Volume 2 Issue 4 pp. 715-736 Fall, 2011


A fast-response production-inventory model for deteriorating seasonal products with learning in set-ups


Ibraheem Abdul and Atsuo Murata


The classical production-inventory model assumes that both demand and set-up costs are constant. However, in real manufacturing environment, managers usually embark on continuous improvement programmes that often lead to more effective use of tools and machineries and consequently reduction in set-up costs. In fact, constant emphasis on reduction of set-up costs is usually cited as one of the factors responsible for the efficiency of Japanese manufacturing methods. On the other hand, the demand for seasonal product is often characterized by a mixture of time-dependent patterns over the entire season. This paper investigates the effect of learning-based reduction in set-up costs on the optimal schedules and costs of a production-inventory system for deteriorating seasonal products. The demand pattern is a general three-phase ramp-type demand function that represents the various phases of demand commonly observed in many seasonal products in the market. A two-parameter Weibull-distribution function is used for the deterioration of items in order to make the model more generalized and realistic. The study further presents two different multi-period production strategies that can ensure a fast-response to customers’ demand and compare them with the usual single period strategy. The Numerical example and sensitivity analysis shows that learning-based reduction in set-up costs leads to higher production frequency and shorter production runs which are vital aspects of the just-in-time (JIT) philosophy.


DOI: 10.5267/j.ijiec.2010.06.008

Keywords: Production, Learning, Set-up reduction, Seasonal products, Deterioration, Varying demand pattern
References

Abdul, I. & Murata, A. (2011). An inventory model for deteriorating items with varying demand pattern and unknown time horizon. International Journal of Industrial Engineering Computations, 2, 81-86.

Adler, G. L. & Nanda, R. (1974). The effects of learning on optimal lot size determination-multiple product case. AIIE Transactions, 6, 21–27.

Alamri, A. A. & Balkhi, Z. T. (2007). The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates. International Journal of Production Economics, 107 (1), 125–138.

Andijani, A. (1998). Set-up cost reduction in a multi-stage order quantity model. Production Planning and Control, 9, 121–126.

Balkhi, Z. T. (2003). The effects of learning on the optimal production lot size for deteriorating and partially backordered items with time varying demand and deterioration rates. Applied Mathematical Modelling, 27 (10), 763–779.

Chand, S. (1989). Lot sizes and set-up frequency with learning and process quality. European Journal of Operational Research, 42, 190–202.

Cheng, M. & Wang, G. (2009). A note on the inventory model for deteriorating items with trapezoidal type demand rate. Computers & Industrial Engineering, 56, 1296-1300.

Cheng, T. C. E. (1994). An economic manufacturing quantity model with learning effects. International Journal of Production Economics, 33, 257–264.

Chiu, H. N., Chen, H. M. & Weng, L. C.(2003). Deterministic time-varying demand lot-sizing models with learning and forgetting in set-ups and production. Production and Operations Management, 12 (1), 120–127.

Darwish, M. A. (2008). EPQ models with varying set-up cost. International Journal Production Economics, 113, 297–306.

Das, D., Roy, A. & Kar, S. (2011). A Production-Inventory Model for a Deteriorating Item Incorporating Learning Effect Using Genetic Algorithm. Advances in Operations Research Volume 2010, Article ID 146042, 26 pages, doi:10.1155/2010/146042.

Dobos, I. & Richter, K. (2003). A production/recycling model with stationary demand and return rates. Central European Journal of Operations Research, 11 (1), 35–46.

Dobos, I. & Richter, K. (2004). An extended production/recycling model with stationary demand and return rates. International Journal of Production Economics, 90 (3), 311–323.

Fisk, J. C. & Ballou, D. B. (1982). Production lot sizing under a learning sect. AIIE Transactions, 14, 257-264.

Gulledge, T. R. & Khoshnevis, B. (1987). Production rate, learning, and program costs: Survey and Bibliography. Engineering Costs and Production Economics, 11, 223–236.

Hill, R. M. (1995). Inventory model for increasing demand followed by level demand. Journal of the Operational Research Society, 46, 1250–1259.

Jaber, M. Y., & Bonney, M. (1999). The economic manufacture/order quantity (EMQ/ EOQ) and the learning curve: past, present, and future. International Journal of Production Economics, 59, 93–102.

Jaber, M. Y., & Bonney, M. (2003). Lot sizing with learning and forgetting in set-ups and in product quality. International Journal of Production Economics, 83 (1), 95–111.

Jaber, M. Y., & Bonney, M. C. (1996). Production breaks and the learning curve: the forgetting phenomena. Applied Mathematical Modelling, 20 (2), 162–169.

Jaber, M. Y., & Bonney, M. C. (1997). A comparative study of learning curves with forgetting. Applied Mathematical Modelling, 21 (8), 523–531.

Jaber, M. Y., Bonney, M. & Guiffrida, A. (2010) Coordinating a three-level supply chain with learning-based continuous improvement. International Journal of Production Economics, 127, 27–38.

Jaber, M. Y., & El Saadany M. A. (2011). An economic production and remanufacturing model with learning effects. International Journal Production Economics, 131, 115–127.

Jaber, M. Y., & Sikström, S. (2004). A numerical comparison of three potential learning and forgetting models. International Journal of Production Economics, 92(3), 281–294.

Karwan, K., Mazzola, J. & Morey, R. (1988). Production lot sizing under set-up and worker learning. Naval Research Logistics, 35, 159–179.

Keachie, E. C., & Fontana, R. J. (1966). Effects of learning on optimal lot size. Management Science,13(2), 102-108.

Manna, S. K., & Chaudhuri, K. S. (2006). An EOQ model with ramp-type demand rate, time dependent deterioration rate, unit production cost and shortages. European Journal of Operational Research, 171, 557–566.

Manna, S. K., & Chiang, C. (2010). Economic production quantity models for deteriorating items with ramp-type demand, International Journal of Operational Research, 7, 429-444.

Paknejad, M., Nasri, F. & Affisco, J. F. (1996). Analysis of set-up cost reduction in a two-stage system with power investment function. ZOR/Mathematical Methods of Operations Research, 43, 389–401.

Panda, S., Saha, S. & Basu, M. (2009). Optimal production stopping time for perishable products with ramp-type quadratic demand dependent production and set-up cost, Central European Journal of Operational Research, 17, 381-396.

Panda, S., Senapati, S. & Basu, M. (2008). Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand. Computers and Industrial Engineering, 54, 301–314.

Porteus, E. (1985). Investing in reduced set-ups in the EOQ model. Management Science, 31, 998–1010.

Rachamadugu, R. & Schriber, T. J. (1995). Optimal and heuristic policies for lot sizing with learning in set-ups. Journal of Operations Management, 13, 229–245.

Replogle, S. (1988). The strategic use of smaller lot sizes through a new EOQ model, Production and Inventory Management, 41-44.

Salameh, M. K., Abdul-Malak, M. U. & Jaber, M. Y. (1993). Mathematical modelling of the effect of human learning in the finite production inventory model. Applied Mathematical Modelling Journal, 17, 613 – 615.

Schonberger, R. (1982). Japanese Manufacturing Technologies, The Free Press, New York.

Şen, A. (2008). The US fashion industry: A supply chain review. International Journal of Production Economics, 114, 571–593.

Steedman, I. (1970). Some improvement curve theory. International Journal of Production Research, 8, 189–205.

Wright, T. (1936). Factors affecting the cost of airplanes, Journal of Aeronautical Science, 3, 122–128.