considering various types of non-perfect products. We classify products in four groups of
perfect, imperfect, defective but reworkable and non-reworkable defective items. The demand
is a power function of price and marketing expenditure and production unit cost is considered to
be a function of lot size. The objective of this paper is to determine lot size, marketing
expenditure, selling price, set up cost and inventory holding cost, simultaneously. The problem
is modeled as a nonlinear posynomial geometric programming and an optimal solution is
derived. The implementation of the proposed method is demonstrated using a numerical
example and the sensitivity analysis is also performed to study the behavior of the model.
How to cite this paper
Barzoki, M., Bayati, M & Hejazi, S. (2011). A joint lot-sizing and marketing model with reworks, scraps and imperfect products.International Journal of Industrial Engineering Computations , 2(2), 395-408.
Refrences
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Bedworth, D. D., & Bailey, J. E. (1987). Integrated production control systems, 2nd ed., John Wiley & Sons, New York.
Beightler, C. S., & Philip, D. T. (1976). Applied Geometric Programming, Wiley, New York.
Ben-Daya, M., Nomana, S. M., & Harigab, M. (2006). Integrated inventory control and inspection policies with deterministic demand. Computers and Operations Research, 33, 1625–1638.
Chan, W. M., Ibrahim, R. N., & Lochert, P. B. (2003). A new EPQ model: Integrating lower pricing, rework and reject situations. Production Planning and Control, 14, 588–595.
Chiu, Y. P. (2003). Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Engineering Optimization, 35, 427–437.
Duffin, R. J., Peterson, E. L., & Zener, C. (1967). Geometric Programming: Theory and application, Wiley, New York.
Fathian, M., Sadjadi, S. J., & Sajadi, S. (2009). Optimal pricing model for electronic products. Computers & Industrial Engineering, 56, 255-259.
Gupta, T., & Chakraborty, S. (1984). Looping in a multistage production system. International Journal of Production Research, 22, 299–311.
Hayek, P. A., & Salameh, M. K. (2001). Production lot sizing with the reworking of imperfect quality items produced. Production Planning and Control, 12, 584–590.
Jaber, M. Y., Bonney, M., & Moualek, I. (2009). An economic order quantity model for an imperfect production process with entropy cost. International Journal of Production Economics, 118, 26–33.
Jamal, A. M. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at a single-stage production system. Computers & Industrial Engineering, 47, 77–89.
Jung, H., & Klein, C. M. Optimal inventory policies under decreasing cost functions via geometric programming. European Journal of Operational Research, 132, 628-642.
Kim, D. S., & Lee, W. J. (1998). Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109, 212-227.
Lee, W. J. (1993). Determining selling price and order quantity by geometric programming, optimal solution, bounds and sensitivity. Decision Sciences, 24, 76-87.
Lee, W. J., & Kim, D. S. (1993). Optimal and heuristic decision strategies for integrated production and marketing planning. Decision Sciences, 24, 1203-1213.
Lee, H. L., & Rosenblatt, M. J. (1968). The effects of varying marketing policies and conditions on the economic ordering quantity. International Journal of Production Research, 24, 593-598.
Lee, W. J., Kim, D. S., Cabot, A. V. (1996). Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28, 941-952.
Lee, H. H., Chandra, M. J., Deleveaux, V. J. (1997). Optimal batch size and investment in multistage production systems with scrap. Production Planning and Control, 8, 586–596.
Lilien, G. L., Kotler, P., & Moorthy, K. S. (1992). Marketing Models, Prentice Hall: Englewood Cliffs, NJ.
Panda, D., & Maiti, M. (2009). Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraints: A geometric programming approach, Mathematical and Computer modeling, 49, 1733-1749.
Sadjadi, S. J., Orougee, M., & Aryanezhad, M. B. (2005). Optimal production and marketing planning. Computational Optimization and Application, 30, 195-203.
Salameh, M. K., Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59–64.
