生產一般產品與再生產品製造商利潤最大化經濟批量

Abstract

經濟批量排程問題(Economic Lot Scheduling Problem, ELSP)最早在 1958年提出雛形後，至今近 50年被學者持續鑽研及提出延伸研究議題，其目標在於決定出能使總成本最小化的生產批量大小和產品生產順序。而為了接近現實的生產情況，現今的學者又將 ELSP細分成各種的情境來探討，其中一種是生產製造的同時，考量有逆物流並且回收再製造之行為。本研究探討不同於已有文獻研究之再製造情境，認為回收回來的原料製成之再生產品因為原料純度或新品有所耗損，造成再生之產品品質會劣於原產品(本研究稱為一般產品)，並且認定再生產品服務與一般產品不同的市場。 本研究使用時間變動批量大小方法(Time-varying lot-sizes approach, TVLS)架構出新的ELSP問題最佳解求解方法，分為三個部分：第一部分目的在於獲取基本週期及基本週期乘數，本研究建構 BP-based模式並分別使用共同週期法、基因演算法，及接合點搜尋法三種方法進行求解之；第二部分使用最長操作時間派工法，將基本週期及基本週期乘數轉換為生產排程及生產總週期；第三部分在給定生產排程及生產總週期的情況下使用內點法(interior point algorithm)搜尋 模式最佳解，改善文獻中使用投機演算法(quick-and-dirty algorithm)，本研究使用MATLAB程式進行內點法的搜尋。接著放鬆總週期，在給定排程下使用二分搜尋法搜尋最佳總週期，最後利用鄰域搜尋法進行改善排程，以求得近似最佳解。 在隨機數值分析中，本研究針對不同機台利用率進行求解，比較共同週期法、基因演算法，及接合點搜尋法三者的求解品質，其中以接合點搜尋法決定出之基本週期及基本週期乘數建構出的生產排程及生產總週期可以獲得最好的目標值，而使用二分搜尋法搜尋最佳總週期的確能在有效率的時間內進一步找到更好之值，然而使用鄰域搜尋法進行改善排程的時間過長且改善的幅度較小。而運算時間的部分主要受排程長度的影響而非受限於求解基本週期乘數之方法，當排程長度越長，求解時間也越長。

Economic lot scheduling problem (ELSP) has been studied over 50 years. In this study, we are interested in the ELSP producing different types of products, namely, regular product and remanufactured product. In the concerned production system, we produce regular products to meet the customers’ demand and also collect the recycled ones for remanufacturing. Because of using the recycled materials, the quality of the remanufactured products could be inferior to the regular ones. We assume that the remanufactured products are sold in different market segments. To solve the concerned problem, we formulate a mathematical model using the time-varying lot-sizes (TVLS) approach. The TVLS approach assists our solution approach in generating feasible production schedules by allowing the lot sizes and cycle times for each product vary over time. We may divide the proposed solution approach into three phases: The first phase acquires the value of basic period and the set of multipliers. We propose three approaches, namely, a common cycle approach, a genetic algorithm, and a junction-point search algorithm for the purpose of the first phase. Taking the obtained basic period and the set of multipliers, the second phase generates a production sequence using a Longest-Processing-Time (LPT) heuristic. Given the production sequence and the value of cycle time, we solve the TVLS model, which is a nonlinear program, by an interior-point algorithm (that outperforms the quick-and-dirty heuristic in the literature) in the third phase. Different from the other approach based on the TVLS method, we employ a bisection search procedure to seek for the optimal cycle time, and also utilize a neighborhood search heuristic to look for a better production sequence to improve the solution quality. Our numerical experiments compare three proposed solution approaches with different utilization rates. It shows that both the junction point search algorithm and the genetic algorithm outperform the common cycle approach. Also, the production sequence obtained from the junction point search algorithm performs better than that of the genetic algorithm. Furthermore, interestingly, the run time is majorly determined by the length of the production sequence rather than the number of items produced in the system.