Mitigating Hard Capacity Constraints with Inventory in Facility Location Modeling (original) (raw)
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Computers & Operations Research, 2014
We consider a class of location-allocation problems with immobile servers, stochastic demand and congestion that arises in several planning contexts: location of emergency medical clinics; preventive healthcare centers; refuse collection and disposal centers; stores and service centers; bank branches and automated banking machines; internet mirror sites; web service providers (servers); and distribution centers in supply chains. The problem seeks to simultaneously locate service facilities, equip them with appropriate capacities, and allocate user demand to these facilities such that the total cost, which consists of the fixed cost of opening facilities with sufficient capacities, the access cost of users' travel to facilities, and the queuing delay cost, is minimized. Under Poisson user demand arrivals and general service time distributions, the problem is set up as a network of independent M/G/1 queues, whose locations, capacities and service zones need to be determined. The resulting mathematical model is a non-linear integer program. Using simple transformation and piecewise linear approximation, the model is linearized and solved to -optimality using a constraint generation method. Computational results are presented for instances up to 400 users, 25 potential service facilities, and 5 capacity levels with different coefficient of variation of service times and average queueing delay costs per customer. The results indicate that the proposed solution method is efficient in solving a wide range of problem instances.
Facility Location with Stochastic Demand and Constraints on Waiting Time
M&som-manufacturing & Service Operations Management, 2008
We analyze the problem of optimal location of a set of facilities in the presence of stochastic demand and congestion. Customers travel to the closest facility to obtain service; the problem is to determine the number, locations, and capacity of the facilities. Under rather general assumptions (spatially distributed continuous demand, general arrival and service processes, non-linear location and capacity costs) we show that the problem can be decomposed and construct an efficient optimization algorithm. The analysis yields several insights, including the importance of "equitable facility configurations", the behavior of optimal and near-optimal capacities and robust class of solutions that can be constructed for this problem.
Joint inventory-location problem under the risk of probabilistic facility disruptions
Transportation Research Part B: Methodological, 2011
This paper studies a reliable joint inventory-location problem that optimizes facility locations, customer allocations, and inventory management decisions when facilities are subject to disruption risks (e.g., due to natural or man-made hazards). When a facility fails, its customers may be reassigned to other operational facilities in order to avoid the high penalty costs associated with losing service. We propose an integer programming model that minimizes the sum of facility construction costs, expected inventory holding costs and expected customer costs under normal and failure scenarios. We develop a Lagrangian relaxation solution framework for this problem, including a polynomial-time exact algorithm for the relaxed nonlinear subproblems. Numerical experiment results show that this proposed model is capable of providing a near-optimum solution within a short computation time. Managerial insights on the optimal facility deployment, inventory control strategies, and the corresponding cost constitutions are drawn.
Risk management in uncapacitated facility location models with random demands
Computers & Operations Research, 2009
In this paper we consider a location-optimization problem where the classical uncapacitated facility location model is recast in a stochastic environment with several risk factors that make demand at each customer site probabilistic and correlated with demands at the other customer sites. Our primary contribution is to introduce a new solution methodology that adopts the mean-variance approach, borrowed from the finance literature, to optimize the "Value-at-Risk" (VaR) measure in a location problem. Specifically, the objective of locating the facilities is to maximize the lower limit of future earnings based on a stated confidence level. We derive a nonlinear integer program whose solution gives the optimal locations for the p facilities under the new objective. We design a branch-and-bound algorithm that utilizes a second-order cone program (SOCP) solver as a subroutine. We also provide computational results that show excellent solution times on small to medium sized problems.
2019
Deciding on the number and configuration of distribution centers (DC) is one of the most impactful decisions that create a pathway for competitiveness and responsiveness. In this research, the allocation of distribution center problem is studied under demand uncertainty. The purposes of this study were to specify the optimal number and allocation of distribution centers out of candidate ones. This paper proposes a three-step model with probabilistically distributed demand where the coefficient of variation is the measure of risk along with the enforced level of service metrics that are focused on responsiveness which aligns with real-world problems and the considered company, working as a backward linkage of the fast fashion industry. To consider uncertainty, a set of scenarios for customer demands is created based on the Monte Carlo simulation. The best network structure is identified by optimizing each scenario and detecting which configuration has been observed the highest amount...
