An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results (original) (raw)

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.

Facility Location Model with Inventory Transportation and Management Costs

Acta logistica

This work is focused on the integration of the standard EOQ (Economic Order Quantity) model within the facility location decision model. This is proposed to extend on the facility location task which is usually performed based on just the overall demand of the customer locations to be served. If the inventory costs are considered within the demand supply process, these may affect the overall transportation costs as these are not linearly dependent of the demand. As such, the extended model considers, besides the distances, performance and capacity of the vehicles, the order quantities and the period in which they should be fulfilled. This model was tested with a reference instance of 200 suppliers and one distribution centre. The distances were estimated by considering the geographical locations of all elements in the network and the spherical model of the Earth's surface to obtain the metric in kilometres. As analysed, by considering the inventory costs within the facility location model, it can lead to refine the location to obtain long-term savings in transportation.

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.

A Relax-and-Price Algorithm for the Inventory-Location-Routing Problem

In this research, a variant of Supply Chain Design Problem (SCDP) (Beamon, 1998) is considered. We address the postulate that poorly located facilities impact the performance of routing decisions and inventory policies in terms of cost and service quality on the long term (Daskin et al., 2005). Thus, the location of depots is optimized by incorporating operational features over a multi-period planning horizon. An approach that combines the problem of locating facilities, designing inventory policies and nding the optimal routing is proposed. Literature on the Inventory-Location-Routing Problem (ILRP) is not vast and most of the research focuses on the Location-Routing Problems (LRP) where inventory decisions are xed (Salhi and G.K. Rand, 1989).

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.

A Joint Replenishment Inventory-Location Model

Networks and Spatial Economics, 2012

We introduce a distribution center location model that incorporates joint replenishment inventory costs at the distribution centers. The model is formulated as a Fixed Charge Location Problem (FCLP) which objectively considers not only location specific costs but also inventory replenishment costs. In the joint replenishment problem we consider a single item and several distribution centers in different locations and apply a similar algorithm to the one used to solve the multi-item problem. We propose a Greedy Randomized Adaptive Search Procedure (GRASP) to solve the problem.

An integrated model for space determination and site selection of distribution centers

2003

In this paper we present an integrated distribution center site selection and space requirement problem on a two-stage network in which products are shipped from plants to distribution centers, where they are stored for an arbitrary period of time and then delivered to retailers. The objective of the problem is to minimize total inbound and outbound transportation costs and total distribution center construction cost -which includes fixed costs related to their locations and variable costs related to their space requirements for given service levels. Each distribution center is modeled as an M/G/c queueing system, in which each server represents a storage slot. 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 restructure this model into a connection location problem. For the discrete size option case, we reformulate the problem into a capacitated connection location problem with discrete size options. Computational results and a comparison of the two cases are provided.

Inventory and Facility Location Models with Market Selection

Lecture Notes in Computer Science, 2005

We consider important generalizations of a wide class of traditional deterministic inventory and facility location models that we call inventory/facility location models with market selection. Instead of the traditional setting, we are given a set of markets, each specified by a sequence of demands and associated with a revenue. Decisions are made in two stages. We first make a decision of what markets to select, where all other markets are rejected. Next we have to construct a minimum-cost production plan (facility layout) to satisfy all of the demands of all the selected markets. The goal is to minimize the overall lost revenues of rejected markets and the production (facility openings and connection) costs. We show how to leverage existing approximation results for the traditional models to corresponding results for the counterpart models with market selection. More specifically, any LP based α−approximation for the traditional model can be leveraged to a 1 1−e − 1 α −approximation algorithm for the counterpart model with market selection. Our techniques are also applicable to an important class of covering problems.