Solution of the Spare Parts Joint Replenishment Problem
with Quantity Discounts Using a Discrete Particle Swarm
Orlando DURÁN1, Luis PÉREZ2
1 Pontificia Universidad Católica de Valparaiso
2 Universidad Técnica Federico Santa Maria
Abstract: Joint Replenishment of spare parts is a common practice in several industries, mainly where logistic difficulties exist, such as mining, petroleum and military missions. In addition, quantity discounts have been considered in many operations and production scenarios, as a useful practice to promote substantial savings to the actors of a supply chain. The model presented corresponds to the Joint Replenishment Problem in a system operating with quantity discounts. This work presents the definition and the solution of the optimization model using techniques based on the Particle Swarm Optimization (PSO) and a Genetic Algorithm (GA). Extensive computational experiments were performed and several performance comparisons are included. Results clearly show that the PSO algorithm achieved better repeatability and the GA presented better performance in terms of minimization capability getting lower fitness values.
Keywords: joint replenishment problem, quantity discounts, metaheuristics, particle swarm, genetic algorithm, logistics.
CITE THIS PAPER AS:
Orlando DURÁN, Luis PÉREZ, Solution of the Spare Parts Joint Replenishment Problem with Quantity Discounts Using a Discrete Particle Swarm Optimization Technique, , Studies in Informatics and Control, ISSN 1220-1766, vol. 22 (4), pp. 319-328, 2013.
The inventory costs occupy an important share in total cost. Replenishment, shipment consolidation/coordination policies, different inventory allocation methods and effective utilization of information are among the most important supply chain management issues today. Optimizing inventory management can make the company agile in the market, maintaining high customer service. On the other hand, the adoption of Just in Time (JIT) has caused a change in the ordering practice (Also, JIT principles have led to supply networks with relatively few direct suppliers, with each of them jointly delivering several items.) Therefore, order processing costs have been reduced through the use of long-term supply contracts, electronic ordering and joint replenishment. Consequently, the transportation costs have been strongly influenced by the joint replenishment practice. Joint replenishment inventory can lower the average cost of the inventory, enlarging the ordering item amount, which make companies more efficient in transport operations. In industry, the spare parts management plays a critical role in searching for a long term efficiency, availability and customer service. Some authors have highlighted the importance of spare management and the impact that causes to logistics. Spudic et al.  addressed the supply management of spare parts in military vehicles. Propadalo  presented an application of reliability-based spare parts management in the airspace industry. This paper presents the definition and solution of the Joint Replenishment Problem in a Consumable Spare parts system operating with suppliers offering quantity discounts, using techniques based on the Particle Swarm Optimization (PSO) and a Genetic Algorithm (GA). Section 2 presents a literature review and section 3, presents the experimental design and the problem definition. Section 4 and 5 present details about the two metaheuristics used in optimization of the model, respectively. Section 6 shows numerical examples; performance comparisons are included. Finally, conclusions are reported in section 7.
- SPUDIC, R., B. IVANKOVIC, V. KOVACEVIC, Testing The Logistics Model Of Supplying Military Vehicles With Spare Parts. PROMET-Traffic & Transportation, vol. 19(4), 2010, pp. 233-236.
- PROPADALO, S., D. BEKAVAC, Z. JAKSIC, Spare Modules Management Optimization of Airspace Surveillance System. PROMET-Traffic & Transportation, vol. 24(4), 2012, pp. 233-236.
- ARKIN, D. J., R. ROUNDY, Computational Complexity of Uncapacitated Multi-echelon Production Planning Problems, Operation Research Letters, vol. 8, 1989, pp. 61-66.
- GOYAL, S., Determination of Optimum Packaging Frequency of Items Jointly Replenished, Management Science, vol. 23, 1974, pp. 436-443.
- GOYAL, S., A. SATIR, Joint Replenishment Inventory Control: Deterministic and Stochastic Models. European Journal of Operational Research, vol. 38, 1989, pp. 2-13.
- KASPI, M., M. ROSENBLATT, On the Economic Ordering Quantity for Jointly Replenished Items. International Journal of Production Research, vol. 29, 1991, pp. 107-114.
- JOHANSEN, S. G., P. MELCHIORS, Can-order Policy for the Periodic Review Joint Replenishment Problem, Journal of the Operational Research Society, vol. 54, 2003, pp. 283-290.
