This algorithm will develop the best schedule based on production costs. This schedule shows the change in production time and the impact on production costs.
Introduction
- Background
- Problem statement
- Project aim
- Scope
- Research design and Deliverables
- Project Approach
- Document Structure
This paper will determine the benefit of removing the problem machines from the larger presses and using them in the problem presses (EP8) and the other 5-inch press (EP6). The 5-inch presses are currently in other factories, one in Cape Town. and the other in Vereeniging. Upon completion of the project, an operational research model will be submitted to the company.
Literature Review
Production process analyses
Baki and Vickson (2004) describe a scheduling problem for N dies for a press as a one operator (the press), N machine (the dies) open shop problem. An open shop production differs from a job shop in the sense that the order in which the various operations are planned is not determined by the previously completed operation.
Scheduling problems
- Scheduling problems in other Industries
- Scheduling problems for foundries
A non-linear model with the objective function of minimizing the delay of orders is used. The formulation for their objective function with their constraints can be used to formulate our second objective function.
Metaheuristics
- Simulated Anneailing
They used a mixed integer linear model along with heuristic strategies to solve the scheduling problem. Dos Santos-Meza et al. 2002) focus on developing a model to solve a lot size problem in an automated foundry. Metaheuristics is an approximation method and can be used to solve complex problems classified as NP-Hard and NP-Complete.
A mixed integer programming model to schedule these processes has been investigated, but is impractical to solve in a reasonable time frame. This paper discussed the use of relaxation and adjustment method, descent heuristics, reduced search and simulated annealing to solve the complex scheduling problem. It has been found that this method can be used to solve real-life problems due to the flexible nature of this algorithm and the ability to solve an NP-Hard problem in a reasonable amount of time.
The aim of the simulated annealing algorithm is to avoid the local optimum as shown in Figure 6. But if the initial solution is better than the "new solution", the new solution will be accepted with a certain probability.
Project Investigation
Press performance
The reason the presses are underperforming is because of the amount of waste caused by die defects. The previous production data from EP5 indicated that this press runs the fast runners and thus produced more output than the other presses. The input for the presses is lower than the target values because the presses are not running at full speed.
Dies performance
A runout is when one or more of the profiles being produced are extruded at a higher rate than the other profiles. When a runout occurs, the extrusion rate is reduced to ensure that minimal damage is caused by the irregular extrusion rate. When this table is full, production must stop for the operators to clear the table.
Next, we looked at the distribution of velocity values for each matrix within a group of cavities. This ensures that the values used for the calculations are a good indication of the group. The speed distribution of 7-inch matrices is shown in the following graphs.
The velocities of the S2 dies follow a normal distribution, but the variance for the dies within the S2 group is very large. This indicates that the average values of the dies cannot be used to determine the impact on the output of the presses.
Problem dies
When analyzing die performance, dies with high error rates had a major impact on press production.
Data Analysis
Cost
Die Input data
The reason for the change is due to the change in power or strength of each press. The algorithm uses this value and the duration of a pattern change (a constant value in the algorithm) to calculate the duration of the production schedule. This stands for Not Applicable, indicating that grill cannot be scheduled in that press.
This spreadsheet uses Excel's built-in If-function, which also ensures that the production timesheet read into Python includes die and press constraints. If the die value on the corresponding press is zero in the condition table, it means that the die cannot be planned for that press. Factors to consider when arranging a die for a press include the size of the die, the runout length of the profile, and the cooling required by the profile.
In addition, the output length of the die is determined by dividing the output value per meter of the die (kg/m) by the weight (kg) of the billet used. Finally, some products are made from hard alloys and aluminum must be cooled quickly to ensure the integrity of the metal.
Conceptual design
Mixed Integer model
𝐼𝑡𝑟𝑎𝑤 ≜ number of tickets in inventory in period t 𝐵𝑖 Constraint (4) ensures that the quantity of items produced in the planning horizon is at least the quantity ordered.
Constraint (5) ensures that the output is less than or equal to the available capacity of the press. Constraint (7) ensures that the number of billets used in production does not exceed the number of billets available.
Development of Supplementary Mechanism
Simulated Annealing
The parameters of the simulated annealing algorithm, that is the initial temperature, the cooling rate and the parameters of the search area are specific to the problem. The performance of the algorithm can be determined by the convergence of the costs accepted by the algorithm. When a low initial temperature and a large cooling factor are used, the cost graph does not converge.
Figure 16 shows that the cost graph performed a broader search within the search area, but at 2000 iterations, the cost graph dropped too quickly. The method used to cool down the temperature is responsible for the rapid drop in cost.
My scheduling problem
The production time of each hat is used to determine the planned machine production space. Production time is calculated using boiler speed, failure time and time required for a changeover (if applicable). This includes random selection of two presses and random selection of a scheduled press for each of the selected presses.
The feasibility test ensures that the new solution does not result in an infeasible solution. The new solution generated must also be approved by the feasibility test. The input data will have the information of the alloy used for the specific die and with a simple 'axis loop'.
The last constraint ensures that the problem dies are planned for EP8 and that these dies are not used to generate a new solution. The cost calculation of the schedule is determined per press, as the presses have different production costs.
Solution
Different Objective Functions
- Minimise Cost
- Increase Output
- Minimise Make span
The second objective of this project is to increase the production output of the company. An alternative method to increase the output of the matrices was to limit the scheduling of the problem matrices to EP8. The planning model must determine what impact this will have on the production of the presses.
In theory, this should make it possible to reduce the production of the other presses, since the dies that will be planned for these presses have higher recycling rates and higher speeds. The restriction of the problem matrices to EP8 resulted in an open capacity of 36809.26 kg on the other presses. This analysis concludes that limiting the problem dies to EP8 will not be beneficial to the company's production output.
To achieve this, the model needs to be modified a bit to include the due date of the orders. The previous production schedule of 200 stamps was used as a benchmark for the results of the algorithms.
Improve Scheduling
The company will earn a profit of R5 per kilogram on the additional product produced from this press resulting in an increase of R3 600 00 per year. The second objective of this project is to reduce the number of backorders of the company. The order completion date is read into the algorithm and constantly compared with the board completion time on the schedule.
A simple strategy to incorporate the due date into the algorithm is to assign a penalty factor to all late orders. When a new neighbor is created and this step replacement strategy causes an order to be late, a penalty factor will be added to the production cost calculation. The company will be able to reduce the number of late orders and reduce the number of lead days.
From the results of the algorithm, the impact of the production costs and the capabilities of the presses in relation to the scheduling is clear/visible. Dies with high recycling rates should be scheduled to Ep3, EP4 and EP5 because they have the highest production costs.
Validation
Sensitivity Analysis
Production cost
Demand
Conclusion
SA Temperature 2
If an order requires an input of more than this, the time associated with the model change must be included in the production time. When such a suit appears in the list of machines to be scheduled, this grill will not follow the scheduling rules and will be scheduled in EP9. The following restriction ensures that products to be treated with water are only scheduled in EP3.
This calculation will be done for each press and it will be the sum of all the dies planned for the press. For the second scenario, the Ep8 is removed and a new machine is purchased that has the same capabilities as the Ep7. The die speed on this press will be faster than the EP8 and will have higher recovery rates.
The new machine reduced the total waste generated by the schedule and total production time. This means the company will be able to improve their production output by 60,000 kg per month and 720,000 kg per year.
