sizing problem where a single buyer plans to purchase a single product in multiple
periods from several qualified suppliers who are able to provide the required product
with the needed quality in a timely manner. Product price and order cost differs
among different suppliers. Buyer’s demand for the product is deterministic and varies
for different time periods. The problem is to determine how much product from which
supplier must be ordered in each period such that buyer’s demand is satisfied without
violating some side constraints. We have developed a mathematical programming
model to deal with this problem, and proposed a forward dynamic programming
approach to obtain optimal solutions in reasonable amount of time even for large scale
problems. Finally, a numerical example is conducted in which solutions obtained from
the proposed dynamic programming algorithm is compared with solutions from the
branch-and-bound algorithm. Through the numerical example we have shown the
efficiency of our algorithm.
How to cite this paper
Moqri, M., Javadi, M & Yazdian, A. (2011). Supplier selection and order lot sizing using dynamic programming.International Journal of Industrial Engineering Computations , 2(2), 319-328.
Refrences
Aissaoui, N., Haouari, M., & Hassini, E. (2007). Supplier selection and order lot sizing modeling: A review, Computers & operations research, 34, 3516–3540.
Aryanezhad, M.B.G. (1992). An algorithm based on a new sufficient condition of optimality in dynamic lot size model, European Journal of Operational Research, 59, 425-433.
Basnet, C., & Leung, J.M.Y. (2005). Inventory lot-sizing with supplier selection, Computers and Operations Research, 32, 1–14.
Brahimi, N., Dauzere-Peres, S., Najid N.M. & Najid, A. (2006). Single item lot sizing problems, European Journal of Operational Research, 168, 1-16.
Cattrysse, D., Maes, J., & Van Wassenhove, L.N. (1990). Set partitioning and column generation heuristics for capacitated dynamic lot-sizing, European Journal of Operational Research, 46, 38–48.
Current, J., & Weber, C. (1994). Application of facility location modelling constructs to vendor selection problems, European Journal of Operational Research, 76, 387–92.
Dai, T., & Qi, X. (2007). An acquisition policy for a multi-supplier system with a finite-time horizon, Computers & Operations Research, 34, 2758 – 2773.
Evans, J.R. (1985). An efficient implementation of the Wagner–Whitin algorithm for dynamic lot sizing, Journal of Operations Management, 5, 235–239.
Hassini, E. (2008). Order lot sizing with multiple capacitated suppliers offering leadtime-dependent capacity reservation and unit price discounts, Production Planning & Control, 19, 142–149.
Heady, R.B., & Zhu Z. (1994). An improved implementation of the Wagner–Whitin algorithm, Production and Operations Management, 3, 55–63.
Liao, Z., & Rittscher, J. (2007). Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions, Int. J. Production Economics, 107, 502–510.
Rezaei, J., & Davoodi M. (2006). Genetic algorithm for inventory lot-sizing with supplier selection under fuzzy demand and costs, Advances in Applied Artificial Intelligence, 4031, 1100–1110.
Rezaei, J., & Davoodi, M. (2008). A deterministic multi-item inventory model with supplier selection and imperfect quality, Applied Mathematical Modelling, 32, 2106–2116.
Rosenblatt, M. J., Herer, Y. T., & Hefter, I. (1998). An acquisition policy for a single item multi-supplier system, Management Science, 44, 96–100.
Sadjadi, S. J., Aryanezhad, M.B.G., & Sadeghi, H.A. (2009). An Improved WAGNER-WHITIN Algorithm, International Journal of Industrial Engineering & Production Research, 20, 117-123.
Tempelmeier, H. (2002). A simple heuristic for dynamic order sizing and supplier selection with time-varying data, Production and Operations Management, 11, 499–515.
Ustun, O., & Demirtas, E. A. (2008a). An integrated multi-objective decision-making process for multi-period lot-sizing with supplier selection, Omega, 36, 509 – 521.
Ustun, O., & Demirtas, E. A. (2008b). Multi-period lot-sizing with supplier selection using achievement scalarizing functions, Computers & Industrial Engineering, 54, 918–931
Wagner, H. M., & Whitin, T.M. (1958). Dynamic version of the eonomic lot-size model, Management Science, 5, 89–96.
Wolsey, L. A. (1995). Progress with single-item lot-sizing, European Journal of Operational Research, 86, 395–401.
Aryanezhad, M.B.G. (1992). An algorithm based on a new sufficient condition of optimality in dynamic lot size model, European Journal of Operational Research, 59, 425-433.
Basnet, C., & Leung, J.M.Y. (2005). Inventory lot-sizing with supplier selection, Computers and Operations Research, 32, 1–14.
Brahimi, N., Dauzere-Peres, S., Najid N.M. & Najid, A. (2006). Single item lot sizing problems, European Journal of Operational Research, 168, 1-16.
Cattrysse, D., Maes, J., & Van Wassenhove, L.N. (1990). Set partitioning and column generation heuristics for capacitated dynamic lot-sizing, European Journal of Operational Research, 46, 38–48.
Current, J., & Weber, C. (1994). Application of facility location modelling constructs to vendor selection problems, European Journal of Operational Research, 76, 387–92.
Dai, T., & Qi, X. (2007). An acquisition policy for a multi-supplier system with a finite-time horizon, Computers & Operations Research, 34, 2758 – 2773.
Evans, J.R. (1985). An efficient implementation of the Wagner–Whitin algorithm for dynamic lot sizing, Journal of Operations Management, 5, 235–239.
Hassini, E. (2008). Order lot sizing with multiple capacitated suppliers offering leadtime-dependent capacity reservation and unit price discounts, Production Planning & Control, 19, 142–149.
Heady, R.B., & Zhu Z. (1994). An improved implementation of the Wagner–Whitin algorithm, Production and Operations Management, 3, 55–63.
Liao, Z., & Rittscher, J. (2007). Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions, Int. J. Production Economics, 107, 502–510.
Rezaei, J., & Davoodi M. (2006). Genetic algorithm for inventory lot-sizing with supplier selection under fuzzy demand and costs, Advances in Applied Artificial Intelligence, 4031, 1100–1110.
Rezaei, J., & Davoodi, M. (2008). A deterministic multi-item inventory model with supplier selection and imperfect quality, Applied Mathematical Modelling, 32, 2106–2116.
Rosenblatt, M. J., Herer, Y. T., & Hefter, I. (1998). An acquisition policy for a single item multi-supplier system, Management Science, 44, 96–100.
Sadjadi, S. J., Aryanezhad, M.B.G., & Sadeghi, H.A. (2009). An Improved WAGNER-WHITIN Algorithm, International Journal of Industrial Engineering & Production Research, 20, 117-123.
Tempelmeier, H. (2002). A simple heuristic for dynamic order sizing and supplier selection with time-varying data, Production and Operations Management, 11, 499–515.
Ustun, O., & Demirtas, E. A. (2008a). An integrated multi-objective decision-making process for multi-period lot-sizing with supplier selection, Omega, 36, 509 – 521.
Ustun, O., & Demirtas, E. A. (2008b). Multi-period lot-sizing with supplier selection using achievement scalarizing functions, Computers & Industrial Engineering, 54, 918–931
Wagner, H. M., & Whitin, T.M. (1958). Dynamic version of the eonomic lot-size model, Management Science, 5, 89–96.
Wolsey, L. A. (1995). Progress with single-item lot-sizing, European Journal of Operational Research, 86, 395–401.