Production planning is one of the main functions within an organization, since through it the factors of labor, raw materials, machinery and equipment are managed.
Production planning involves translating annual and quarterly business plans into comprehensive medium-term production and work plans. Its objective is to minimize the cost of the resources required to satisfy the demand during that period.
Planning and scheduling in a company translate into mathematical techniques and heuristic methods to allocate limited resources to the activities that must be done. This allocation of resources has to be done in a sense in which the company optimizes its objectives and achieves its goals. Resources can be machines in a workshop, routes in an airport, equipment in a building, or processors in a computational environment. The activities can be operations in a workshop, takeoffs and landings in an airport, stages in a construction project, or computer programs that must be executed. Each activity should have a priority level, a start as early as possible, and an end date. Goals can take different forms, such as minimizing the time to complete all activities, minimizing the number of activities that have been completed after the committed delivery dates, etc.
This document explains the Planning and Scheduling of production in various stages. The first part shows the main characteristics of the models that are used to do the planning, within these characteristics are the necessary variables that are involved in the calculations of the planning models. The variables involve everything related to jobs, machines and facilities and to the types of restrictions that exist in the real world.
Characterization of Production Planning and Scheduling models
The planning and scheduling models of production in manufacturing companies can be characterized by a variety of factors; the number of resources and machines available, their characteristics and configurations, the level of automation of the system, the type of material handling system, etc.
In general, manufacturing models have to do with "machines" that refer to resources and "jobs" that are the tasks that must be done. In production processes, a job can be a single operation or many operations on different types of machines.
In general terms, the models used for the Planning and scheduling of production include within their calculations variables mainly related to the resources they have, machines, number of workers, type of facilities, types of processes, etc. In turn, there are a series of restrictions in all production processes which must be taken into account in order to obtain task plans similar to reality that allow control of production.
In the following chapters the main resources available and the necessary restrictions in the production planning models are studied.
Works, Machines and Installations
Regarding the works, the machines and the facilities, we have the following parameters that are involved in the planning and scheduling models:
The parameters necessary to develop the models can be classified into process and product parameters and into machine and plant parameters.
For the first we have some initial data which if they are data that remain constant over time (Static) or changing data during modeling (Dynamic).
The static data required are:
- Process time: time to carry out a job on a machine.
- Launch date: Date in which a job can start the process.
- Expiration date: Committed date of delivery of the product with the client.
- Weight: It is the priority of a job. It can represent the cost of maintaining a job in the system as well as the cost of storage or the added value assigned to the job.
The dynamic data is listed below:
- Starting point: It is the moment in which a job begins its process in the factory.
- Completion time: It is the moment in which a job is completed on a machine.
On the other hand, there are important characteristics of the planning and scheduling models are the configurations of the machines, for this we have:
- Models of a single machine: they are important since almost all systems can be of this type. When you have a bottleneck, the machine that causes it determines the performance of the entire system, due to this it can be modeled as a single machine. These models have been highly analyzed for this reason there is a collection of rules that determine the behavior, some of these are: The earliest expiration date first, or the shortest processing time first.
- Model of machines in parallel: it is a generalization of the model of a single machine. The bottlenecks have been groups of identical machines.
- Flexible flow workshop: this is the case when there are multiple jobs on different machines in parallel. The jobs go through identical processes but each process has several machines.
- Workshops (Jobshop): these are workshops with multiple operations, each job has different routes.
- Models of the supply chain: They are the most general, it is a network that interconnects different facilities, either with flexible flow or Jobshops. Planning focuses on the production of each of the facilities as well as the transport of the products within the established network.
All these parameters and configurations must comply with a series of restrictions that determine and configure the complete model.
Process restrictions
The production planning models should try to simulate the reality of production in companies. The parameters that configure the models are seen in "Jobs, machines and facilities". The restrictions that must be met with the variables involved in the model are listed below.
- Precedence restrictions: it has to do with some jobs not being able to start until others have finished.
- Machine eligibility restrictions: in parallel machine models, jobs can only go to certain machines.
- Restriction of manpower: Manpower is needed to operate the machines, and there are only few people to operate them. A job must wait if there is no available labor to do it. In addition, it must be taken into account that not all people have the same qualities and skills, there are groups of people with specific specialties.
- Route restrictions: this restriction specifies the route that a job must follow to be performed, that is, the order in which a job must visit the different machines.
- Material handling restriction: This restriction depends on the degree of automation of the jobs, highly automated jobs require automatic material handling systems. When the positions are manual, the material handling time must be adjusted to the process time. The material handling system forces to have a great dependence between the start times of an operation and the completion times of its predecessor. Even if you have a material handling system, there will always be a stock space, which is called Work-in-process.
- Sequence-dependent setup times and costs: machines must be reconfigured or cleaned between jobs. If the magnitude of the change depends on the work that is completed and the work that continues, they are said to depend on the sequence. All these times translate into costs either of poor quality since the first products in general are not accepted, in addition to labor costs, since it is a time in which added value is not generated, among others.