Stochastic Transportation-Inventory Network Design Problem
Operations Research, 2005
We study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand, and safety stock must be maintained to achieve suitable service levels. However, riskpooling benefits may be achieved by allowing some retailers to serve as distribution centers for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. formulated this problem as a set-covering integer-programming model. The pricing problem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. In this paper, we show that by exploiting certain special structures, we can solve the general pricing problem in Shen et al. efficiently. Our approach utilizes the fact that the set of all lines in a two-dimension plane has low VC-dimension. We present computational results on several instances of sizes ranging from 40 to 500 retailers. Our solution technique can be applied to a wide range of other concave cost-minimization problems.
Ensuring feasibility in location problems with stochastic demands and congestion
Iie Transactions, 2009
A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be available to respond to an arriving call, with some prespecified probability. The objective is to minimize the total number of servers. It is shown that earlier models quite often overestimate servers' availability and thus may lead to infeasible solutions (i.e., solutions that fail to satisfy the service level constraint). System stability conditions and lower bounds on system availability are developed by analyzing the underlying partially accessible queueing system. These lead to the development of two new models for which feasibility is guaranteed. Simulation-based computational experiments show that the proposed models achieve feasibility without significantly increasing the total number of servers.
An Efficient Approach for Solving Reliable Facility Location Models
INFORMS Journal on Computing, 2013
We consider reliable facility location models in which facilities are subject to unexpected failures and customers may be reassigned to facilities other than their regular facilities. The objective is to minimize the total expected costs in normal and failure scenarios. We allow facilities to have different failure rates and do not limit the number of facilities that might be assigned to a customer. Lower bounds for Reliable Uncapacitated Fixed-charge Location Problem (RUFLP) are derived and used to introduce a class of efficient algorithms for solving the RUFLP problem. the rare occasion in which all facilities assigned to a customer have failed, a penalty cost is incurred. The penalty cost can be taken as lost sales, loss of goodwill, or the cost to serve the customer at a competitor's facility. In this paper, we study the reliable version of the uncapacitated fixed-charge location problem (U F LP), but our model can be easily extended to address other facility location problems. Here, the objective is to minimize the sum of fixed location costs, the expected transportation costs (at all levels), and the expected penalty costs. This problem will be referred to as the reliable uncapacitated fixed-charge location problem (RU F LP). When compared with cost minimizing supply network design, the reliable facility networks, in general, tend to require more facilities for backup solutions. While adding facilities increases the system's overall fixed cost, it helps to hedge against the excessive transportation and penalty costs in case of failures within the network. Note that our problem should not be confused with the "k-level facility location problem", where each customer must be served by a sequence of k different kinds of facilities located in k levels of hierarchy (see Sahin and Sural (2007)). Our work is related to the emerging literature of facility location under uncertainty. Some of the earlier literature focuses on demand uncertainty, motivated by facility congestion in emergency service systems. This includes Daskin (1982, 1983), Batta et al. (1989), Ball and Lin (1993) among others. Also see Daskin et al. (1988) for a survey of covering models under demand uncertainty. Snyder and Daskin (2005) studied the facility reliability issues with a different motivation, where uncertainty comes from the supply side, or more specifically, the disastrous facility disruptions. In Snyder and Daskin (2005), the reliability models of U F LP and the P-median problem were introduced and a multi-objective formulation was used to demonstrate trade off between the cost and reliability. Assuming that all facilities have identical failure probability, the authors formulated the problem as a linear mixed integer program, and employed Lagrangian relaxation for efficient solutions. The uniform failure probability assumption is also taken in other related papers on disruption management, including Snyder and Daskin (2006) and Lim et al. (2009). Facility location in context of facility failure has also been studied in the "fault-tolerant facility location problem" literature. In this problem, to hedge against facility failures, each demand point is supposed to be assigned to a certain number of distinct facilities, but unlike
An approximation algorithm for a facility location problem with stochastic demands and inventories
Operations Research Letters, 2006
In this article we propose, for any > 0, a 2(1+ )-approximation algorithm for a facility location problem with stochastic demands. At open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs of the facilities and the investment in inventory.