The first priority of an apparel factory is to maximize the overall throughput, which is determined by the schedule of the sewing operation – the bottleneck of the apparel factory. The second priority is to maximize fabric utilization, which is determined by the cutting plan. Cut pieces produced by cutting operation is the most important wip material that is the input to sewing operation (the bottleneck), a high level of cut pieces inventory not only requires extra storage space but also cause the difficulty of shop floor control management. Therefore, the third priority of an apparel factory is to minimize the cut piece inventory level, which is determined by the cutting schedule. Based on to these priority levels, a sewing schedule and a cutting plan are calculated separately first without considering cutting schedule. Then, the sewing schedule and the cutting plan serve as input information to the calculation of cutting schedule. The focus of this study is determining the ideal cutting times of fabric lays that minimize cut piece wip level under the constraint that sufficient cut pieces are produced in time to satisfy the usage by sewing operations.
This study proposes a mixed integer programming model and a heuristic method to solve such a cutting schedule problem for apparel manufacturing. The experiment results show that the larger the problem size, the longer it takes to solve the mixed integer programming model. Although the solutions generated by heuristic method is no as good as those calculated by mixed integer programming, the computation times of heuristic method is so short that can be neglected. In a relatively large size problem, even not very common, the performance of the mixed integer programming is not satisfactory. Thus, combining the two methods by having the heuristic method to provide an initial solution to MIP is suggested. The results of the experiment show that the efficiency of MIP is significantly improved by starting from an initial solution provided by the proposed heuristic method, especially in large size problems.

對於成衣產業的生產製程而言，首要的目標為最大化產出，而產出的多寡是由車縫製程─即成衣生產流程中的瓶頸製程之排程規劃所決定；次要的目標則是最小化裁切製程時所產生的布料浪費，裁切計畫影響此項目標。裁片為車縫製程（瓶頸）上游之裁切製程所產出的半成品。由於過多的裁片不僅會增加儲存的成本，也會造成現場管理的困難，因此第三個目標為最小化裁片的庫存水準，且裁片的庫存水準是取決於裁切製程的排程規劃。根據目標的優序，車縫排程以及裁切計畫必須要優先被決定，至於裁切製程的排程則必須遵照已訂定之車縫排程及裁切計畫進行後續規劃。當裁切部門在決定各裁切工作適當的裁切時間時，除了需確保所有車縫生產線（瓶頸）不會因缺少裁片而閒置，也需考慮已排定裁切計畫之各裁切工作對應產出之多餘裁片種類，盡量降低裁片的在製品庫存。因此本論文將車縫排程以及裁切計畫作為已知的資訊，將滿足車縫線排程之生產需求做為限制條件，以最小化裁片之庫存水準為目標，探討如何進行裁切排程。
論文中針對成衣工廠中的裁切排程問題提出了混合整數規劃及啟發式方法。實驗結果顯示，裁切床數多寡對於混合整數規劃的求解速度有決定性的影響，而啟發式方法在大部分的問題中雖無法提供與混合整數規劃一樣良好的解，但都能在極短時間內求解完成。因此我們建議結合兩種方法，將啟發式方法的解做為混合整數規劃的起始解。實驗結果顯示在大型問題中顯著地改善了求解的效率。

References
Degraeve, Z., Gochet, W., and Jans, R. (2002), “Alternative formulations for a layout problem in the fashion industry”, European Journal of Operational Research, Vol. 143, No. 1, pp. 80-93.
Degraeve, Z., and Vandebroek, M. (1998), “A mixed integer programming model for solving a layout problem in the fashion industry”, Management Science, Vol. 44, No. 3, pp. 301-310.
Dyer, M. E., and Wolsey, L. A. (1990), “Formulating the single machine sequencing problem with release dates as a mixed integer program”, Discrete Applied Mathematics, Vol. 26, No. 2-3, pp.255-270.
Jacobs-Blecha, C., Ammons, J. C., Schutte, A., and Smith, T. (1998), “Cut order planning for apparel manufacturing”, IIE Transactions, Vol. 30, No. 1, pp. 79-90.
Johnston, R. E., and Sadinlija, E. (2004), “A new model for complete solutions to one-dimensional cutting stock problems”, European Journal of Operational Research, Vol. 153, No. 1, pp. 176–183.
Keha, A. B., Khowala, K., and Fowler, J. W. (2009), “Mixed integer programming formulations for single machine scheduling problems”, Computers and Industrial Engineering, Vol. 56, No. 1, pp. 357-367.
Kim, Y. D., Shim, S. O., Choi, Y. C., and Yoon, H. M. (2004), “Parallel machine scheduling considering a job-splitting property”, International Journal of Production Research, Vol. 42, No. 21, pp. 4531-4546.
Logendran, R., and Subur, F. (2004), “Unrelated parallel machine scheduling with job splitting”, IIE Transactions, Vol. 36, No. 4, pp. 359-372.
Martens, J. (2004), “Two genetic algorithms to solve a layout problem in the fashion industry”, European Journal of Operational Research, Vol. 154, No. 1, pp. 304-322.
Reinertsen, H., and Vossen, T. W. M. (2010), “The one-dimensional cutting stock problem with due dates”, European Journal of Operational Research, Vol. 201, No. 3, pp. 701-711.
Rose, D. M., and Shier, D. R. (2007), “Cutting scheduling in the apparel industry” Computers and Operations Research, Vol. 34, No.11, pp. 3209-3228.
Serafini, P. (1996), “Scheduling jobs on several machines with the job splitting property”, Operations Research, Vol. 44, No. 4, pp. 617-628.
Shim, S. O., and Kim, Y. D. (2008), “A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property”, Computers and Operations Research, Vol. 35, No. 3, pp. 863-875.
Tahar, D. N., Yalaoui, F., Chu, C., and Amodeo, L. (2006), “A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times”, International Journal of Production Economics, Vol. 99, No. 1-2, pp. 63-73.
Wong, W. K., and Leung, S.Y.S. (2008), “Genetic optimization of fabric utilization in apparel manufacturing”, International Journal of Production Economics, Vol. 114, No. 1, pp. 376-387.
Xing, W., and Zhang, J. (2000), “Parallel machine scheduling with splitting jobs”, Discrete Applied Mathematics, Vol. 103, No. 1-3, pp. 259-269.
Yalaoui, F., and Chu, C. (2003), “An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times”, IIE Transactions, Vol. 35, No. 2, pp. 183-190.
Yanasse, H. H., and Lamosa, M. J. P. (2007), “An integrated cutting stock and sequencing problem”, European Journal of Operational Research, Vol. 183, No. 3, pp. 1353-1370.
Yuen, B. J. (1995), “Improved heuristics for sequencing cutting patterns”, European Journal of Operational Research, Vol. 87, No. 1, pp. 57-64.
Yuen, B. J., and Richardson K. V. (1995), “Establishing the optimality of sequencing heuristics for cutting stock problems”, European Journal of Operational Research, Vol. 84, No. 3, pp. 590-598.