The challenge of the medium-term production planner sub-system is the timing of the production activities over a typically 3-6 months long time horizon with a time unit of one week. The generated plans must comply with the project deadlines and raw material arrivals, and respect the capacity constraints of the machines and workers of the factory. At the same time, they should keep production cost as low as possible by minimizing extra capacity usage and work-in-process. All in all, the production planner produces the following outputs.
Figure 4.3: Tables in the database and their relations.
84 4.4 The Production Planner Sub-system
• A medium-term production plan that assigns operations to weeks of the plan-ning horizon.
• A medium-term capacity plan that specifies the resource requirements of each week within the planning horizon.
• Suggested outgoing and incoming dates of OSP operations.
Furthermore, the medium-term plan can also serve as a material requirement plan that specifies the weekly requirements for raw materials and components. Clearly, this is practicable only for raw materials whose order period is calculable.
Due to the variance of products and the fluctuation of production load, all the above aims cannot be achieved by traditional material requirements planning (MRP) logic. Moreover, the planner must cope with a hard combinatorial optimization problem that cannot be solved for each individual manufacturing operation, because of the sheer size of the problem. Hence, we applied the aggregate production planning approach introduced in Chapter 2. In the production planning problem, we regard each customer order as one project. Aggregate models of projects are formed from the BOMs and routings by using the methods proposed in Sect. 2.3 and the bi-criteria tree partitioning algorithm described in Sect. 2.4.5. During the creation of the aggregate models, the throughput time of the activities is estimated by using the LFT heuristic (see Sect. 2.5.1). The result of the aggregation procedure is an in-tree of activities that are linked by end-to-start precedence relations. For example, from the routings displayed in Fig. 4.4 the system prepares the aggregate model with 5 activities presented in Fig. 4.5.1
Then, the production plan is prepared for the activities whichmust be performed within the planning horizon, based on their distance from the root activity in the project’s aggregate model and the project’s deadline. All the activities of a project have to fit into the project’s time window set by the forecasted raw material arrival and the deadline.
We consider both machines and workers to be finite capacity resources. Activities may require different amounts of an arbitrary number of these resources for their processing. Normal weekly capacities of the resources can be computed from the resource calendars, by applying a security factor to the total working hours of the given resource. The security factor is indispensable because effective utilization of
1All data in the figures are distorted for reasons of confidentiality.
Figure 4.4: Routing of a product. Excerpt from the MS Access database.
304
308 307
306 305
Figure 4.5: An aggregate project model. Excerpt from the MS Access database.
resources never reaches 100% in practice. By default, we set this factor to 0.8 for the upcoming weeks and 0.7 for distant weeks in order to allow for unforseen projects as well. Extra capacities are also limited, they extend the normal capacities to the
86 4.4 The Production Planner Sub-system
theoretical total working hours of the resource. However, there is a possibility to plan for infinite extra capacities as well.
In the aggregate project models, OSP operations take place in separate activities.
It is assumed that the outgoing and incoming dates of the OSP operations fall on borders of the one-week time units. There are two ways to handle these dates. Those which are already negotiated and fixed in the input of the planner, post temporal constraints on the predecessors or successors of the corresponding OSP operations.
Hence, the generated plan will always comply with the negotiated OSP dates. For other OSP operations, the dates specified in the plan can be regarded as a suggestion.
When solving the planning problem, our primary objective is to minimize extra capacity usage. In this way, the planner attempts to keep the works allotted for a medium-term horizon within the factory. There is also a secondary objective: in order to minimize inventory costs, theWIP level should be minimal.
The planning problem is translated into a mixed-integer linear program, and solved by the branch-and-cut algorithm described in Sect. 2.3. The proposed algo-rithm isany-time: it generates a series of solutions with better and better objective values, thus a first feasible solution is generated quickly, and then it can be refined to converge towards the optimum. The first phase of the solution process, i.e., find-ing a plan with minimum extra capacity usage generally takes a few seconds only.
However, minimizing WIP subject to this capacity constraint requires a significantly higher effort. Finding a sufficiently good solution took between 5 and 60 minutes. At the same time, reaching the theoretically optimal WIP level was not always possible within a reasonable amount of time. Table 4.1 shows the typical size of the problems we tackled.
Fig. 4.6 presents a fragment of a production plan prepared by our PPS system.
It is filtered for one of the product families. In this chart, the red and blue vertical lines delimit the planning horizon, and each row stands for one project. White bars show the allowed time windows of the projects, while green stripes indicate weeks when one or more activities of the given projects have to be performed. A low WIP level corresponds to relatively short green stripes shifted to the right hand side of the white time windows. This particular production plan reflects an overloaded factory where resource shortage causes temporary breaks in several projects.
Fig. 4.7 shows a capacity plan for the NC milling machinist worker group, for the same period of time. The height of the green columns in the figure indicates the total amount of work of the resource in the given weeks. The yellow and orange areas in
Planning horizon 15–30 weeks
Time unit 1 week
Running projects 600–1200
Operations per projects 20–500
Activities per projects 1–10
Resources, total ca. 100
Individual machines ca. 80
Machine groups ca. 10
Worker groups ca. 10
Solution time
Minimal extra capacities 2–15 sec.
Minimal extra capacities, minimal WIP ≥5 min.
Table 4.1: Typical size of a medium-term planning problem.
Figure 4.6: Project view of the production plan.