scholarly journals A Diffusion Limit for a Finite Capacity Storage Allocation Model

2016 ◽  
Author(s):  
Charles Knessl ◽  
Eunju Sohn
Keyword(s):  
Diffusion Limit ◽  
Finite Capacity ◽  
Storage Allocation ◽  
Allocation Model

scholarly journals Asymptotic Analysis of a Storage Allocation Model with Finite Capacity: Joint Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-56 ◽  
Author(s):  
Eunju Sohn ◽  
Charles Knessl
Keyword(s):  
Steady State ◽  
Joint Distribution ◽  
Arrival Rate ◽  
Kolmogorov Equation ◽  
Finite Capacity ◽  
Storage Allocation ◽  
Allocation Model ◽  
Singular Perturbation Analysis ◽  
Poisson Arrival ◽  
Time Period

We consider a storage allocation model with a finite number of storage spaces. There aremprimary spaces andRsecondary spaces. All of them are numbered and ranked. Customers arrive according to a Poisson process and occupy a space for an exponentially distributed time period, and a new arrival takes the lowest ranked available space. We letN1andN2denote the numbers of occupied primary and secondary spaces and study the joint distributionProb[N1=k,N2=r]in the steady state. The joint process(N1,N2)behaves as a random walk in a lattice rectangle. We study the problem asymptotically as the Poisson arrival rateλbecomes large, and the storage capacitiesmandRare scaled to be commensurably large. We use a singular perturbation analysis to approximate the forward Kolmogorov equation(s) satisfied by the joint distribution.

On a storage allocation model with finite capacity

2016 ◽  
Vol 27 (5) ◽  
pp. 738-755 ◽  
Author(s):  
EUNJU SOHN ◽  
CHARLES KNESSL
Keyword(s):  
Random Walk ◽  
Steady State ◽  
Finite Number ◽  
Poisson Process ◽  
Joint Distribution ◽  
Marginal Distribution ◽  
Finite Capacity ◽  
Storage Allocation ◽  
Allocation Model ◽  
Numerical Studies

We consider a storage allocation model with a finite number of storage spaces. There are m primary spaces that are ranked {1,2,. . .,m} and R secondary spaces ranked {m + 1, m + 2,. . .,m + R}. Items arrive according to a Poisson process, occupy a space for a random exponentially distributed time, and an arriving item takes the lowest ranked available space. Letting N1 and N2 denote the numbers of occupied primary and secondary spaces, we study the joint distribution Prob[N1 = k, N2 = r] in the steady state. The joint process (N1, N2) behaves as a random walk in a lattice rectangle. We shall obtain explicit expressions for the distribution of (N1, N2), as well as the marginal distribution of N2. We also give some numerical studies to illustrate the qualitative behaviors of the distribution(s). The main contribution is to study the effects of a finite secondary capacity R, whereas previous studies had R = ∞.

scholarly journals Storage allocation optimization model in a Colombian company

DYNA ◽  
2019 ◽  
Vol 86 (209) ◽  
pp. 255-260 ◽  
Author(s):  
Julian Andres Zapata-cortes ◽  
Martin Dario Arango-Serna ◽  
Frank Alexander Ballesteros Riveros ◽  
Wilson Adarme - Jaimes
Keyword(s):  
Optimization Model ◽  
Cost Efficiency ◽  
Time Horizon ◽  
Material Handling ◽  
Storage Allocation ◽  
Product Allocation ◽  
Allocation Model ◽  
Specific Position ◽  
Material Handling Costs ◽  
The Cost

The storage allocation in warehouse is about of deciding the corresponding areas in which the products must be allocated. It can be made using different techniques to stablish the specific position for the products. Some applications provide solutions and evaluate results independently, allowing the identification of its potential in warehouses. This paper presents the application of a storage allocation model in a food company considering several products in a defined time horizon. The algorithm identifies the operation area and the corresponding spaces that are required for the products allocation, aimed to reduce holding and material handling costs. As a result, the application of the algorithm produces a complete product allocation in each period and improves the cost efficiency in the warehouse.

scholarly journals Robust energy storage allocation for transmission grid integrated by multiple wind farms

2019 ◽  
Vol 107 ◽  
pp. 02005
Author(s):  
Cheng Jinmin ◽  
Wang Weiyuan ◽  
Yu Xuan ◽  
Xia Kai ◽  
Xu Yiqing ◽  
...  
Keyword(s):  
Energy Storage ◽  
Wind Power ◽  
Deterministic Model ◽  
Optimization Theory ◽  
Wind Farms ◽  
Planning Problem ◽  
Storage Allocation ◽  
Energy Storage Devices ◽  
Allocation Model ◽  
Transmission Grid

