The studied BFS

BFS organize the work and make possible the use of an all-in/all-out management that improves the health status of the herd and thus increases its productivity (Carr Reference Carr, Kyriazakis and Whittemore2006). The most common BFS space farrowing batches from 1 to 5 weeks. The week after weaning, sows are inseminated and farrowing occurs about 16 weeks after conception. The most usual lactation lengths in Europe are about 3 or 4 weeks. Thus, the full productive cycle lasts about 20–21 weeks. The number of batches in the herd can be calculated by dividing the cycle length by the time interval between subsequent batches. This number varies in the current study from 4 batches (5-week interval with a lactation of 3 weeks) to 20 or 21 (1-week interval with a lactation of 3 or 4 weeks, respectively). The distribution of the periodic tasks over time differs between BFS. All the periodic tasks occur each week in the 1-week BFS, one different task occurs each week in the 3-week BFS and some weeks are free of any periodic task in the 4- and 5-week BFS. Thus, for each BFS, the farmer can plan on a weekly basis the occurrence of these different tasks. However, it is more difficult to plan the exact day and time when these events will occur, because of the natural variability of animal biology. For the same number of sows in a herd, the number of sows per batch will differ between BFS resulting in different work load distribution within the week. The preferred BFS seems to vary between countries, often in connection with the size of herds. For instance, in North America the 1-week BFS is generally used whereas in France the 3-week BFS is the most common. Moreover, due to the possibility of having some weeks without periodic tasks, the interest for the 4- and 5-week BFS grows worldwide. This led to the choice of the BFS compared in the current paper: 1-, 3- and 4-week BFS.

Herd representation in the MaProSH model

Several specifications for the MaProSH model were formulated: (1) it should reproduce the herd operation with different BFS; (2) it should give an account of the effect of modifications to the scheduling of periodic tasks execution on the herd operation and productivity: and 3) it should give an account of the effect of modifications to a sow biological parameter on the periodic task distribution and on the herd operation and productivity. According to these specifications the model represents several entities (Fig. 1). The principal entity is the sow. This entity has different processes (oestrous onset and farrowing) able to simulate the information needed for the reproduction of the animals. During the lactation period sow entities are related to several piglet entities. The sows are assigned to the following pools: replacement gilts, batches and culled sows. All sows start as members of the replacement gilts pool and move to one batch for their first productive cycle. Afterwards during their lifetime they may move to another batch depending on their biology, BFS and culling rules. They finish as part of the pool of culled sows. All the batches together and the replacement gilt pool compose the herd entity. The number of batch entities is variable to represent several types of management. The other entity needed to answer to the specifications is the farmer. The farmer is a manager and makes strategic and tactical decisions. The farmer is also able to plan the execution of periodic tasks. As a simplified representation of the farm labour force, the farmer carries out tasks on both sows and batches. A time representation close to a calendar was chosen in order to produce output on the distribution of periodic tasks. The time step for the simulation was chosen in order to be able to represent the biological phenomena and their interaction with the work. A time step of 1 day is sufficient to represent the distribution of events and tasks within the week, but the time step of one hour seems closer to the real management and was chosen. The specifications of the model directed the entities and time representation. The entities representation guided the choice of an object-oriented model whereas the time representation guided the choice of a discrete-event simulation controlled by a clock. The programming language used for the implementation of MaProSH is Python2.4 (Python Software Foundation 2004).

Fig. 1.

Entities in the model and relationships between them. A B means that A is composed of B. The numbers indicate the number of A and B in relation. * stands for 0 to infinity, 1..* stands for 1 to infinity and 3..21 stands for from 3 to 21. A — B means that A and B are associated. A → B means that A operates on B.

Animal representation

The representation of the animals was directed by the elements comprising the global sow productivity which is mainly described as the number of weaned piglets (WP) per sow per year. This production parameter is a combination of two other parameters that are the number of litters per sow per year and the number of piglets weaned per litter. The number of litters per sow per year is dependent on the duration of the reproductive cycle (weaning-to-weaning interval) which depends on weaning-to-conception interval (WCI), gestation duration and lactation duration. The WCI depends on the weaning-to-oestrus interval (WOI), the oestrus-to-oestrus interval (OOI), the fertility rate and the farmer decision rules used to manage the infertile sows. The WOI used for this calculation is therefore dependent on the sow and the farmer. The sow part corresponds to the WOI observed if the oestrous detection was perfect whereas the farmer part corresponds to the oestrous detection rate. The number of WP per sow per litter depends on the number of live-born piglets (LBP) piglet survival and cross-fostering practices. The representation of sow biology also needs to take into account the random nature of the biological processes. This is why each sow is individually represented in the model with biological characteristics that are randomly estimated according to distribution curves. Thus to model the reproductive cycle duration, the sow part of WOI, the OOI and the gestation length were estimated from a normal univariate distribution according to the parity of the sows. The farmer part of the WOI is modelled as a detection rate according to the parity and the sow fertility was modelled by a threshold. When oestrus is detected, insemination occurs and a uniform random number is generated. If this number is below the fertility threshold, insemination is not successful and the sow will return to oestrus following the OOI distribution. In the other case another random number is generated in order to determine if the sow will abort or not. If the sow aborts, the duration between insemination and abortion is obtained from a uniform distribution generated between 21 and 110 days whereas if the sow does not abort, farrowing is scheduled according to the gestation length distribution. The number of LBP is estimated from a normal univariate distribution according to the parity of the sows. The number of piglets at weaning is estimated from a relationship between LBP and WP which integrates the piglet mortality rate and the cross-fostering practices.

