An effective and efficient heuristic for no-wait flow shop production to minimize total completion time

Highlights

• We present a current and future idle time (CFI) heuristic for no-wait flow shop production.

• We use the initial sequence algorithm and neighborhood exchanging method to improve effectiveness.

• We use the objective increment method to reduce the computational complexity.

• We show that our CFI heuristic is more effective than three typical heuristics.

• We can improve the efficiency of operating room scheduling using our CFI heuristic.

Abstract

No-wait flow shop production has been widely applied in manufacturing. However, minimization of total completion time for no-wait flow shop production is NP-complete. Consequently, achieving good effectiveness and efficiency is a challenge in no-wait flow shop scheduling, where effectiveness means the deviation from optimal solutions and efficiency means the computational complexity or computation time. We propose a current and future idle time (CFI) constructive heuristic for no-wait flow shop scheduling to minimize total completion time. To improve effectiveness, we take current idle times and future idle times into consideration and use the insertion and neighborhood exchanging techniques. To improve efficiency, we introduce an objective increment method and determine the number of iterations to reduce the computation time. Compared with three recently developed heuristics, our CFI heuristic can achieve greater effectiveness in less computation time based on Taillard’s benchmarks and 600 randomly generated instances. Moreover, using our CFI heuristic for operating room (OR) scheduling, we decrease the average patient flow times by 11.2% over historical ones in University of Kentucky Health Care (UKHC).

Introduction

No-wait flow shop production is essential for many processes in manufacturing. For example, in steel rolling, the heated metal should proceed continuously through a sequence of operations to prevent defects before being cooled down (Aldowaisan & Allahverdi, 2003); in food processing, the quality of food is jeopardized if the processing is intermittent (Ye, Li, & Miao, 2016); and in concrete processing, operations of compounding, hardening, and cutting should be done continuously because of relative technical requirements on the hardness, strength and elasticity for concrete products (Grabowski & Pempera, 2000). Management concerns, such as meeting due dates and reducing the maximum lateness, are necessary for no-wait flow shop scheduling (Cheng and Liu, 2003, Lin and Cheng, 2001, Wang and Cheng, 2006). In these manufacturing processes, all n jobs are processed in the same order on each of m machines, and there should be no waiting time between any two operations until the process is finished. Therefore, the start time on the first machine could be delayed to avoid waiting times during the process. For operating room (OR) scheduling across the three-stage perioperative (periop) process in healthcare systems, patients are also not supposed to wait during the process, especially from ORs in the intraoperative (intraop) stage after the surgery to the postoperative (postop) stage for recovery. Waiting between any stages across the periop process increases patient flow times and generates unnecessary cost. For more details about applications of no-wait flow shop production, see Hall and Sriskandarajah (1996).

Total completion time (TCT) is defined as the sum of completion times of all jobs on the last machine. Minimization of total completion time, min(TCT), is the same as minimizing the average flow time of products in manufacturing, or smoothing the flow of customers in services (Shyu, Lin, & Yin, 2004). Other objectives to optimize the performance of no-wait flow shop production are correlated to minimization of total completion time, such as minimization of maximum completion time or makespan (Grabowski and Pempera, 2005, Lin and Ying, 2016), minimization of total tardiness (Ding, Song, Zhang, Gupta, & Wu, 2015), minimization of makespan and total completion time (Laha & Gupta, 2016), and minimization of weighted mean completion time and weighted mean tardiness (Tavakkoli-Moghaddam, Rahimi-Vahed, & Mirzaei, 2007).

No-wait flow shop production to minimize total completion time can be written as $F_m$ $\mid$nwt$\mid$ $\sum C_j$, where $F_m$ is for a flow shop problem with m machines, nwt for the constraint of no-wait, and $\sum C_j$ for the objective to minimize total completion time (Graham, Lawler, Lenstra, & Kan, 1979). $F_m$ $\mid$nwt$\mid$ $\sum C_j$ problems are NP-complete when the number of machines is larger than or equal to two (Röck, 1984). Due to the NP-completeness for $F_m$ $\mid$nwt$\mid$ $\sum C_j$ problems, it is extremely time consuming to seek optimal solutions by using exact methods even for moderate-scale problems. Therefore, it is practical to seek near-optimal solutions by using heuristics, especially for large-scale problems. Effectiveness and efficiency should be used to evaluate heuristics, where effectiveness means the deviation from the optimum, and efficiency means the computational complexity or computation time (Li, Luo, Xue, & Tu, 2011). Currently, few heuristics are both effective and efficient.

To achieve greater effectiveness in less computation time, we propose a current and future idle (CFI) constructive heuristic for a no-wait flow shop to min(TCT). The basis of our study is that current and future idle times should be treated differently as introduced in Li, Nault, Xue, and Tu (2011). Consequently, in the initial sequence, we assign higher weights to current idle times generated by jobs in the head of a sequence than those generated by jobs in the tail of the sequence. This initial sequence improves effectiveness of our CFI heuristic. To improve efficiency of our CFI heuristic, we introduce an objective increment method, integrated with the neighborhood exchanging technique. In this method, we calculate the increment of TCT after a pair of jobs in the sequence are exchanged, instead of calculating TCT for the whole sequence after neighborhood exchanging.

The remainder of this paper is organized as follows. Section 2 provides literature review of $F_m$ $\mid$nwt$\mid$ $\sum C_j$ problems, including discussion of three typical heuristics: PH1(p), FNM and LS heuristics. Section 3 presents our proposed CFI heuristic. Section 4 discusses the computational results from a comparison of heuristics based on a large number of instances of various sizes. Section 5 presents the results of case study based on historical data from University of Kentucky Health Care (UKHC). And finally, Section 6 draws conclusions and proposes future work.