Since optimal planning for energy storage sizing and locating is critical to meet the requirement of total wind power absorption, a robust optimization theory based energy storage allocation model for transmission grid with multiple wind farms integrated is proposed in this paper. The model fully considers the transmission capacity limitation, and uses linear decision rule to optimize the allocation of the reserve capacity of the adjustable units and energy storage devices to cope with the fluctuation of wind power, which makes full use of the regulation capacity in the system. Some statistical information of wind power, such as expectation and interval, is used to describe the uncertainty of wind power. The uncertainty model is transformed into a deterministic model by using the duality optimization theory, which provides convenience for engineering application. The Garver’s 6-bus transmission system model is used for example analysis, which shows that the proposed method can effectively solve the energy storage planning problem for uncertain wind power integrated power systems.

scholarly journals A simple direct solution to a storage allocation model

2008 ◽  
Vol 21 (2) ◽  
pp. 172-175 ◽  
Author(s):  
Eunju Sohn ◽  
Charles Knessl
Keyword(s):  
Direct Solution ◽  
Storage Allocation ◽  
Allocation Model

scholarly journals Dynamic Picking and Storage Optimization of Robotic Picking Systems

2021 ◽  
Author(s):  
Cheng Chi ◽  
Shasha Wu ◽  
Delong Xia ◽  
Yaohua Wu
Keyword(s):  
Practical Significance ◽  
Storage Allocation ◽  
Allocation Model ◽  
Dynamic Storage Allocation ◽  
System A ◽  
Additional Equipment ◽  
Picking Systems ◽  
Dynamic Storage ◽  
The Cost ◽  
And Storage

Abstract With the development of e-commerce and the improvement of logistics requirements, more and more ‘parts-to-picker’ picking systems begin to replace the inefficient ‘picker-to-parts’ picking systems in various scenarios. As the mainstream ‘parts-to-picker’ system, the robotic mobile fulfillment system has been attracting much attention in recent years. In addition to the customer's changing requirements, the rapid response of the picking system to the order is particularly important. In the above context, to seek a breakthrough in the picking system's picking efficiency without increasing the cost of additional equipment, the storage allocation of the pods becomes very important. This article focuses on the dynamic storage allocation of robotic mobile fulfillment system, which has positive theoretical and practical significance. By analyzing the pod storage process of the robotic mobile fulfillment system, a dynamic pod storage allocation model suitable for the robotic mobile fulfillment system is established with the goal of minimizing the pod handling distance. Two dynamic pod storage allocation strategies are proposed for the system. By simulating the picking systems of different scales, the effectiveness of the dynamic storage allocation strategy is verified, which has a certain reference to the operation of the robotic mobile fulfillment system in practice.

scholarly journals Storage allocation in a warehouse based on the forklifts fleet availability

2018 ◽  
Vol 12 (2) ◽  
pp. 127-135 ◽  
Author(s):  
Iman Ghalehkhondabi ◽  
Dale T Masel
Keyword(s):  
Operation Time ◽  
Working Hours ◽  
Storage Space ◽  
Storage Allocation ◽  
Efficient Utilization ◽  
Product Allocation ◽  
Allocation Model ◽  
Space Allocation ◽  
Storage Space Allocation ◽  
Proposed Model

Product allocation is one of the most important duties in warehousing operations. Based on the time and the number of products to put away and retrieve, storage allocation can directly affect the efficiency of a warehouse in terms of both response and operation time. Traditionally, the product storage allocation is done based on the less distance of shipment but focusing on distance may decrease the efficiency of a warehouse in terms of efficient utilization of resources such as warehouse inbound shipping fleet. This paper proposes a storage space allocation model that considers the availability of forklift fleet in a warehouse instead of product shipping distance. The numerical example shows that storing the products based on the proposed model can reduce the volume of forklift fleet idle hours on days with fewer volume of receiving and shipping outs. The proposed model also reduces the overtime working hours on days with higher volume of receiving and shipping out products.

scholarly journals Storage allocation under processor sharing II: Further asymptotic results

2010 ◽  
Vol 22 (1) ◽  
pp. 45-82 ◽  
Author(s):  
EUNJU SOHN ◽  
CHARLES KNESSL
Keyword(s):  
Joint Probability ◽  
Arrival Rate ◽  
Service Rate ◽  
Joint Probability Distribution ◽  
Processor Sharing ◽  
Storage Allocation ◽  
Asymptotic Results ◽  
Allocation Model ◽  
Sample Paths ◽  
Single Processor

We consider a processor-sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items. All of the spaces are numbered and ordered. An arriving customer takes the lowest available space. Dynamic storage allocation and the fragmentation of computer memory are well-known applications of this model. We define the traffic intensity ρ to be λ/μ, where λ is the customers' arrival rate and μ is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. We study the problem in two asymptotic limits: (1) m → ∞ with a fixed ρ < 1, and (2) ρ ↑ 1, m → ∞ with m(1-ρ) = O(1). The asymptotics yield insight into how many secondary spaces tend to be needed, and into the sample paths leading to the occupation of the two types of spaces. We show that the asymptotics lead to accurate numerical approximations.

Sign in / Sign up

Export Citation Format

Share Document