- Restrictions on storage space and lead time: In almost all production systems there are space limitations for Work-in-process. For this reason it becomes a restriction, since when the stock between two machines is full, the previous machine must stop its production.
- Make-to-Stock (MTS) and Make-to-order (MTO): A factory may choose to have products in stock when there are stable demands and with little risk of obsolescence. The Make-to-Stock decision affects the planning process, as the products would not have tight delivery dates. When the stock of products reaches zero or a certain level according to production time, new production orders are launched and in this way to re-establish the inventory. Inventory levels depend on process times and the cost of holding inventory. Make-to-Order jobs have a specific delivery date and the quantities are established by the clients. Many factories work on a mix of the two MTS and MTO.
- Priorities: Sometimes during the execution of a job, an event occurs that causes a work order to be interrupted to prepare the machine and get it ready for another work order. This occurs when you have a higher priority order. With these priorities, there may be that interrupted work is continued later, or sometimes interrupted work is lost.
- Transportation constraints: If you have facilities connected to each other by a network, then planning and scheduling of the supply chain becomes important. Transportation is the time required to move products between two facilities. There are restrictions on the departure times of a facility according to the amount of products to be transported.
These parameters and restrictions characterize the production planning models.
The second part shows the main models used to carry out the planning and scheduling of production, divided according to the needs of the company.
Models for Production Planning
The models for production planning are divided into certain classes:
The first class of models is the planning and scheduling of projects. Its characteristics are: they are made up of a series of jobs that begin according to the restrictions of the previous jobs. Until certain tasks are accomplished, no others begin. The goal is to minimize the total completion time. It is important to determine the series of jobs that determine the "Makespan" (Time between the beginning and the end of a job), these tasks determine the time of completion of the project and in conclusion it is these tasks that cannot be delayed.
Project Planning and Scheduling
Critical Path Method (CPM)
This method takes into account a number of jobs with precedence restrictions, which have a certain processing time. There is an unlimited number of machines in parallel and the goal is to minimize the “Makespan”. Besides a machine (and there is always one available) a job does not need any other resources. This method is explained by means of the following algorithm:
Starts at zero time in which the processing of jobs that have no predecessors begins. Every time a job finishes its process, it begins the processing of those jobs which all its predecessors have finished processing. In this type of sequence, all jobs without predecessors would start processing at the earliest possible start time and are completed at the earliest possible finish time. Doing this would not be necessary to minimize the "Makespan", it is possible to delay the start of certain jobs and would not affect it.
The next algorithm shows the last possible start time and end time that would not affect the “Makespan”, this is called the backward procedure. In this procedure, you do not start at time zero but rather at the maximum end time, and search for the last start and end times.
A job in which the earliest start time is ahead of the latest possible start time is termed as a loose job. The time between the last and the earliest is the loose time, it is usually called floating. A job in which the earliest start time equals the last possible start time is termed as the critical job. A set of critical jobs form a critical path. There may be several critical paths and they may overlap.
Program evaluation and review technique (PERT)
In contrast to the prior art in this process times are variable for each of the jobs. Each process time has a mean and a variance that are known for each job. The algorithm is the same as for CPM, but the calculation to minimize the “makespan” is more complicated. It is taken into account that three different scenarios will be obtained. The optimist, the pessimist and the desired.
TRADE OFFS: TIME / COST
In the previous processes we can see that if the resources assigned to a job are increased, the processing times can be shortened, for that we must assume that we have a budget to be able to place more resources in some established activities. According to this, there is a cost that depends on the amount of time that you want to save in each of the jobs. According to this, a minimum time that can be reached and a maximum time can be established and in turn the cost of the work depending on whether it is delivered in the minimum or maximum time. In order to know the cost of the project, it is necessary to determine what are the most appropriate times in which each job can be carried out and in this way optimize the project obtaining better delivery times without sacrificing the budgeted costs of the project.
Scheduling of projects with labor restrictions
In the real world there are a number of restrictions related to labor. The workforce consists of a series of groups which have a certain number of operators with a specific skill. Each job requires a certain number of operators from each group to be executed. The goal at all times is to maximize profit so labor must be assigned to jobs in the best way.
Scheduling of a Machine and a Workshop
The second class includes a simple machine, parallel machines and the jobshop. The jobs are basically operations that are done on a machine. In the jobshop, a job is a series of operations on different machines that configure a product, these have a defined route. Operations should be organized to minimize one or more objectives such as Makespan or the number of backlogs.
This section reviews the models that involve workshops or also known as Jobshops. Normally in a workshop a job visits different types of machines and can also go through the same machine several times. Workshops are generally prevalent in industries where each client is unique and has their own parameters, for example a hospital in which the patients are the jobs, each has a unique and different disease and procedure.
Initially we are going to look at the workshops with a single machine which is the simplest case study of the model. Even the most complicated cases of workshop production planning break down into problems of a single machine within a network.