The gilts are assumed to be sexually mature and hormonally synchronized. The interval between the end of the synchronization treatment and the onset of oestrus is represented by a normal univariate distribution similar to the distribution of WOI observed in primiparous sows. A constant mortality rate per day (annual rate divided by 365) is used. All parameter values and equations used in the simulation were obtained from the analysis of the Technical Sow Herd Management System (TSHMS) in France during the year 2006 (IFIP 2007) (Table 1).

Table 1.

Default values of biological parameters included in the model according to the 2006 data from the Technical Sow Herd Management System (TSHMS) in FranceFootnote *

WOI, weaning-to-oestrus interval; OOI, oestrus-to-oestrus Interval.

* Data collected on about 3000 farms. Available at http://www.ifip.asso.fr/service/chai1.htm.

† WOI observed resulted from the combination of the WOI supposed and detection rate. WOI observed equals WOI supposed if the detection rate equals 100%. WOI observed is calculated in TSHMS.

‡ WOI for parity 0 correspond to the delay between the end of the synchronization treatment and oestrous behaviour.

Decision rules

The study aims to compare different herd management systems on the basis of productive performances, periodic task event distribution and the capacity to maintain a minimum number of sows at farrowing. These elements of comparison are defined as the herd objectives which are reached by applying strategic rules and tactical rules (Sauvant Reference Sauvant2005).

The strategic decisions considered in this model are the type of BFS (all systems are available), the duration of lactation (3 or 4 weeks), the scheduling of periodic tasks and the maintenance of a minimum number of sows at farrowing. The periodic tasks to schedule include the weaning of piglets, and the oestrous detection period. In order to have some outputs on the distribution of these tasks over working days (Monday to Friday) and weekends (Saturday and Sunday), the model has to manage the occurrences of these activities on a daily basis. The number of sows per batch at farrowing depends on the number of sows inseminated per batch and the conception, abortion and mortality rates. The number of sows inseminated is dependent on the number of sows tested for oestrous behaviour and on the oestrous detection rate. Sows tested for oestrous behaviour are those weaned the week before oestrous detection, the replacement gilts and sows from the batch inseminated 3 weeks before when it is possible. It is assumed in the model that the number of gilts included in a batch always fits the need to meet the target number of sows at farrowing. This assumption implies that the gilt pool is unlimited which differs from the reality of on-farm management. This choice was made for simplification and also because the decision rules concerning the management of replacement gilts are not well known.

Tactical decision rules included in the model concern the rules for the culling of sows at each step of the reproductive cycle (at weaning, at the end of the week of oestrous detection, at detection of return into oestrus and at ultrasonography). The culling decision rules may differ between BFS and will be detailed below.

Discrete event simulation controlled by a clock

A discrete event simulation corresponds to a representation of the system based on the discrete organization of time and the notion of a scheduled event being a modification of the state of a system at a predefined time. Two kinds of events are included in MaProSH which are linked to the animal (for instance oestrous behaviour, farrowing or death) or to the farmer (for instance oestrous detection, weaning or ultrasonography). Biological events may modify the sow physiological state, plan a new biological event or create some new entities called ‘piglets’. Task events may modify the sow physiological state, plan a new task or biological event or activate some decision rules. All the events that are supposed to occur are stacked in a calendar with the date and time of occurrence. Simulation date and time are controlled by a clock with a time step of 1 h. At each step, the simulator checks in the calendar for an event to proceed. If an event is found, it is processed otherwise simulation time is increased. This model conceptualization offers a flexible framework for herd operation close to the real operational management. It allies individual event occurrence (for biological responses) to the batch management of the farmer and is so designed to simulate the interactions between management and animals.

Outputs

The model provides information on sow productivity and time of the events. Productivity data concern the performance of individual sows (number of piglets born and weaned, WOI, fertility and gestation duration) and farrowing batches (number of sows at service, farrowing and weaning; replacement rate; and fertility and number of piglets weaned). The global herd productivity will be expressed as the number of WP per productive sow per year i.e. number of piglets weaned per sow×number of farrowing per sow per year. The data relative to the dates of the events are analysed on a daily basis in order to produce outputs such as the percentage of sows farrowing during the weekend or the distribution of the oestrous onsets.

