zbMATH — the first resource for mathematics

Mathematical modelling of the order-promising process for fruit supply chains considering the perishability and subtypes of products. (English) Zbl 07163483
Summary: This paper proposes a mixed integer mathematical programming model to support the complex order promising process in fruit supply chains. Due to natural factors, such as land, weather or harvesting time, these supply chains present units of the same product that differ in certain relevant attributes to customers (subtypes). This becomes a managerial problem when customers require specific subtypes in their orders. Additionally, the deterioration of the original characteristics of subtypes over time generates waste and gives rise to a shelf life-based pricing policy. Therefore, the developed model should ensure that customers are served not only the quantities and dates, but also the required homogeneity and freshness. The model aims to maximise two conflicting objectives: total profit and mean product freshness. The novelty of the model derives from considering both homogeneity in subtypes as a requirement in customer orders and the traceability of product deterioration over time. Different scenarios are defined according to the weight assigned to each objective, shelf-life length and pricing policy in a rolling horizon scheme. The numerical experiments conducted for a real orange and tangerine supply chain, show the model’s validity and the conflicting behaviour of the two objectives. The highest profit is made at the expense of the lowest mean freshness delivered, which is reinforced by the narrower the price variation with freshness. Finally, the positive impact of prolonging the product’s shelf life on both objectives is shown.

90-XX Operations research, mathematical programming
91-XX Game theory, economics, finance, and other social and behavioral sciences
Full Text: DOI
[1] Fleischmann, B.; Meyr, H., Planning hierarchy, modeling and advanced planning systems, Handb. Oper. Res. Manag. Sci., 11, 455-523 (2003)
[2] Okongwu, U.; Lauras, M.; Dupont, L.; Humez, V., A decision support system for optimising the order fulfilment process, Prod. Plann. Control, 23, 8, 581-598 (2011)
[4] Alemany, M. M.E.; Ortiz, A.; Boza, A.; Fuertes-Miquel, V. S., A model driven decision support system for reallocation of supply to orders under uncertainty in ceramic companies, Technol. Econ. Dev. Econ., 21, 4, 596-625 (2015)
[5] Amorim, P.; Gunther, H. O.; Almada-Lobo, B., Multi-objective integrated production and distribution planning of perishable products, Int. J. Prod. Econ., 138, 1, 89-101 (2012)
[6] Nahmias, S., Perishable inventory theory: a review, Oper. Res., 30, 4, 680-708 (1982) · Zbl 0486.90033
[7] Ahumada, O.; Villalobos, J. R., Operational model for planning the harvest and distribution of perishable agricultural products, Int. J. Prod. Econ., 133, 2, 677-687 (2011)
[8] Qin, Y.; Wang, J.; Wei, C., Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Int. J. Prod. Econ., 152, 42-48 (2014)
[9] Blanco, A.; Masini, G.; Petracci, N.; Bandoni, J., Operations management of a packaging plant in the fruit industry, J. Food Eng., 70, 3, 299-307 (2005)
[10] Chaudhuri, A.; Dukovska-Popovska, I.; Damgaard, C. M.; Hvolby, H.-H., Supply uncertainty in food processing supply chain: sources and coping strategies, Proceedings of the 2014 IFIP International Conference on Advances in Production Management Systems, 183-191 (2014), Springer
[11] Yu, M.; Nagurney, A., Competitive food supply chain networks with application to fresh produce, Eur. J. Oper. Res., 224, 2, 273-282 (2013) · Zbl 1292.90034
[12] Kärkkäinen, M., Increasing efficiency in the supply chain for short shelf life goods using RFID tagging, Int. J. Retail Distrib. Manag., 31, 10, 529-536 (2003)
[13] Grillo, H.; Alemany, M. M.E.; Ortiz, A., A review of mathematical models for supporting the order promising process under lack of homogeneity in product and other sources of uncertainty, Comput. Ind. Eng., 91, 239-261 (2016)
[14] Alarcón, F.; Alemany, M. M.E.; Lario, F. C.; Oltra, R. F., The lack of homogeneity in the product (LHP) in the ceramic tile industry and its impact on the reallocation of inventories, Bol. De La Soc. Esp. De Ceram. Y Vidr., 50, 1, 49-57 (2011)
[15] Kilic, O. A.; van Donk, D. P.; Wijngaard, J.; Tarim, S. A., Order acceptance in food processing systems with random raw material requirements, OR Spectrum, 32, 4, 905-925 (2010) · Zbl 1230.90128
[16] Alemany, M. M.E.; Lario, F. C.; Ortiz, A.; Gomez, F., Available-to-promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case, Appl. Math. Model., 37, 5, 3380-3398 (2013) · Zbl 1351.90087
[17] Alemany, M. M.E.; Grillo, H.; Ortiz, A.; Fuertes-Miquel, V. S., A fuzzy model for shortage planning under uncertainty due to lack of homogeneity in planned production lots, Appl. Math. Model., 39, 15, 4463-4481 (2015) · Zbl 1443.90090