- BOCTOR, F., G. LAPORTE, J. RENAUD, Models and Algorithms for the Dynamic Demand Joint Replenishment Problem, International Journal of Production Research, vol. 42, 2004, pp. 2667-2678.
- KLEIN, C. M., J. A. VENTURA, An Optimal Method for a Deterministic Joint Replenishment Inventory Policy in Discrete Time, Journal of the Operational Research Society, vol. 46(5), 1995, pp. 649-657.
- KHOUJA, M., Z. MICHALEWICZ, S. SATOSKAR, A Comparison Between Genetic Algorithms and the RAND Method for Solving the Joint Replenishment Problem. Production Planning & Control, vol. 11, 2000, pp. 556-564.
- CHAN, C. K., B. K. S. CHEUNG, A. LANGEVIN, Solving the Multi-buyer Joint Replenishment Problem with a Modified Genetic Algorithm. Transportation Research Part B-Methodological, vol. 37(3), 2003, pp. 291-299.
- HOQUE, M. A., An Optimal Solution Technique for the Joint Replenishment Problem with Storage and Transport Capacities and Budget Constraints, European Journal of Operational Research, vol. 175, 2006, pp. 1033-1042.
- MOON, I. K., B. C. CHA, The Joint Replenishment Problem with Resource Restrictions, European Journal of Operational Research, vol. 173, 2006, pp. 190-198.
- BAYINDIR, Z. P., S. I. BIRBIL, J. B. G. FRENK, The Joint Replenishment Problem with Variable Production Costs, European Journal of Operational Research, vol. 175, 2006, pp. 622-640.
- GOYAL, S. K., B. C. GIRI, Recent Trends in Modelling of Deteriorating Inventory. European Journal of Operational Research, vol. 134(1), 2001, pp. 1-16.
- CHA, B., I. MOON, The Joint Replenishment Problem with Quantity Discounts, OR Spectrum, vol. 27, 2005, pp. 569-581.
- HONG, S. P., Y.-H. KIM. A Genetic Algorithm for Joint Replenishment based on the Exact Inventory Cost. Computers & Operations Research, vol. 36, 2009. pp. 167-175.
- LEUNG, T. W., C. K. CHAN, M. D. TROUTT, A Mixed Simulated Annealing-genetic Algorithm Approach to the Multi-buyer Multi-item Joint Replenishment Problem: Advantages of Meta-heuristic, Journal of Industrial and Management Optimization, vol. 4(1), 2008, pp. 53-66.
- OLSEN, A., An Evolutionary Algorithm to Solve the Joint Replenishment Problem using Direct Grouping. Computers & Industrial Engineering, vol. 48(2), 2005, pp. 223-235.
- OLSEN, A., Inventory Replenishment with Interdependent Ordering Costs: An Evolutionary Algorithm Solution. International Journal of Production Economics, vol. 113(1), 2008, pp. 359-369.
- DYE, C. Y., T. P. HSIEH. A Particle Swarm Optimization for Solving Joint Pricing and Lot-sizing Problem with Fluctuating Demand and Unit Purchasing Cost. Computers & Mathematics with Applications, vol. 60(7), 2010, pp. 1895-1907.
- COELLO, C. Introducción a la computación evolutiva. Notes CINVESTAV – IPN, Departamento de Computación, México. 2008.
- EBERHART, R. C., J. KENNEDY, A New Optimizer using Particle Swarm Theory, Proceedings of the Sixth International Symposium on Micromachine and Human Science, Nagoya, Japan. 1995, pp. 39-43.
- CORREA, E. S., A. FREITAS, C. G. JOHNSON, A New Discrete Particle Swarm Algorithm Applied to Attribute Selection in a Bioinformatics Data Set. In Proceedings of the Genetic and Evolutionary Computation Conference – Seattle, WA, 2006, pp.35-42.
- CABRERA, G., S. D. RONCAGLIOLO, J. P. RIQUELME, C. CUBILLOS, R. SOTO, A Hybrid Particle Swarm Optimization – Simulated Annealing Algorithm for the Probabilistic Travelling Salesman Problem, Studies in Informatics and Control, vol. 21(1), pp. 49-58, 2012.
- LEE, S., H. PARK, M. JEON, Binary Particle Swarm Optimization with Bit Change Mutation. IEICE Transactions .on Fundamentals of Electronics, Communications and Computer Sciences, vol. 90(10), 2007, pp. 2253-2256.