A farmer has to plan what to produce and how to produce it. To assist his decision-making a number of techniques are employed. A work study shows in detail how the production is or can be done. On the other hand linear programming is a tool for selecting crops. Work management (machinery selection and scheduling of operations) is somewhere in between these two approaches. The machinery selection problem and the selection of crops depend on each other and so both require constraints for man and workable time of machine operations. These constraints are insufficient to represent correctly the scheduling of operations.
The scheduling of farm operations depends on the available men and machinery, on the available materials (products, cattle) and on the weather and properties of materials (moisture content). Scheduling has been studied for one material (corn) or one operation (harvesting), but seldom for several materials and operations competing for the use of men and machinery. This scheduling problem is a dynamic programming problem where each stage of the system coincides with a decision date.
Three subsystems can be distinguished. The biological subsystem consists of materials waiting for operations which are performed by gangs from the man/machine subsystem. The climate subsystem influences the properties of the materials and the application of gangs. In Fig. 1 terms and relations for the grain harvest are given.
The aim of the present study is to develop a simulation method to solve the scheduling problem that correctly represents the use of men and machinery and the resulting flow of materials and uses hourly data on weather and properties of materials. To decide at each decision date which operations are to be executed, a heuristic strategy is developed to evaluate the current state of the system. This detailed model of the scheduling problem is simplified by omitting, for example, the setup and service of machines and by aggregating the weather information within days or weeks. So a range of problems is formulated that are solved by the simulation model. The most simple problem can easily be tailored for a linear programming model. With a range of problems we can evaluate to what extent scheduling problems might be relaxed (using less constraints).
The heuristic strategy uses the concept of urgency of processing a material. This idea is based on the existence of a timeliness function of each material with a maximum return at a given date (moment of time for example 1 August 20h00). After that optimum date the return diminishes with time. These timeliness losses are partly unavoidable because the capacity of men and machinery to process materials is limited. With the given men and machinery the decision maker only can decide to process a material or not, where not processing means an avoidable timeliness loss (the urgency). The urgency of a material is calculated for each material separately on the basis of the available quantity.
For the grain harvest a state of the system is given in Fig.2. The quantity of materials (wheat, straw etc.) is represented by a queue of so-called 'fields'. Fields differ in some property of a material, for instance ripening date or moisture content and may also refer to geographical position.
The operation period for the available quantity of a material is derived from the expected workable time, the estimated fraction of the time men and machinery are available for processing the material and the capacity of processing the material. Not starting the processing of some acreage of a material at the current decision date is equivalent to a delay until the end of the operation period. So the value of the timeliness function at the decision date minus the value at the end of the period is the avoidable loss, and an element of the urgency of a material. The fraction of the time men and machine are available for processing the material is derived from a linear programming model with weekly periods and is input for the simulation models. The capacity of processing the material is derived from the combinations (sets of gangs) and the capacity of the gangs (men and machinery performing an operation on a material according to a method).
The farmer can only decide to use one combination or another or none at all. Therefore it is necessary to assign the urgency of materials to the gangs and to the combinations by distributing the urgency of materials among the gangs processing that material relative to their capacities. Such an urgency of a gang (in $ per hour) is corrected by subtracting the variable costs of, for example, overtime. The urgency of a combination is the sum of the urgency of those gangs which have a positive corrected urgency and can operate in the combination. Whether a gang is applied depends on equipment, weather, material properties (moisture content), available material for processing and available storage for the materials delivered. After selecting the preferred combination (with maximum urgency), the next decision date is found as the minimum from a number of potential decision dates determined by end of operation, filling the storage, start of overtime or pause or no- work time, change of weather expectation or properties of materials, machine failure or by finish of repair or service.
Executing operations performed by the gangs in the preferred combination results in processing and delivering materials. Thus transformation of the quantity of materials is necessary to learn the state of the system on the next decision date. This state again is evaluated by the strategy resulting in urgencies of processing materials and a preferred combination; this cycle is repeated until the job is completed. The transformation also results in recording the timeliness loss of materials, the use of men, machinery and variable costs for overtime or drying. The delivery of materials introduces new fields.
The grain harvest in the Netherlands is used to learn about the behaviour of the simulation model. The wheat is harvested with a combine harvester and the wet grain (19-23% moisture content) is dried; the straw is baled, loaded and stored in the barn and the stubble is ploughed. Eight years with hourly weather and material data from 1 August-15 September are used.
Some general results from the experiments are that the simulation model is suitable for deriving relations between acreage, yield and machinery (Section 3.5.5) and that relaxed problems (simplified problems; Section 3.5.6) result in lower estimated costs or are more optimistic about the scheduling of operations than the strategy in the detailed scheduling problem. So if the detailed problem is acceptable for scheduling operations with a satisfactory use of equipment and variable costs and a correct representation of the flow of materials, then the simplified problems and the linear programming model result in too low estimated costs. The validation of the heuristic strategy is impossible because there are no data available. The results of the experiments, however, contribute to our knowledge of the scheduling problem and so the model is useful. Comparing different experiments shows the danger of using relaxed problems. Experiments with the simulation model for the scheduling problem show the sensitivity of different machinery systems, which is of use in training farmers to improve their management ability.
Further research is necessary to find better urgencies simultaneously for all materials, gangs and combinations and to optimize the schedule for a number of decision dates instead of only one.