[18] Soto-Silva, W. E.; Nadal-Roig, E.; González-Araya, M. C.; Pla-Aragones, L. M., Operational research models applied to the fresh fruit supply chain, Eur. J. Oper. Res., 251, 2, 345-355 (2016) · Zbl 1346.90056
[19] Akkerman, R.; Farahani, P.; Grunow, M., Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges, Or Spectrum, 32, 4, 863-904 (2010)
[20] Ahumada, O.; Villalobos, J. R., Application of planning models in the agri-food supply chain: a review, Eur. J. Oper. Res., 196, 1, 1-20 (2009) · Zbl 1159.90441
[21] Bakker, M.; Riezebos, J.; Teunter, R. H., Review of inventory systems with deterioration since 2001, Eur. J. Oper. Res., 221, 2, 275-284 (2012) · Zbl 1253.90017
[22] Ahuja, R. K.; Huang, W.; Romeijn, H. E.; Morales, D. R., A heuristic approach to the multi-period single-sourcing problem with production and inventory capacities and perishability constraints, INFORMS J. Comput., 19, 1, 14-26 (2007) · Zbl 1241.90188
[23] Eks̨ioğlu, S. D.; Jin, M., Cross-facility production and transportation planning problem with perishable inventory, Proceedings of the 2006 International Conference on Computational Science and its Applications, 708-717 (2006), Springer · Zbl 1172.90380
[24] Zhang, G.; Habenicht, W.; Spieß, W. E.L., Improving the structure of deep frozen and chilled food chain with tabu search procedure, J. Food Eng., 60, 1, 67-79 (2003)
[25] Rong, A.; Akkerman, R.; Grunow, M., An optimization approach for managing fresh food quality throughout the supply chain, Int. J. Prod. Econ., 131, 1, 421-429 (2011)
[26] Nagurney, A.; Masoumi, A. H.; Yu, M., Supply chain network operations management of a blood banking system with cost and risk minimization, Comput. Manag. Sci., 9, 2, 205-231 (2012) · Zbl 1273.90028
[27] Nagurney, A.; Masoumi, A. H., Supply chain network design of a sustainable blood banking system, Sustainable Supply Chains, 49-72 (2012), Springer
[28] Amorim, P.; Antunes, C. H.; Almada-Lobo, B., Multi-objective lot-sizing and scheduling dealing with perishability issues, Ind. Eng. Chem. Res., 50, 6, 3371-3381 (2011)
[29] Farahani, P.; Grunow, M.; Guenther, H. O., Integrated production and distribution planning for perishable food products, Flex. Serv. Manuf. J., 24, 1, 28-51 (2012)
[30] Firoozi, Z.; Ismail, N.; Ariafar, S.; Tang, S. H.; Ariffin, M.; Memariani, A., Distribution network design for fixed lifetime perishable products: a model and solution approach, J. Appl. Math., 2013, 13 (2013) · Zbl 1266.90008
[31] Amorim, P.; Curcio, E.; Almada-Lobo, B.; Barbosa-Póvoa, A. P.; Grossmann, I. E., Supplier selection in the processed food industry under uncertainty, Eur. J. Oper. Res., 252, 3, 801-814 (2016) · Zbl 1346.90070
[32] Rijpkema, W. A.; Hendrix, E. M.T.; Rossi, R.; van der Vorst, J., Application of stochastic programming to reduce uncertainty in quality-based supply planning of slaughterhouses, Ann. Oper. Res., 239, 2, 613-624 (2016) · Zbl 1337.90048
[33] Goyal, S. K.; Giri, B. C., Recent trends in modeling of deteriorating inventory, Eur. J. oper. Res., 134, 1, 1-16 (2001) · Zbl 0978.90004
[34] Tsao, Y.-C.; Sheen, G.-J., Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Comput. Oper. Res. Part Spec. Issue: Top. Real-time Supply Chain Manag., 35, 11, 3562-3580 (2008) · Zbl 1140.91358
[35] Rahdar, M.; Nookabadi, A. S., Coordination mechanism for a deteriorating item in a two-level supply chain system, Appl. Math. Model., 38, 11, 2884-2900 (2014) · Zbl 1427.90026
[36] Önal, M.; Romeijn, H. E.; Sapra, A.; Van den Heuvel, W., The economic lot-sizing problem with perishable items and consumption order preference, Eur. J. Oper. Res., 244, 3, 881-891 (2015) · Zbl 1346.90044
[37] Ali, S. S.; Madaan, J.; Chan, F. T.; Kannan, S., Inventory management of perishable products: a time decay linked logistic approach, Int. J. Prod. Res., 51, 13, 3864-3879 (2013)
[38] Coelho, L. C.; Laporte, G., Optimal joint replenishment, delivery and inventory management policies for perishable products, Comput. Oper. Res., 47, 42-52 (2014) · Zbl 1348.90025
[39] Duan, Q. L.; Liao, T. W., A new age-based replenishment policy for supply chain inventory optimization of highly perishable products, Int. J. Prod. Econ., 145, 2, 658-671 (2013)
[40] Haijema, R., A new class of stock-level dependent ordering policies for perishables with a short maximum shelf life, Int. J. Prod. Econ., 143, 2, 434-439 (2013)
[41] Kristjansson, B.; Lee, D., The MPL modeling system, Modeling languages in mathematical optimization, 239-266 (2004), Springer
[42] Mavrotas, G., Effective implementation of the e-constraint method in multi-objective mathematical programming problems, Appl. Math. Comput., 213, 2, 455-465 (2009) · Zbl 1168.65029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.