Available online at www.sciencedirect.com Omega 33 (2005) 97–106 www.elsevier.com/locate/dsw Production and inventory control with chaotic demands Kung-Jeng Wang a; b , Hui-Ming Wee b; ∗ , Shin-Feng Gao b , Shen-Lian Chung b; c a Department of Business Administration, National Dong Hwa University, Taiwan b Department of Industrial Engineering, Chung-Yuan Christian University, Taiwan, ROC c Department of Information Management, St. John’s & St. Mary’s Institute of Technology, Tamsui, Taipei, Taiwan 25135, ROC Received 7 November 2003; accepted 2 April 2004 Abstract This study explores an ecient approach for identifying chaotic phenomena in demands and develops a production lot-sizing method for chaotic demands. Owing to the buttery eect of chaotic demands, precise prediction of long-term demands is dicult. The experiments conducted in this study reveal that the maximal Lyapunov exponent is very eective in classifying chaotic and non-chaotic demands. A computational procedure of the Lyapunov exponent for production systems has been developed and some real world chaotic demands have been identied using the proposed chaos-probing index. This study proposes a modied Wagner–Whitin method that uses a forward focused perspective to make production lot-sizing decision under chaos demands for a single echelon system. The proposed method has been empirically demonstrated to achieve lower total production costs than three commonly used lot-sizing models, namely: lot-for-lot method, periodic ordering quantity, and Silver-Meal discrete lot-size heuristic under a xed production horizon, and the conventional Wagner–Whitin algorithm under chaotic demands. Sensitivity analysis is conducted to compare changes in total cost with variations in look-ahead period, initial demand, setup cost and holding costs. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Production and inventory control; Chaotic demands; Lot sizing 1. Introduction Facing a changing market environment, the most dicult parameter to manage is adjusting production to meet market demand. This study derives an economic production plan under chaotic demands to minimize overall cost. Recent studies have showed that when demand is lumpy, order quantity changes signicantly between periods. The traditional economic order quantity (EOQ) models cannot be applied to solve these types of production problems [1]. Moreover, other sophisticated algorithms such as the Wag- ner–Whitin dynamic technique, have not been successful in solving these types of problems due to the extreme sensi- tivity of the solution to changes in the estimates of future ∗ Corresponding author. E-mail address: weehm@cycu.edu.tw (H.-M. Wee). demands. Carlson et al. [2] presented a solution procedure, which incorporates the cost of changing the current produc- tion schedule to alleviate such nervousness in the face of uctuating demand. Previous studies such as Backburn and Millen [3] and Zhao et al. [4] describe lot-sizing approaches for rolling and xed time horizons. However, lot-sizing ap- proaches for dealing with chaotic demand remain in their infancy. This study considers the buttery eect of chaotic de- mands, and develops a corresponding production lot-sizing strategy. Researchers have long lacked methods for describ- ing or analyzing chaotic natural environments, for exam- ple, weather changes and the wave motions in an ocean. A chaotic model has a special characteristic in that the start- ing value strongly inuences system behavior. Small drift in predicting an initial demand ultimately may cause a sig- nicant dierence to real demand. This phenomenon is nor- mally called the “buttery eect”. An example of this eect 0305-0483/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.omega.2004.04.001