Warehouse storage configuration and storage policies
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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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B: 15/5 = 3

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

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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

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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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