covered (cont.)
  • Storage sizing for various SKU’s: Determine the number of storage locations to be assigned to each SKU / group of SKU’s.

Criterion:

    • provide a certain (or a maximal) “service level”
    • minimize the total (space+equipment+labor+shortage) cost over a planning horizon
  • Next major theme: Storage Configuration for better space exploitation
    • floor versus rack-based storage for pallet-handling warehouses
    • determining the lane depth (mainly for randomized storage)

(based on Bartholdi & Hackman, Section 6.3)

determining the employment and configuration of rack based storage
Determining the Employment (and Configuration) of Rack-based storage
  • Basic Logic:
    • For each SKU,
      • compute how many pallet locations would be created by moving it into rack of a given configuration;
      • compute the value of the created pallet locations;
      • move the sku into rack if the value it creates is sufficient to justify the rack.
  • Remark: In general, space utilization will be only one of the factors affecting the final decision on whether to move an SKU into rack or not. Other important factors can be
    • the protection that the rack might provide for the pallets of the considered SKU;
    • the ability to support certain operational schemes, e.g., FIFO retrieval;
    • etc.
examples on evaluating the efficiencies from moving to rack based storage
Examples on evaluating the efficiencies from moving to rack-based storage
  • Case I: Utilizing 3-high pallet rack for an SKU of N=4 (pallets), which is not stackable at all.
    • Current footprint: 4 pallet positions
    • Introducing a 3-high rack in the same area creates 3x4=12 position, 8 of which are available to store other SKU’s. What are the gains of exploiting these new locations vs the cost of purchasing and installing the rack?
  • Case II: Utilizing a 3-high pallet rack for an SKU with N=30 (pallets), which are currently floor-stacked 3-high, to come within 4 ft from the ceiling.
    • Current footprint: 10 pallet positions
    • Introducing a 3-high rack does not create any new positions, and it will actually require more space in order to accommodate the rack structure (cross-beams and the space above the pallets, required for pallet handling)
determining an efficient lane depth in case of randomized storage

Lane Height

Lane Depth

(3-deep)

Lanes

Determining an efficient lane depth(in case of randomized storage)
  • A conceptual characterization of the problem:
    • More shallow lanes imply more of them, and therefore, more space is lost in aisles (the size of which is typically determined by the maneuvering requirements of the warehouse vehicles)
    • On the other hand, assuming that a lane can be occupied only by loads of the same SKU, a deeper lane will have many of its locations utilized over a smaller fraction of time (“honeycombing”).
    • So, we need to compute an optimal lane depth, that balances out the two opposite effects identified above, and minimizes the average floor space required for storing all SKU’s.

Aisle

notation
Notation
  • w = pallet width
  • d = pallet depth
  • g = gap between adjacent lanes
  • a = aisle width
  • x = lane depth
  • n = number of SKU’s
  • N_i = max storage demand by SKU i
  • z_i = column height for SKU I
  • lane footprint = (g+w)(d*x+a/2)
key results
Key results
  • Assuming that the same lane depth is employed across all n SKU’s, under floor storage, the average space consumed per pallet is minimized by a lane depth computed approximately through the following formula:

x_opt = [(a/2dn)*_i (N_i /z_i)]

  • The optimal lane depth for any single SKU i, which is stackable z_i pallets high, is

x_opt = [(a/2d)*(N_i /z_i)]

  • Assuming that the same lane depth is employed across all n SKU’s, under rack storage, the average space consumed per pallet is minimized by a lane depth computed approximately through the following formula:

x_opt = [(a/2dn)*_i N_i ]

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