Inventory and Facility Location Models with Market Selection (original) (raw)

A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints

Networks & Spatial Economics, 2006

Traditionally, logistics analysts divide decisions levels into strategic, tactical and operational. Often these levels are considered separately for modeling purposes. The latter may conduce to make non-optimal decisions, since in reality there is interaction between the different levels. In this research, a cross-level model is derived to analyze decisions about inventory control and facility location, specially suited to urban settings, where the storage space is scarce and the vehicles’ capacity is usually restricted. Both conditions, on the one hand make the problem difficult to solve optimally but on the other hand make it more realistic and useful in practice. This paper presents a simultaneous nonlinear-mixed-integer model of inventory control and facility location decisions, which considers two novel capacity constraints. The first constraint states a maximum lot size for the incoming orders to each warehouse, and the second constraint is a stochastic bound to inventory capacity. This model is NP-Hard and presents nonlinear terms in the objective function and a nonlinear constraint. A heuristic solution approach is introduced, based on Lagrangian relaxation and the subgradient method. Numerical experiments were designed and applied. The solution procedure presented good performance in terms of the objective function. One of the key conclusions of the proposed modeling approach is the fact that a reduction of the inventory capacity does not necessarily imply an increase in the number of installed warehouses. In fact, reducing the order size allows the optimal allocation of customers (those with higher variances) into different warehouses, reducing the total system’s cost.

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.

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.

Approximation algorithms for a facility location problem with service capacities

ACM Transactions on Algorithms, 2008

In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1 + , 1)-reduction of the facility location problem with subadditive costs to the soft capacitated facility location problem, which implies the existence of a 2(1 + )-approximation algorithm. For a special subclass of subadditive functions, we obtain a 2-approximation algorithm by reduction to the linear cost facility location problem.

A study on the budget constrained facility location model considering inventory management cost

RAIRO - Operations Research, 2012

One of the important issues on the distribution network design is to incorporate inventory management cost into the facility location model. This paper deals with a network model making the decisions on the facility location such as the number of DCs and their locations as well as the decisions on the inventory management such as the ordering quantity and the level of safety stock at each DC. The considered model differs from the previous works by classifying the related costs into the operating cost and the investment cost. For this model, a solution procedure based on the Lagrangian relaxation method was proposed and tested for its effectiveness with various numerical examples.

Improved approximation guarantees for lower-bounded facility location problem

2010

We consider the lower-bounded facility location (LBFL) problem (also sometimes called load-balanced facility location), which is a generalization of uncapacitated facility location (UFL), where each open facility is required to serve a certain minimum amount of demand. More formally, an instance I of LBFL is specified by a set F of facilities with facility-opening costs {f i }, a set D of clients, and connection costs {c ij } specifying the cost of assigning a client j to a facility i, where the c ij s form a metric. A feasible solution specifies a subset F of facilities to open, and assigns each client j to an open facility i(j) ∈ F so that each open facility serves at least M clients, where M is an input parameter. The cost of such a solution is i∈F f i + j c i(j)j , and the goal is to find a feasible solution of minimum cost. The current best approximation ratio for LBFL is 448 [18]. We substantially advance the state-of-theart for LBFL by devising an approximation algorithm for LBFL that achieves a significantly-improved approximation guarantee of 82.6. Our improvement comes from a variety of ideas in algorithm design and analysis, which also yield new insights into LBFL. Our chief algorithmic novelty is to present an improved method for solving a more-structured LBFL instance obtained from I via a bicriteria approximation algorithm for LBFL, wherein all clients are aggregated at a subset F ′ of facilities, each having at least αM co-located clients (for some α ∈ [0, 1]). One of our key insights is that one can reduce the resulting LBFL instance, denoted I 2 (α), to a problem we introduce, called capacity-discounted UFL (CDUFL). CDUFL is a special case of capacitated facility location (CFL) where facilities are either uncapacitated, or have finite capacity and zero opening costs. Circumventing the difficulty that CDUFL inherits the intractability of CFL with respect to LP-based approximation guarantees, we give a simple local-search algorithm for CDUFL based on add, delete, and swap moves that achieves the same approximation ratio (of 1 + √ 2) as the corresponding local-search algorithm for UFL. In contrast, the algorithm in [18] proceeds by reducing I 2 (α) to CFL, whose current-best approximation ratio is worse than that of our local-search algorithm for CDUFL, and this is one of the reasons behind our algorithm's improved approximation ratio. Another new ingredient of our LBFL-algorithm and analysis is a subtly different method for constructing a bicriteria solution for I (and hence, I 2 (α)), combined with the more significant change that we now choose a random α from a suitable distribution. This leads to a surprising degree of improvement in the approximation factor, which is reminiscent of the mileage provided by random α-points in scheduling problems.