تولید و کنترل موجودی با خواسته های پر هرج و مرج

This study explores an efficient approach for identifying chaotic phenomena in demands and develops a production lot-sizing method for chaotic demands. Owing to the butterfly effect of chaotic demands, precise prediction of long-term demands is difficult. The experiments conducted in this study reveal that the maximal Lyapunov exponent is very effective 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 identified using the proposed chaos-probing index. This study proposes a modified 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 fixed 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.

Facing a changing market environment, the most difficult 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 significantly 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 Wagner–Whitin dynamic technique, have not been successful in solving these types of problems due to the extreme sensitivity of the solution to changes in the estimates of future demands. Carlson et al. [2] presented a solution procedure, which incorporates the cost of changing the current production schedule to alleviate such nervousness in the face of fluctuating demand. Previous studies such as Backburn and Millen [3] and Zhao et al. [4] describe lot-sizing approaches for rolling and fixed time horizons. However, lot-sizing approaches for dealing with chaotic demand remain in their infancy. This study considers the butterfly effect of chaotic demands, and develops a corresponding production lot-sizing strategy. Researchers have long lacked methods for describing or analyzing chaotic natural environments, for example, weather changes and the wave motions in an ocean. A chaotic model has a special characteristic in that the starting value strongly influences system behavior. Small drift in predicting an initial demand ultimately may cause a significant difference to real demand. This phenomenon is normally called the “butterfly effect”. An example of this effect is shown in Fig. 1. For production systems facing chaotic demands, the butterfly effect implies that a production schedule based on a long-term ‘accurate’ prediction may be useless given chaotic demand. Therefore, this study recommends using a production plan with a short-term planning horizon.The butterfly effect in chaotic demands makes precise prediction of long-term demands difficult. Moreover, even when long-term demand is predictable, they can be distorted dramatically owing to the butterfly effect. In such a case, long-term production planning may damage the system because of incorrect demand information. Therefore, the production horizon should be divided into segments to reduce computational effort and increase lot-sizing decision accuracy. This study identifies the chaotic demands and formulates a production lot-sizing strategy for the system. This paper is organized as follows: Section 2 presents an efficient approach for identifying chaotic demands. Section 3 then introduces several approaches for the deterministic dynamic lot-sizing model with lumpy demand models for lumpy demands. Subsequently, Section 4 proposes a heuristic production lot-sizing strategy for dealing with chaos demands. Next, Section 5 compares the total production costs of the proposed method and some other widely used approaches for different chaotic demand types. Finally, Section 6 examines the validity of the method developed here, and demonstrates how changes in planning horizon, initial value, setup cost and unit holding costs influence total production costs.

This study has developed an efficient approach that uses the maximal Lyapunov exponent to identify chaotic demand phenomenon. Some chaotic demands in practice have been identified. To the best of our knowledge, this study is a pioneering work, being the first to identify practical production demands with chaotic properties. To deal with chaotic demands, this study proposed a modified Wagner–Whitin method based on the look-ahead concept for making production lot-sizing decisions. The proposed MWW is empirically demonstrated to outperform (in terms of total production cost) the LFL, POQ, and SM production lot-sizing methods, all of which are well known for their efficiencies for various demand patterns. Sensitivity analysis has shown that the proposed MWW is robust with respect to changes in demand patterns, initial demands, various cost parameter settings, and different demand entropy. Possible future research directions include: (i) developing more efficient approaches to determine look-ahead parameter, (ii) expanding the proposed modified Wagner–Whitin to a multiple-echelons production system. Additionally, we speculate that chaos property may be embedded in certain production systems that output unstable performance. Such chaotic production systems should be identified and controlled if possible.