Teunter, R., & van der Laan, E. (2002). On the non-optimality of the average cost approach for inventory models with remanufacturing. International Journal of Production Research, 79, 67–73.
Van Beek, P., & Putten, C. (1987). OR contributions to flexibility improvement in production/inventory systems. European Journal of Operational Research, 31, 52-60.
Warets, C. D. J. (1994). Inventory control and management. Wiley, New York.
Bedworth, D. D., & Bailey, J. E. (1987). Integrated production control systems, 2nd ed., John Wiley & Sons, New York.
Beightler, C. S., & Philip, D. T. (1976). Applied Geometric Programming, Wiley, New York.
Ben-Daya, M., Nomana, S. M., & Harigab, M. (2006). Integrated inventory control and inspection policies with deterministic demand. Computers and Operations Research, 33, 1625–1638.
Chan, W. M., Ibrahim, R. N., & Lochert, P. B. (2003). A new EPQ model: Integrating lower pricing, rework and reject situations. Production Planning and Control, 14, 588–595.
Chiu, Y. P. (2003). Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Engineering Optimization, 35, 427–437.
Duffin, R. J., Peterson, E. L., & Zener, C. (1967). Geometric Programming: Theory and application, Wiley, New York.
Fathian, M., Sadjadi, S. J., & Sajadi, S. (2009). Optimal pricing model for electronic products. Computers & Industrial Engineering, 56, 255-259.
Gupta, T., & Chakraborty, S. (1984). Looping in a multistage production system. International Journal of Production Research, 22, 299–311.
Hayek, P. A., & Salameh, M. K. (2001). Production lot sizing with the reworking of imperfect quality items produced. Production Planning and Control, 12, 584–590.
Jaber, M. Y., Bonney, M., & Moualek, I. (2009). An economic order quantity model for an imperfect production process with entropy cost. International Journal of Production Economics, 118, 26–33.
Jamal, A. M. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at a single-stage production system. Computers & Industrial Engineering, 47, 77–89.
Jung, H., & Klein, C. M. Optimal inventory policies under decreasing cost functions via geometric programming. European Journal of Operational Research, 132, 628-642.
Kim, D. S., & Lee, W. J. (1998). Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109, 212-227.
Lee, W. J. (1993). Determining selling price and order quantity by geometric programming, optimal solution, bounds and sensitivity. Decision Sciences, 24, 76-87.
Lee, W. J., & Kim, D. S. (1993). Optimal and heuristic decision strategies for integrated production and marketing planning. Decision Sciences, 24, 1203-1213.
Lee, H. L., & Rosenblatt, M. J. (1968). The effects of varying marketing policies and conditions on the economic ordering quantity. International Journal of Production Research, 24, 593-598.
Lee, W. J., Kim, D. S., Cabot, A. V. (1996). Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28, 941-952.
Lee, H. H., Chandra, M. J., Deleveaux, V. J. (1997). Optimal batch size and investment in multistage production systems with scrap. Production Planning and Control, 8, 586–596.
Lilien, G. L., Kotler, P., & Moorthy, K. S. (1992). Marketing Models, Prentice Hall: Englewood Cliffs, NJ.
Panda, D., & Maiti, M. (2009). Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraints: A geometric programming approach, Mathematical and Computer modeling, 49, 1733-1749.
Sadjadi, S. J., Orougee, M., & Aryanezhad, M. B. (2005). Optimal production and marketing planning. Computational Optimization and Application, 30, 195-203.
Salameh, M. K., Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59–64.
Teunter, R., & van der Laan, E. (2002). On the non-optimality of the average cost approach for inventory models with remanufacturing. International Journal of Production Research, 79, 67–73.
Van Beek, P., & Putten, C. (1987). OR contributions to flexibility improvement in production/inventory systems. European Journal of Operational Research, 31, 52-60.
Warets, C. D. J. (1994). Inventory control and management. Wiley, New York.