Developing a multi-objective, multi-item inventory model and three algorithms for its solution (original) (raw)
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International journal of engineering. Transactions A: basics, 2018
This paper considers a multi-period, multi-product inventory-routing problem in a two-level supply chain consisting of a distributor and a set of customers. This problem is modeled with the aim of minimizing bi-objectives, namely the total system cost (including startup, distribution and maintenance costs) and risk-based transportation. Products are delivered to customers by some heterogeneous vehicles with specific capacities through a direct delivery strategy. Additionally, storage capacities are considered limited and the shortage is assumed to be impermissible. To validate this new bi-objective model, the e-constraint method is used for solving problems. The e-constraint method is an exact method for solving multi-objective problems, which offers Pareto's solutions, such as meta-heuristic algorithms. Since problems without distribution planning are very complex to solve optimally, the problem considered in this paper also belongs to a class of NP-hard ones. Therefore, a non-...
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Journal of Industrial and Production Engineering, 2016
Different inventory control systems attempt to determine how much and when to order at the least relevant cost, while maintaining a desirable service level for customers. In this paper, a continuous review stochastic inventory system, with three objectives and certain resource constraints is studied. In the model for this system, contrary to the traditional inventory models, customer service is not considered a shortage cost in the objective function. Moreover, the frequency of stock-out occasions and the number of items stocked out annually are to be minimized. For determining the Pareto optimal set, Constrained Multi-Objective Evolutionary Algorithms are used. Constrained Reference-point-based Non-dominated Sorting Genetic Algorithm (C-R-NSGA-II) which integrates decision-makers' preferences in the optimization process, is compared with the basic algorithm, constrained non-dominated sorting genetic algorithm (C-NSGA-II). Then, the best algorithms for each criterion are presented. Results show that C-R-NSGA-II has good scores for most criteria.
A Multiobjective Evolutionary Approach to the Inventory and Transportation Problem
svn.assembla.com
The Inventory and Transportation Problem (ITP) can be seen as a generalisation of the Periodic Vehicle Routing Problem that takes into consideration the inventory costs, plus a set of delivery frequencies instead of a single delivery frequency for each shop. Additionally, the ITP can also be viewed as a generalisation of the Inventory Routing Problem to the multiproduct case. EVITA, standing for Evolutionary Inventory and Transportation Algorithm, is a two-level methodology designed to address this problem. The top level uses an evolutionary algorithm to obtain delivery patterns for each shop on a weekly basis so as to minimise the inventory costs, while the bottom level solves the Vehicle Routing Problem (VRP) for every day in order to obtain the transport costs associated to a particular set of patterns.
Computing Research Repository, 2009
EVITA, standing for Evolutionary Inventory and Transportation Algorithm, is a two-level methodology designed to address the Inventory and Transportation Problem (ITP) in retail chains. The top level uses an evolutionary algorithm to obtain delivery patterns for each shop on a weekly basis so as to minimise the inventory costs, while the bottom level solves the Vehicle Routing Problem (VRP) for every day in order to obtain the minimum transport costs associated to a particular set of patterns. The aim of this paper is to investigate whether a multiobjective approach to this problem can yield any advantage over the previously used single objective approach. The analysis performed allows us to conclude that this is not the case and that the single objective approach is in gene- ral preferable for the ITP in the case studied. A further conclusion is that it is useful to employ a classical algorithm such as Clarke & Wright's as the seed for other metaheuristics like local search or tabu search in order to provide good results for the Vehicle Routing Problem.
Application of Multi-objective Simulation-optimization Techniques to Inventory Management Problems
Proceedings of the Winter Simulation Conference, 2005.
In this paper, we present how a solution framework developed for (a special case of) the multi-objective simulationoptimization problems can be applied to evaluate and optimally select the non-dominated set of inventory policies for two case study problems. Based on the concept of Pareto optimality, the solution framework mainly includes how to evaluate the quality of the selected Pareto set by two types of errors, and how to allocate the simulation replications according to some asymptotic allocation rules. Given a fixed set of inventory policies for both case study problems, the proposed solution method is applied to allocate the simulation replications. Results show that the solution framework is efficient and robust in terms of the total number of simulation replications needed to find the nondominated Pareto set of inventory policies.
