Concurrent Solution of WATC Scheduling with WPPW Due Date Assignment for Environmentally Weighted Customers , Jobs and Services Using SA and its Hybrid

Received Sept 01, 2018 Revised Oct 20, 2018 Accepted Dec 20, 2018 After industrial revolution environmental problems increased drastically. Air, water and soil pollution became a serious threat for the mankind. In order to overcome this threat everyone should take responsibility and try to preserve environment as much as possible. Environmentally conscious actions, people, law and foundations should be supported. When it came to determining due dates and scheduling, one of the important criteria should be the supporting the environment. In this study environmentally conscious customers, jobs, and services are rewarded, on the other hand unconscious customers, jobs, and services are penalized, while determining due dates and schedules. Simulated annealing and its hybrid with random search are applied to get environmentally better due dates and schedules. Keyword:


Introduction
Energy demands of developing countries has been increased rapidly with the globalization and technology developments [1].Almost half of the world's total energy is consumed by manufacturing industries [2].Relatively rapid increase of energy consumption rates triggers global warming and cause serious environmental problems.Due to environmental issues, organizations and manufacturing systems are encouraged for research and development (R&D) over renewable energy sources such as sunlight, wind, flowing water, the earth's internal heat and green [3].Sustainable economic development may be real if manufacturing become environmental friendly [4], [5].For the same purpose, organizations have also researched intensively in the field of job scheduling because the interest on environmental friendly production is increased.Job scheduling deals with the assignment of the jobs in which to be done in the process from the raw material to the finished product to the machines.An evaluation of job shop dispatching rules was conducted in paper [6].Thus, it is ensured that the customer which has more importance for the manufacturer has a priority.In a typical scheduling model, weight of customers are determined with the quantities in the order list.In this study, a distinction was made between the customers regarding their consciousness in environmental friendly production.It is aimed to encourage the manufacturers who produces environmental friendly products by scheduling them firstly.A substantial energy have been consumed on inefficient processes such as cooling, heating, pressing etc. in all over the Europe [7].Therefore, the improvements made on production methods affects the sustainability of production at a large scale.
In this study, the scheduling problem and the due date assignment problem are integrated to make production planning considering environmental issues.Job shops consisting of more than one job, and machine are studied in the scheduling problem.It is assumed that there is single route for each job.In due date assignment phase, environmental friendly customers are also considered, which are manufacturing products in a proper way to protect environment.Each job in an organization can be classified as a customer.The weighting of the jobs is not done by only considering the single criteria as it is done in the traditional scheduling problems.Also, other criteria are used to calculate weights for a job.In the literature, there are many studies which have given weights to the jobs according to different criteria.In 2000, Agnetis et al. carried out the weighting of the jobs according to the amount of work in the workshop.Besides, they have tried to minimize the completion times and the number of jobs delayed [8].Furthermore, integrated process planning and scheduling problem (IPPS) is also a new trend topic in terms of decreasing energy consumption in a manufacturing process.Zhang et al. have conducted a machine scheduling system to save energy in manufacturing system [9].In this study, the energy consumption of machines and equipment is modeled as Therblig base in the process of manufacturing.In IPPS, process planning, and scheduling functions are integrated with alternative process plans.It has resulted in higher efficiency in energy saving.First study on IPPS was made by Wilhelm and Shin.They conducted a study to use production sources in an efficient way using alternative operations in 1985 [10].Before studies on IPPS, process planning, and scheduling have been taken separately like a one function.Only scheduling functions are classified as NP-Hard problem.So, it is almost impossible to find optimal results in real applications for IPPS [11].That is why, there are many studies on IPPS using meta-heuristic approaches such as genetic algorithm [12]- [16], simulated annealing [12], taboo search [17], particle swarm optimization [18], [19], agent-based [20], [21] and ant colony optimization [22].Other integration problem is the scheduling with due date assignment problem (SWDDA).Basic principle of a just-in-time (JIT) philosophy is to minimize the unnecessary costs in production and to ensure a job is to be completed on its time.It is advised to finish products as close as possible to the due date in JIT.If an organization can schedule its production on the due dates which are reasonable, it will have optimum capacity planning.Using resources in an efficient way, may prevent labor cost and unnecessary energy consumption.The completion time of jobs before their due date could lead to an increase in energy costs and a decrease in customer satisfaction and customer loss.Integrated systems are determined by considering the scheduling and due date assignment together to avoid inefficient production plan.Some earlier studies reported that it was possible to find the optimal due dates and optimal sequences of jobs using different heuristic algorithms [8]- [16].The objective of these studies is to minimize the cost related to due date assignment and scheduling function.Besides, some recent studies on SWDDA can be listed as; [17]- [36].The remainder of the paper is organized as follows.In Section 2 modelling integrated production plan is discussed and the data used for the problem is described.Results of the schedules are given in Section 3. Section 4 includes conclusions and the discussing part of the study.

