An open-source framework for solving shop scheduling problems in manufacturing environments

Abstract

Scheduling problems refer to the decision-making process of allocating tasks to resources, usually scarce and in high demand, to optimize different performance measures. We consider the class of shop scheduling problems arising in the context of manufacturing systems, which are often NP-hard and challenging to solve. Exact methods have limitations in finding optimal solutions in reasonable computation times, even for instances of moderate size. Therefore, in real-life production environments, finding high-quality solutions is often satisfactory, even if they are not optimal. We contribute to the solution of shop scheduling problems with the design and implementation of the SSP-3M framework, oriented by three main guidelines: versatility, extensibility, and independence of the optimization method. These characteristics reduce the gap between scheduling theory and practice in real-life environments and improve the integration of the scheduling framework with other process planning or functions such as Computer-aided Process Planning, Advanced Planning and Scheduling, Integrated Process Planning and Scheduling, and Computer Integrated Manufacturing. The problem and solution representations adopted in our framework design make it possible to handle six shop scheduling problem variants, illustrating its versatility: job shop, flow shop, permutation flow shop, generalized flow shop, flexible flow shop, and flexible job shop. SSP-3M is open-source and can be used by any interested party. Our experimental evaluation shows that it can successfully be integrated with external optimization methods. We claim that SSP-3M is a good choice for companies that need free and quick-to-develop solutions to shop scheduling problems.

Appendix A: Greedy randomized G &T algorithm

The greedy randomized G &T algorithm of Giffler and Thompson (1960) takes as input the set of jobs $J=\{J_1,\ldots ,J_n\}$, the set of machines $M=\{M_1,\ldots ,M_m\}$, and, for each job $J_i$, $i=1,\ldots ,n$, the number of operations $\#op(i)$ to be processed, a list $L^i = [L^i[1],\ldots ,L^i[\#op(i)]]$ with the sequence of machines where it has to be processed, and the processing times $p_{i,1},\ldots ,p_{i,\#op(i)}$ of each operation. The algorithm outputs a schedule represented by an operation sequence (possibly with repetitions), with each operation defined by a job, a machine, and the time this job should start to be processed in this machine. The main steps of its pseudo-code appear in Algorithm 1, which is our formalization of the original algorithm textually described in Giffler and Thompson (1960).

Line 1 initializes the set A that stores the candidate operations, i.e., those that are ready to be scheduled. Each iteration $i=1,\ldots ,n$ of the loop in lines 2 to 6 places the first operation of job $J_i$ in the candidate set A in line 3 and sets its starting time to 0 in line 4. Line 5 sets to 1 the position of the first operation of job $J_i$ ready to be scheduled. Line 7 sets to 0 the counter of scheduled operations. The while loop in lines 8 to 20 runs until all operations are scheduled. Line 9 selects from the candidate set A the operation $o_{i',k'}$ with the shortest completion time, corresponding to the execution of job $J_{i'}$ in machine $M_{k'}$. Line 10 creates the set $B \subseteq A$ formed by the candidate operations that guarantee the construction of an active schedule. It contains all operations that use machine $M_{k'}$ and may start before the shortest completion time determined in line 9. Line 11 randomly selects an operation $o_{i^*,k^*}$ from B. Line 12 removes the newly selected operation from the candidate set A. Line 13 updates the counter of scheduled operations, and line 14 schedules operation $o_{i^*,k^*}$ in this position of the operation sequence. Line 15 checks if operation $o_{i^*,k^*}$ is not the last of job $J_{i^*}$. In this case, line 16 updates the position of the subsequent operation of job $J_{i^*}$ ready to be scheduled. Line 17 adds the next operation of job $J_i$ to the candidate set A, and its starting time is set to the completion time of operation $o_{i^*,k^*}$ in line 18. Line 21 returns the schedule represented as an operation sequence.

Algorithm 1

G &T algorithm

We remark that other dispatching rules can be used at step 11 instead of a simple random choice, such as shortest processing time (SPT), longest processing time (LPT), start as-early-as-possible (SEP), earliest completion time (ECT), earliest due date (EDD), longest number of successors (LNS), and shortest number of successors (SNS). They all lead to active schedules and different variants of the algorithm (Pfeiffer et al., 2006).