Abstract
Contents
- 1. General formulation of the problem
- 2. Description of the object of research
- 3. Analytical formulation of the task
- 4. Mathematical formulation of the task
- Conclusions
- Bibliography
1. General formulation of the problem
With the rapid development of mechanical engineering automation load mechanical equipment is an urgent task. operational planning automation problems are studied for a long time, and, as experience shows, organizational tasks quite difficult to automate.
Nowadays, machine-building enterprises seek to improve profitability for a long period of time, as it can provide the necessary financial stability of the enterprise. In this connection, there is the task of good governance all sorts of industrial features, one of which is operational and scheduling on the shop floor. Indeed, already at the shop floor level of production should provide a quality service that can offer a product that will meet the requirements of quality and made in the declared terms.
Today, there are a large number of tools for enterprise management. However, a number of reasons the introduction of these products on the modern machine-building enterprises is not beneficial.
In this paper, we consider a machine-building enterprise, which is engaged in small-scale and custom-made production. Automating the management of loading of this kind of workshop equipment allows you to avoid or reduce the negative impact of a number of difficulties associated with the characteristics of this type of production:
– The multiplicity of the range;
– Instability of production volumes;
– Various deviations of the production process from a given rhythm.
2. Description of the object of research
Before we begin the process of developing an information system for managing an object, we should outline the general goals of the enterprise.
One of the main goals of production for a machine-building enterprise with a small-batch type of production is the timely execution of orders of adequate quality.[1] Due to the presence of large amounts of work and information characterizing the production processes in an enterprise, it becomes necessary to perform a number of tasks for the shop management of the enterprise, which should include:
– Organization of data collection on the work of processing machines and other production equipment;
– Distribution of the fulfillment of production orders for equipment and tracking the execution of orders;
– Formation of electronic passports of the parties, containing information about equipment and materials that was used in making that product;
– Monitoring the operation of machine tools, machining centers, industrial robots, tooling for calculating the operating time and monitoring the values of technological parameters (temperature, pressure, cycle time, etc.);
– Display of the current state of the equipment at users' workstations or on large screens located in workshops;
– Maintaining a centralized database of technical documentation and control programs, as well as sending control programs to machine control systems.[2]
One of the most important tasks is the distribution of the fulfillment of production orders for equipment, which is associated with a number of other tasks by the flow of information. Such problems are solved with the help of network planning and management systems (CMS) [2].
The SPU system has three stages of production organization:
– preliminary (initial) stage;
– stage of development and optimization of network graphics;
– stage of operational control over the progress of work
At the preliminary stage, a logical description of the work package is given, the sequence and interrelation of the individual stages, the composition and interrelation of the work performers, approximate delivery times, resource requirements and financing are determined. It also sets performance criteria.[2]
The development and optimization stage includes:
– the dismemberment of the whole complex of works into stages and the issuance of tasks to performers for the compilation of fragments of the network model for each stage;
– creation of a list of works with a description of their content;
– creation a list of events with the necessary detail and a clear wording that does not allow different interpretations;
– determination of the sequence and parallelism of the work;
– construction of local network graphs (fragments) in stages;
– construction (“stitching”) of local graphs into a complex (consolidated) network model;
– calculation of the basic parameters of the network model and its optimization;
– paperwork and bringing tasks and deadlines to work to performers.
In most cases, the time factor is taken as the decisive factor. In this case, the main parameters of the network are:
– the duration of the work;
– early and late dates of events;
– critical path;
– time reserves for events.[2]
3. Analytical formulation of the task
In this work it's solving the task of constructing local network graphs (fragments) in stages, in other words finding the order of processing parts for workplaces of the technological process, drawing up a calendar schedule of equipment loading for a certain planned period. The final document that creates in this phase is a shift task for jobs.
The following input information is used for solving this task:
– composition of product designs;
– availability and capabilities of processing equipment and personnel;
– ordered quantity of products;
– directive production time.
To set the task more correctly, it is necessary to analyze the process and features in details.
In an order that comes to a machine-building enterprise, there may be one or several products. Each product consists of n groups of parts to be processed. All groups of parts have a certain technological route of processing, which they have to go through, which describes the sequence of operations, as well as groups of machines on which these operations can be performed. In addition, products can have different directive deadlines, i.e. the period until which the product must be completed before it arrives at the assembly.
Having considered the technological process from different angles, the following task was set: to determine such a sequence of launching parts for processing and distribute them among the machines so as to fulfill the order on time and minimize equipment downtime.
4. Mathematical formulation of the task
Lets consider the mathematical formulation of the task on the example of a typical technological process in a mechanized workshop in enterprise.
Let be:
n – the number of machines that are involved in the process,
tпij, tфij – the planned i-detail processing time on the j-th machine, where i = 1,2,…,k), j=(1,2,…,n),
Δtпр – idle time of the j-th machine.
Then the objective function will be as follows:
From the objective function it can be seen that the downtime on each machine should be minimized.
The above objective function is affected by a number of limitations.
Let be Тдi, Тфi – directive and the actual production time of i-detail,
Nнi, Nфi – the necessary and the actual number of machined details,
i – batches of details,
tlk – he duration of the technological operation k on the detail l,
ml is the total number of operations on parts, then all restrictions will be as follows:
The constraints described in formula 2 can be analytically expressed as follows:
– production of the part must be completed on time, i.e. the actual time of manufacture of the part must not exceed the directive;
– the work must be done in full, i.e. the number of details actually processed must be equal to the required;
– each subsequent operation in the process route for a particular part cannot be started until the previous operation is completed.
In addition, there are additional restrictions that are not always possible to consider in advance:
– overhaul of equipment;
– scheduled inspection of equipment;
– lack of staff.
The task of managing the equipment load is reduced to the selection of such an optimal production program that will allow the best use of existing production capacity.
Conclusions
As a result of the research, the relevance of creating an automated network planning subsystem when loading equipment at a machine-building enterprise was justified. The main stages of the development of the calendar plan. The main mathematical methods used to optimize the schedule are analyzed, the options for using them in the network planning problem to be solved are considered.
Bibliography
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