Initial structure of the herd

In order to reduce the calculation time required between the initial situation and the situation at equilibrium, the initial herd structure was created by affecting the parity of sows according to a beta distribution (Β_{(0·98, 2·6)}) obtained from the parity distribution observed in the experimental herd of INRA (Saint-Gilles, France). The herd size was fixed at 210 sows which corresponded to 21 batches of 10 sows, 7 batches of 30 sows and 5 batches of 42 sows in the 1-, 3- and 4-week BFS, respectively.

Number and length of sow herd simulations

Before being able to use the model to compare various management strategies, it is necessary to determine the minimal length of simulation for reaching the steady state and the number of replications needed to estimate the variability of the results. For this, the approach consisted in analysing the data obtained from 20 replications of simulation with the 3-week BFS over 20 years (49 reproductive cycles). The results were analysed according to four variables (i) the number of sows per batch at farrowing standing for the ability of the simulator to maintain a constant number of sows in the herd; (ii) the mean parity of sows at weaning which is an indicator of herd demography; (iii) the number and parity of culled sows per cycle as indicators of sow longevity; and (iv) the distribution of periodic tasks over several weeks.

Number of sows at farrowing

The average number and the minimum and maximum numbers of farrowing sows per batch and per cycle calculated over the 20 replications are illustrated in Fig. 2. The mean number of sows per batch (30·0±0·14) is very close to the objective of 30 sows fixed for this BFS. The maximum number of sows never exceeded 32, which is in agreement with the culling rules after ultrasonography and the minimum number of sows never fell under 21. This validates the capacity of the simulator to maintain the number of sows per batch over a long period of time. Moreover it appears that the average, minimum and maximum number of sows per batch stabilize after about two cycles of simulation.

Fig. 2.

Minimum, mean and maximum number of farrowing sows per batch for the different cycles.

Mean parity at weaning

The mean parity per batch is calculated for each replication, cycle and batch. Mean, minimum and maximum batch average parity are thereafter determined for each cycle. The evolutions of these criteria over the 49 reproductive cycles are illustrated in Fig. 3. It takes about 15 cycles for the mean parity to stabilize, whereas the amplitude of variation of mean parity remains quite constant over the whole simulation period. This indicates that the first 15 cycles must not be considered when analysing the distribution of sow parity nor for all criteria affected by parity such as prolificacy or WOI (results not presented).

Fig. 3.

Minimum, mean and maximum of the mean parity of sows at farrowing for the different cycles.

Culling

The minimum, maximum and mean numbers of culled sows per batch per cycle over 20 replications are shown in Fig. 4. The mean number of sows culled per batch at equilibrium is approximately six, which corresponds to a culling rate of about 20% per cycle and about 48% per year. A statistical comparison of means indicated that the mean and the amplitude of variation in the number of sows culled reached equilibrium after eight cycles. Since the culling rules do not oblige some sows to be culled at each cycle, the minimum number of sow culled could be zero, as shown in Fig. 4. In the same way there was no upper limit to the number of sows culled which explain that some batches might have a high culling rate during one cycle. A chi-square test indicated that the parity distribution of sows at culling reached stability after 15 cycles. Sows were culled at all parities. About 20% of culling occurred at parity 8 which corresponded to the maximal number of parities allowed in the simulator.

Fig. 4.

Minimum, mean and maximum number of culled sows per batch for the different cycle.

Distribution of periodic task events

The number of occurrences of weaning, oestrous detection and farrowing events was recorded for each simulation. The average results obtained over the 49 cycles and 20 replications are presented in Fig. 5. The alternation of periodic tasks over three successive weeks which characterize the 3-week BFS appears clearly with a week with oestrous events (mainly on Monday and Tuesday), a week with farrowing events (mainly on Wednesday, Thursday and Friday) and a week with the weaning event. It appears that with a weaning occurring on Thursday some sows (about 15%) are in oestrus during the weekend and about 10% farrow during the weekend.

Fig. 5.

Distribution of periodic tasks in the 3-week BFS.

The method used to determine the number of replications needed to estimate the variability of parameters of interest consisted in analysing the mean and standard deviation of the average value of these parameters at steady state according to the number of replications performed (Schwartz Reference Schwartz1993). Two examples of this analysis are illustrated in Figs 6 and 7. Figure 6 illustrates the evolution of mean and standard deviation of the number of farrowing sows per batch and indicates that these values stabilize with 12 replications or more. Figure 7 shows the same for the average parity of sows at weaning and leads to the same conclusion.

Fig. 6.

Average and standard deviation of the number of farrowing sows between cycles 16 and 30 for 1–20 replications.

Fig. 7.

