A Mixed Integer Programming Model for the Production-Inventory-Distribution-Routing Problem (original) (raw)
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The Egyptian International Journal of Engineering Sciences and Technology, 2016
Integration of decisions in supply chain management has received increasing consideration recently. The Production-Inventory-Distribution-Routing Problem (PIDRP) is a recent and complex problem that integrates decisions on lot-sizing, inventory management, distribution planning, and vehicle routing problems. In this paper, a generic problem description is given and a Mixed-Integer Programming model (MIP) is proposed to solve the PIDRP, the objective is to minimize the total cost of the combined functions while satisfying the required service levels. The proposed model contributes to the existing literature since it deals with multiple products, split deliveries, a heterogeneous fleet of vehicles, and puts a limit on the duration of the route performed by each vehicle. The proposed model was successfully validated and tested by using small-sized instances from literature. Also, a sensitivity analysis was performed to investigate the effect of estimated parameters on the model results.
2015 International Conference on Industrial Engineering and Operations Management (IEOM), 2015
Supply chain management includes several functions that are planned and managed to improve the total performance of the supply chain, the general objective is to minimize system-wide costs while satisfying service level requirements. Previously, each function was addressed as an isolated problem, however, it was found that focusing on cost minimization in one area of the supply chain often leads to higher costs in other areas; this is why the integration of different supply chain management functions has received increasing consideration recently. The production-inventory-distribution-routing integrated planning is a step forward towards more integration and realism in supply chain management, as it integrates lot-sizing, inventory management, distribution planning, and vehicle routing problems. In this paper, a review of the recent literature addressing the joint consideration of these aspects is presented and research gaps are highlighted. It was noticed that the existing models tackle relatively simple cases. However, in real life, more complex systems and variants exist. To make a step forward, a generic problem description and a mathematical model are proposed to address the production-inventory-distribution-routing problem. Finally, a conceptual framework is presented to illustrate the existing and potential work in this topic; this framework is expected to provide good directions for researchers to work in this area.
2015
Integration of decisions in supply chain management has received increasing consideration recently. The production-inventory-distribution-routing problem (PIDRP) is a recent and complex problem that integrates decisions on lot-sizing, inventory management, distribution planning, and vehicle routing problems. In this paper, a generic problem description is given and a mixed-integer programming model is proposed to solve the PIDRP, the objective is to minimize the total cost of the combined functions while satisfying the required service levels. The proposed model contributes to the existing literature since it deals with multiple products, split deliveries, a heterogeneous fleet of vehicles, and puts a limit on the duration of the route performed by each vehicle. The proposed model was successfully validated and tested by using small-sized instances from literature. Also, sensitivity analysis was performed to investigate the effect of parameter estimates.
A branch-and-price algorithm for an integrated production and inventory routing problem
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With globalization, the need to better integrate production and distribution decisions has become ever more pressing for manufacturers trying to streamline their supply chain. This paper investigates a previously developed mixed-integer programming (MIP) model aimed at minimizing production, inventory, and delivery costs across the various stages of the system. The problem being modeled includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of homogeneous vehicles. Demand can be satisfied from either inventory held at a customer site or from daily product distribution. Whether a customer is visited on a particular day is determined by an implicit tradeoff between inventory and distribution costs. Once the decision is made, a vehicle routing problem must be solved for those customers who are scheduled for a delivery.
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The paper considers a production inventory network whose multiple plants and warehouses are located in different geographic regions with customer demands for multiple products, and discusses how to design such kind of network so that the total cost is minimized. We formulate the problem as a mixed integer programming model, and conduct the numerical experiments to provide the managerial insights into production inventory network design.
On the integrated production, inventory, and distribution routing problem
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The integrated production, inventory and distribution routing problem (PDRP) is concerned with coordinating the production, inventory and delivery operations to meet customer demand with an objective to minimize the cost. The particular PDRP that we consider in this study also involves heterogeneous transporters with non-instantaneous traveling times and many customer demand centers each with its own inventory capacities. Optimally solving such an integrated problem is in general not easy due to its combinatorial nature, especially when transporter routing is involved.
Heuristics for a multiperiod inventory routing problem with production decisions
Computers & Industrial Engineering, 2009
Manufacturers who resupply a large number of retailers on a periodic basis continually struggle with the question of how to formulate a replenishment strategy. This paper presents a comparative analysis of a series of heuristics for an inventory routing problem (IRP) that arises in a manufacturing supply chain. The IRP is formulated as a mixed integer program with the objective of maximizing the net benefits associated with making deliveries in a specific time period to a widely dispersed set of customers. It is assumed that inventory can accumulate at the customer sites, but that all demand must be met without backlogging. Because optimal solutions were not within reach of exact methods, a two-step procedure was developed that first estimates daily delivery quantities and then solves a vehicle routing problem for each day of the planning horizon. As part of the methodology, a linear program is used to determine which days it is necessary to make at least some deliveries to avoid stockouts.
Modeling inventory routing problems in supply chains of high consumption products
European Journal of Operational Research, 2006
Given a distribution center and a set of sales-points with their demand rates, the objective of the inventory routing problem (IRP) is to determine a distribution plan that minimizes fleet operating and average total distribution and inventory holding costs without causing a stock-out at any of the sales-points during a given planning horizon. We propose a new model for the long-term IRP when demand rates are stable and economic order quantity-like policies are used to manage inventories of the sales-points. The proposed model extends the concept of vehicle routes (tours) to vehicle multi-tours. To solve the nonlinear mixed integer formulation of this problem, a column generation based approximation method is suggested. The resulting sub-problems are solved using a savings-based approximation method. The approach is tested on randomly generated problems with different settings of some critical factors to compare our model using multi-tours as basic constructs to the model using simple tours as basic constructs.