The case of a simple machine takes into account that the launch date is zero and the expiration date is infinite, it means that for the purpose of minimizing the makespan (job processing time) it would not depend on the production program, it means that the process time has no restrictions.
But for other purposes there are certain rules that manage to optimize production schedules. If the objective is to minimize the total weighted completion time, then the rule of "Weighted Shortest Processing Time first" (WSPT) is optimal, which schedules the jobs in decreasing order according to the weighted processing time.. On the other hand, if the goal is the maximum delay and the jobs start on a zero release date, then the rule of the "Earliest Due Date first" (EDD) in which the jobs are scheduled in increasing order according to the processing time is the most optimal. The above are static priority rules.
There is another rule related to the EDD which is the “minimum slack first” (Minimum Slack first - MS) rule, which chooses, when a machine is available, the job that is waiting to have the least slack. Slack is the time a job has before it has to begin processing to reach completion in the required due time. This is a dynamic priority rule since this priority is a function of the time of each job.
There are other objectives such as total delay and weighted total delay, which are more complicated to optimize, this is achieved through a heuristic process called the “Apparent Tardiness Cost First” (ATC) this process is a mix between MS and WSPT.
For the cases in which there are machines in parallel, the makespan depends on the production program. The makespan goal, which plays an important role when parallel machine loads must be balanced, gives rise to another priority rule, the "Longest Processing Time first" (LPT), in this rule when a machine is released, the longest waiting job is selected to continue. The logic is that if shorter jobs are left for last, it is easier to balance the machines.
The SPT and WSPT rules are also important in parallel machines, as well as the ATC heuristic rule.
In conclusion, depending on the objectives set in terms of the service to be provided to customers, the most appropriate priority rule must be taken and the production program executed according to it.
Scheduling in Flexible Assembly Systems
The third class is focused on flexible assembly production systems. The means of transport controls the movement of each job as well as the process time in each machine. The objective is generally to maximize the Throughput (Production Rate).
Flexible assembly systems differ from the Jobshops discussed in the previous section. In the workshops, each job has its own identity and can be different from the other jobs, on the contrary, in a flexible assembly system, there is a certain limited quantity of products and normally established quantities of each type of product are produced. Two units of the same product are identical.
Job movements in a flexible assembly system are often controlled by a material handling system, which imposes restrictions on job start-up times on machines or workstations. The start time of a job on a machine is a function of the completion time of the preceding machine according to the job path. The material handling system also limits the number of jobs waiting in stock between machines.
For this type of production systems we will explain two models:
Rhythmless assembly system programming
This consists of a production line with a number of machines and workstations in series. The line is arrhythmic, this means that a machine can use the necessary time in any job. There are certain stocks between successive machines which can cause delays and inflexibility. A number of different types of products are produced in given quantities and the goal is to maximize throughput. This type of lines is seen for example in photocopier production lines. Different types of photocopiers are produced on the same line. Different models are usually from the same family and have many common characteristics. However they differ with respect to the options. Some have an automatic feeding system while others do not.some others have better-made lenses than others. The reason that different copiers have different options means that the processing times of certain stations can vary. To do the programming, you start by making a sequence of the jobs given in a certain order, after this the same sequence is repeated several times, the result is a cyclical sequence. Each of these repetitions is known as the Minimum Part Set (MPS - Minimun Part Set). In order to maximize throughput, the MPS must be minimized. To achieve this, we start by choosing the job with the longest processing time, then some of the missing jobs are chosen and scheduled after the one chosen and the non-productive times of the machines are calculated.Then the other jobs are chosen and the previous step is repeated. When all the jobs have been analyzed, the one that generates the least non-productive time is chosen and is the correct one to follow the sequence.
Paced assembly system programming
This system contains a conveyor that moves at a constant speed. The units to be produced are moved from one work station to another at a fixed speed. Each workstation has its capacity and restrictions. Again a number of different types of products must be assembled. The goal is to schedule jobs so that no workstation is overloaded and setup times are minimized. This system is very common in automobile production lines, where different models must be assembled on the same production line. Vehicles must have different colors and different equipment options. Vehicle scheduling must take into account balancing setup times and workloads.
An important characteristic must be considered for this system: the cycle time per unit, is the time between the exit of the line of two successive products. The cycle time is the reciprocal of the production rate.
Taking into account the variables involved with these systems there are 4 types of objectives that should be sought in programming.
- Minimize preparation times between different types of products.
- Comply with the delivery dates of the products.
- Optimize physical spaces defining the length of the production line
- Keep the consumption of materials and parts at good levels
To carry out the production scheduling there is a method called grouping and spacing (Grouping and Spacing - GS), this consists of 4 phases:
1. Determine the number of jobs to be scheduled
2. Group the jobs with respect to the operations that have the longest setup times.
3. Order these subgroups taking into account the dispatch dates
4. Space out the work of the subgroups taking into account the operations that have capacity restrictions.
More information at: Production Planning.com
Source: HERRMANN, Jeffrey W. "Handbook of production scheduling". Springer Science-Bussines Media, Inc. 2006.