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How much to order'' and ''when to order'' are the two fundamental issues managers have to resolve in an inventory system. Making these decisions in inventory systems with multiple products is a challenging task for managers because these decisions are often subject to several constraints due to limited resources such as budget, space, and the maximum weight of goods that can be stored. Most approaches in the literature for optimizing decisions in such an environment consider only a single budgetary constraint. This paper presents a mixed-integer programming model to optimize the two fundamental decisions of inventory management for ordering multiple inventory items subject to multiple resource constraints. It also determines whether a fixed cycle for all products or an independent cycle for each should be used for a lower total cost. The solution of the model does not seem to require excessive central processing unit (cpu) time as indicated by the computational experience reported in this paper; solution of the largest test problem, with 30 products and five resource constraints, required less than 20 cpu seconds on a personal computer. r
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This study presents a seasonal multi-product multi-period inventory control model with inventory costs obtained under inflation and all-unit discount policy. The products are delivered in boxes of known quantities and both backorder and lost-sale quantities are considered in case of shortage. The goal is to find a representative set of Pareto optimal solutions (including the ordering quantities) in different periods and to minimize both the total inventory cost (i.e. ordering, holding, shortage, and purchasing costs) and the total storage space, simultaneously. Three multi-objective optimization algorithms of nondominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), and multi-objective particle swarm optimization (MOPSO) are proposed to solve the problem. The Taguchi approach with a novel metric (based on the coefficient of variation) is utilized to model the response variable and compare the performances of the algorithms. Three numerical examples are used to demonstrate the applicability and exhibit the efficacy of the procedures and algorithms. The results of statistical analyses show significant differences in the performance metrics for all three algorithms and in all three numerical examples.
Novel NSGA-II and SPEA2 Algorithms for Bi-Objective Inventory Optimization
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Abstract: Inventory optimization is a significant problem that is tied directly to financial gains. Its complexity has led to the development of new inventory models and optimization techniques. Evolutionary algorithms, particularly Pareto based evolutionary algorithms have been proven to be reliable for solving such problems. However, these evolutionary algorithms concentrate mostly on global search and have limited local search abilities. This leads to a poor convergence to the Pareto front. Among these algorithms the most studied are non-dominated sorting genetic algorithm-II and strength Pareto evolutionary algorithm2. This paper proposes a novel method that increases their convergence. The novelty is based on three techniques: Firstly, a time-based fitness assignment that favours solutions from previous generations is employed. Secondly, before the crossover process, the mating pool is updated with a positive bias towards better solutions. Finally, a more disruptive mutation scheme is used to prevent premature convergence. The novel algorithms were tested on a benchmark problem suite and two inventory problems. The performance of the algorithms is measured using hypervolume, generational distance and spacing metrics. The results illustrated by graphics indicate that the novel algorithms can obtain better convergence without increasing the time complexity.
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International Journal of Supply Chain and Inventory Management, 2017
The purpose of this paper is to determine the optimum lot-sizes and reorder intervals of a 3-echelon supply chain system. The mathematical model is built based on Roundy's PO2 policy and integer policy of ordering as a constrained non-linear programming problem. For illustration purpose, we took two problems of single and fifty products distribution systems under deterministic condition. Problems are solved with exhaustive search method on spreadsheet and through Matlab programming. Though PO2 policy is very simple and is able to provide a few solutions, and faster, many times it fails to find an optimal solution and sometimes, any feasible solution at all. On the contrary, integer policy gives many including optimum and all PO2 solutions. Result shows that our proposed model and the simple algorithm applied for the solution have superiority and is effective on reducing the total cost of the multi-product, multi-echelon inventory system. Further, the products are grouped based on reorder interval using joint replenishment strategy.