Solution procedures for sizing of warehouses

doi:10.1016/S0377-2217(97)00159-8

European Journal of Operational Research

Volume 108, Issue 1, 1 July 1998, Pages 16-25

https://doi.org/10.1016/S0377-2217(97)00159-8 Get rights and content

Abstract

In the past, researchers presented a linear programming formulation for the economic sizing of warehouses when demand is highly seasonal and public warehouse space is available on a monthly basis. The static model was extended for the dynamic sizing problem in which the warehouse size is allowed to change over time. By applying simplex routine, the optimal size of the warehouse to be constructed could be determined. In this paper, an alternative and simple method of arriving at an optimal solution for the static problem is given. Three extensions of the static model are given. These extensions involve costs varying over time, economies of scale in capital expenditure and/or operating cost and stochastic version. The dynamic warehouse sizing problem is shown to be a network flow problem which could be solved by using network flow algorithms. The structure of an optimal solution is also given. The concave cost version of the dynamic warehouse sizing problem is also discussed and it is shown that this problem can be solved efficiently using dynamic programming.

References (7)

J. Ashayeri et al.
Warehouse design optimization
European Journal of Operational Research
(1985)
M.S. Hung et al.
Economic sizing of warehouses - A linear programming approach
Computers and Operations Research
(1984)
H.R. Ballou
Business Logistics Management
(1974)

There are more references available in the full text version of this article.

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Citation Excerpt :
Unlike prior studies, we evaluate the impact of increasing levels of online demand by comparing four channel designs with models that can close stores and optimize warehouse locations and capacity. Our research also models economies of scale in warehouse costs (similar to Rao & Rao, 1998; and Correia & Melo, 2017), with elastic demand based on delivery time and the level of competition in each market (as in Millstein & Campbell, 2018). In this research we study a single product category omnichannel retailer (the focal firm) that serves a set of discrete markets where there is both (i) demand from customers who purchase in stores and (ii) demand from customers who purchase online.
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This paper is related to the papers on warehouse space management (Gong & De Koster, 2011; Gu, Goetschalckx, & McGinnis, 2010). Some researchers focus on the topic of sizing warehouse space to seek cost-effective ways to satisfy storage demand by optimizing the portfolio of self-building and leasing warehouse spaces (Chen, Hum, & Sun, 2001; Cormier & Gunn, 1996; Goh, Jihong, & Chung-Piaw, 2001; Lee & Elsayed, 2005; Rao & Rao, 1998; White & Francis, 1971). Most of these studies are based on deterministic economic order quantity or lot-sizing models and pay less attention to storage demand uncertainties.
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Joint optimization of dynamic lot and warehouse sizing problems
2018, European Journal of Operational Research
Citation Excerpt :
Lowe, Francis, and Reinhardt (1979) further develop a greedy algorithm to solve the corresponding network flow problem. Similar multi-period WS problems with different cost structures are discussed by Hung and Fish (1984) and Rao and Rao (1998). The separation of studies on lot sizing and warehouse sizing problems implies that these decisions are made in a sequential manner.
We consider an integrated model of inventory and warehousing decisions for a single product. In this model, dynamic lot size decisions are considered under constraints of the warehouse size that can be either increased or decreased at the beginning of each period. The ordering cost is typically a fixed cost and the holding cost is assumed to be a linear function. Each adjustment of the warehouse size incurs a fixed-plus-linear adjustment cost. A lease cost has to be paid for the warehouse size in each period. We provide an efficient algorithm to solve the problem. Further, we present computational experiments that show the efficiency of the algorithm and the effectiveness of the model.
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Sung and Han [23] formulated the problem of determining the optimal size of an automated storage and retrieval system as queueing models. Multi-period warehouse leasing problems were investigated by White and Francis [28], Lowe et al. [10] and Rao and Rao [16]. The demand for the warehouse space is estimated by a discrete probability distribution.
In this paper we present an integrated model for site selection and space determination for warehouses in a two-stage network in which products are shipped from part suppliers to warehouses, where they are stored for an uncertain length of time and then delivered to assembly plants. The objective is to minimize the total inbound and outbound transportation costs and the total warehouse operation costs, which include the fixed costs related to their locations and the variable costs related to their space requirements for given service levels. Each warehouse is modeled as an $M / G / c$ queueing system in which each storage slot acts as a server. We formulate this problem as a nonlinear mixed integer program with a probabilistic constraint. Two cases are considered. For the continuous unbounded size case, we find an approximate formula for the overflow probability and reformulate the problem into a set-covering problem. For the discrete size option case, we reformulate the problem into a capacitated connection location problem with discrete size options. Computational experiments are performed and the results show that the continuous model is appropriate for the small and median size problems and the discrete model is a good choice for the large size problems.
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Citation Excerpt :
In contrast, simulation serves as an effective tool in understanding a real and complex system which is difficult to analyse (Simchi-Levi et al., 2007). Simulation has been used to study the impact of information sharing in an abundant literature, see Byrne and Heavey (2006), Rao and Rao (1998), Lee and Elsayed (2005). Through simulation, dynamic behaviour of member enterprises can be captured, and thus observations can be obtained for a more realistic industrial park.
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Solution procedures for sizing of warehouses

Abstract

European Journal of Operational Research

Computers and Operations Research

Business Logistics Management