Materials and Method
Random Search (RS), Simulated Annealing (SA) and their hybrid is used in this study.Ordinary solution indicates the initially generated random solution.Random Search (RS): RS uses new random solutions at each iteration.It has the advantage of fast improvement in the beginning of the iterations.Later rate of improvement quickly reduces.Simulated Annealing (SA): SA used to solve large scale optimization problems, which was developed by Kirkpatrick et al. [52] in 1983.It is used in many problems in numerous discipline especially global extremum is searched within the many local extrema [53].Random and Simulated Annealing (RS/SA): Random search was combined with SA and this hybrid method is utilized.Initial 5% of iterations are made with random search and rest of the iterations are made with SA.It is aimed to take advantage of wide search capability of random search, and more focused search capability of SA to obtain better solutions.Random search scans the solution space to faster and better only at the very beginning.Later SA focuses this solutions to get better ones.As scheduling rules WATC (Weighted Apparent Tardiness Cost), ATC (Apparent Tardiness Cost) and SIRO (Service in random order) rules are utilized throughout the study.As due date assignment rules WPPW (Weighted process plus wait), PPW (Process plus wait) and RDM (Random) rules are applied.Rules for Scheduling and Due date assignment are explained in Appendix A and B respectively.
For the solution of the integrated problem a program is coded in C++ which performs Random Search, Simulated Annealing and Hybrid Simulated Annealing algorithms.Initially jobs are given proper due-dates by using WPPW, PPW or RND due-date assignment techniques and later jobs are scheduled according to WATC, ATC or SIRO rules and performance of the solution is calculated.After that in every iteration performance measure is tried to be improved by using RS, SA or RS/SA techniques.Four different integration levels are utilized, which are SIRO-RDM, WATC-RDM, SIRO-WPPW, WATC-WPPW, and for the full integration level the combination ATC-PPW is also tested for unweighted customer case.SIRO-RDM: There is no integration in this level.Jobs are scheduled according to service in random order rule and due dates are assigned randomly.WATC-RDM: WATC scheduling rule is integrated with process plan selection.Due dates are still randomly assigned.SIRO-WPPW: WPPW weighted due date assignment rule is used to determine due dates in this combination.On the other hand scheduling is made with service in random order rule.WATC-WPPW: Process planning is integrated with WATC weighted scheduling and WPPW weighted due date assignment in this integration level.This s the best level and full integration level of the problem.Here weights of the customers were also taken into account.ATC-PPW: This level is same as the WATC-WPPW method except customers are not weighted with their environmental manner.This combination is given to compare solutions, thus observing the effect of weighting customers.Eight different shop floors with varying size are studied.Smallest shop floor has 5 machines and 25 jobs.There are 5 operations in each route.Processing time of each operation practically changes in between 1 and 30 minutes according to formula ⌊(12+z*6)⌋.Largest shop floor has 10 machines, 200 jobs and same number of operations in each route as in smallest shop floor.Processing times are same as in other shop floors.Characteristics of each shop floor are listed at Table 1.

Results
Everyone must take responsibility to preserve the environment as our world has limited resources.In this study customers are prioritized in terms of their attitudes towards preserving the environment.Comparison of twenty solution combinations for all the shop floors are given in Table 2. Results of weighted and unweighted fully integrated level of all shop floors are given in Fig. 1-8.Obtained results indicate that weighting the customers according to their environmental consciousness has a positive effect on schedule in all eight shop floors.CPU time of programs are under one second for small shop floors and under one minute for largest shop floors.Although as integration levels increases better schedules are obtained, weighting the customers are much more improved the solution.Random Search, Simulated Annealing and their hybrid gave close results.Ordinary solutions are worst compared the search methods.As they are not given in figures for readability.It has been seen that the range of change is decreases as the integration level increases.Thus, more integrated solutions gave similar results independently of method used.It is also noteworthy that RS has minimum values amongst worst solutions.

Conclusions
In this study scheduling with due-date assignment problem is studied for environmentally weighted customers.
Step by step scheduling and due-date assignment functions are integrated.Initially SIRO scheduling and RDM due-date assignment combinations are tested and as expected this level found as the poorest integration level.Later WATC dispatching is introduced to the problem and integrating scheduling with the problem is found useful.After that WPPW is integrated with the problem but this time jobs or services are scheduled according to SIRO rule.Finally WATC scheduling and WPPW due-date assignment rules are integrated and full integrated level is tested and found as the best level of integration.
For the fully integrated level ATC scheduling and PPW due-date assignment integration is also tested where weights of the customers are not taken into account.WATC-WPPW integration is found much better compared to the ATC-PPW integration levels and results can be found in the Section 3 where the results are discussed.According to the results it is much better to schedule customers according to environmentally given weights.

Table 1 .
Shop floors

Table 2 .
Comparison of twenty solution combinations for all of the shop floors Best Avg.Worst Best Avg.Worst Best Avg.Worst Best Avg.Worst Best Avg.Worst Best Avg.Worst Best Avg.Worst Best Avg.Worst