ระบบการจัดเก็บในคลังสินค้า

Storage Systems Dedicated Storage Location Policy Randomized Storage Location Policy Class-based Dedicated Storage Location Policy Shared Storage Location Policy Continuous Warehouse Layout

Determination of Space Requirement

Dedicated Storage Location Policy Also call “fixed slot storage” Specific storage location is assigned to each product Storage system Part number sequence Throughput-based dedicated storage Throughput: Number of storages or retrievals per time period เช่น 320 storages ต่อ 8 ชั่วโมงการทำงาน เป็นต้น

Space Requirement One and only one product is assigned to a specific location Number of storage locations assigned must be capable of satisfying the maximum storage requirement of product. Determination method Maximum storage location Service level Cost based

Space Requirement Maximum storage requirement The number of storage slots provided  max. storage requirement See example (workshop)

Space Requirement Service Level Can be determined based on a probability of having sufficient storage slots to satisfy storage demand Service level = Demand Satisfied/Total Demand Let’s Qj = Number of slots provided for product j

Space Requirement Probability of having sufficient slots for product j is: P[Sj  Qj] Sj represent the slot demand for product j The CDF of the function is: Fj(Qj) = P[Sj  Qj]

Space Requirement Probability of 1 or more slot shortage P[1 or more shortage] = 1 – P[no shortage] Hence, probability of no shortage for all product j = 1, 2, …, n P[no shortage] = (P[no shortage of product j]) P[1 or more shortage] =1-(P[no shortage of product j])

Space Requirement Service Level จากทฤษฎีความน่าจะเป็น เมื่อกำหนดให้ Z แทนค่ามาตรฐานของตัวแปรสุ่มที่แจกแจงแบบปกติมาตรฐาน มีค่าเฉลี่ย และค่าเบี่ยงเบนมาตรฐาน เท่ากับ 0 และ 1 ตามลำดับ  แทนระดับบริการ (service level) ที่ต้องการ

Space Requirement จะได้ จำนวน Slots ที่รับประกันระดับบริการ  คือ Qj = Mj + ZSDj เมื่อ Qj = จำนวน slots ที่ต้องการเพื่อรับประกันระดับบริการ  Mj = จำนวน Slots เฉลี่ยที่ต้องการต่อวัน SDj = ค่าเบี่ยงเบนมาตรฐานของ Slots ที่ต้องการต่อวัน See example (workshop)

Optimized Qj Minimize Qj ST: (Fj(Qj))  P Qj  0 P = minimum probability of no shortage of storage slot

Space Requirement Maximize (Fj(Qj)) ST: Qj  S Qj  0 S = Total slots available

Space Requirement Cost-based Mathematical model is needed, (example) Conditions: There are fixed cost Co for “owned” storage Qj The operating cost for owned storage is C1,t per space period If owned storage is less than demand, the excess requirement can be leased at an operating cost of C2,t per space period

Example math. Model (cont.) Definition of parameters - Qj : ‘owned’ storage capacity for product j - T : length of the planning horizon in time period - dt,j: storage space required for product j during period t - TC(Q1,…,Qn) : Total cost function over the planning horizon as a function of the set of storage capacities - Co : discount present worth cost per unit storage capacity owned during planning horizon of T time period - C1, t: discount present worth cost per unit stored in owned space during planning time t - C2,t: discount present worth cost per unit stored in leased space during planning time t

Example math. Model (cont.) Therefore, the Total Cost function is: Fixed cost + Operating cost

Example math. Model (cont.) min(dt,j,Qj) = dt,j if dt,j < Qj = Qj if dt,j ≥ Qj max(dj,t-Qj,0) = 0 if dt,j-Qj < Qj = dt,j-Qj if dt,j-Qj ≥ Qj

Example math. Model (cont.) Solution technique (one of them) Let’s C’ = C0/(C2-C1) Then, Sequence in decreasing order the demand for space Sum the demand frequencies over the sequence When partial sum is first equal to or greater than C’, stop; the optimum capacity equals that demand level

Example math. Model (cont.) Take a hand on example and see if we can…

Assigning Products Storage/Retrieval Locations Given That s = number of storage slots or location n = number of product to be stored m = number of inputs/outs (I/O) points Sj = storage requirement for product j, expressed in number of storage slots Tj = throughput requirement or activities level for product j, expressed by the number of storage/retrievals (S/R) performed per unit time

Assigning Products Storage/Retrieval Locations pi,j = percent of S/R tripe for product j that are from/to I/O point i Ti,k = time required to travel between I/O point i and S/R location k Xj,k = 1 if product i is assigned to S/R location k or 0 otherwise f(x) = expect time required to satisfies the throughput requirement for the system See workshop

Assigning Products Storage/Retrieval Locations Mathematical model as shown can be used (also discuss via workshop)

Assigning Products Storage/Retrieval Locations

Randomized Storage Location Policy Also known as “Floating Slot Storage” Each open storage slot has equal chance of being assigned when a load arrive In practice, when the load arrive, it is placed in the “closest” open feasible location Retrieval occurs on a FIFO basis

Space Requirement Storage space requirement equal the maximum of the aggregate storage requirements for products. See example (workshop)

Dedicated (D) VS Randomized (R) Storage Location Policy R requires less space than D It is more difficult to determine the exact location of R than that of D D requires less travel time (on average) in storages and retrievals of products

Class-based Dedicated Storage Location Policy A compromise between dedicated and randomized storage location policies Products are classified into classes according to their S/R ratios Dedicated policy applies between classes while Randomized policy applies within each class. See example (workshop)

Shared Storage Location Policy Shared storage recognizes and takes advantage of the inherent differences in lengths of time that individual pallet loads remain in storage