Average and standard deviation of sow parity at weaning between cycles 16 and 30 for 1–20 replications.

Thus, in the following simulations the average value of sow and herd productivity at steady state will be estimated between the 16th and the 30th and 15 replications, corresponding to data from about 47 000 litters for a 210 sow herd. These data were collected in approximately 8 min.

Effect of changes on production strategies

Three production strategies combining a BFS (1-, 3- and 4-week) and the most usual lactation duration observed for each BFS (4 weeks for the 3-week BFS, 3 weeks for the 4-week BFS and both durations for the 1-week BFS, but only the results of the 4 weeks lactation duration will be presented) were compared. In addition to the number of farrowing batches in the herd and the lactation duration, these productive systems differed by their capacity to manage infertile sows and by their periodic task distribution. Whatever the production strategy simulated, herd productivity reached steady state with a variation coefficient between replications of only 0·5% (Table 2). This variation coefficient gives an estimate of the variability between herds with the same management rules and the same sow characteristics. This variability is lower than the variability observed in the French national database (IFIP 2007). This was expected because of heterogeneity of the database concerning farm management rules and animal characteristics.

Table 2.

Mean and standard deviation between replications of herd productivity indicators and event distribution in different batch farrowing systems (BFS)

WCI, weaning-to-conception interval.

* Standard deviation in replications made between the 16th and the 30th reproduction cycles.

† Including the culled gilts.

With the MaProSH model, no effect of production strategy was observed on sow productivity per litter and the simulated average lactation duration corresponded to the strategy adopted for each BFS. In the same way, the average number of sows at farrowing was close to the objective. The WOI differed between BFS. It was shorter for the 4-week BFS because, in this system, sows which are not seen in oestrus within a week are culled and so not considered in the calculation of WOI. Also due to the differences between production strategies concerning the culling of infertile sows, the WCI of 4-week BFS is shorter than the observed in the other two systems. In relation to these results, the number of culled sows per batch per cycle is increased with this BFS and culling concerned mostly the young sows which are more difficult to detect in oestrus and less fertile resulting in a low mean parity at culling. Despite these drawbacks, the number of piglets weaned per productive sow per year is higher with the 4-week production strategy (P<0·001). No difference in herd productivity was found between 3-week and 1-week production strategies. Distribution of events (detection of oestrus, farrowing and weaning) is presented in Fig. 8 and summarized by four criteria in Table 2. In the 4-week BFS, the week following weaning is devoted to oestrous detection as for the other BFS but is also the week of farrowing. After this week of heavy work load, there are 2 weeks without any specific periodic task events. In the 3-week BFS, no task superposition is observed and the number of periodic tasks per week is almost constant. However, this system has fewer week and weekend days free of periodic tasks. In the 1-week BFS, the number of periodic tasks per week remains constant, but all the tasks occurred each week and there is no day without periodic tasks. With this system, the beginning of the week (including Sunday) is mostly concerned with oestrus whereas the end of the week (including Saturday) is concerned by farrowing. The total number of periodic task events that have to be performed is not different between BFS, only the distribution over time changes.

Fig. 8.

Event distribution over week in 4-week BFS (a), 3-week BFS (b) and 1-week BFS (c).

Effect of period of oestrous detection

With the default management strategy, farmers plan oestrous detection days from the Saturday following weaning until the Monday 10 days afterwards. In order to limit work during the weekend it is convenient to evaluate the consequences of a shorter oestrous detection period, that is, from Monday following weaning until next Thursday. Results are shown in Table 3, columns A. The reduction of the oestrous detection period implies that fewer sows will be detected in oestrus which affects herd productivity due to less sows at farrowing, more young sows culled (decrease in the mean parity at culling and overall increase of in the number of culled sows per batch) and increased WCI, in particular in the 3- and 1- week BFS (more sows not seen in oestrus the first week are kept for another detection 3 weeks later). However, only a slight but significant (P<0·001) decrease in the number of piglets weaned per productive sow per year was observed for these BFS. The week distribution of task events is modified with a strong reduction in the number of events occurring during the weekend but no consequences on the distribution of the farrowing events.

Table 3.

Effect of changesFootnote * in practices (duration of oestrous detection (A) and day of weaning (B)) or in biological parameters (variability of the WOI (C) and fertility (D)) on sow productivity and distribution of events (farrowing, oestrus and weaning) in three BFS

* Control corresponds to a 10-days period of oestrous detection, weaning on Thursday, average variability of WOI and 90% of fertility.

A corresponds to a 4 day period of oestrous detection, weaning on Thursday, average variability of WOI and 90% of fertility.

B corresponds to a 10-days period of oestrous detection, weaning on Wednesday, average variability of WOI and 90% of fertility.

C corresponds to a 10-days period of oestrous detection, weaning on Thursday, increased variability of WOI and 90% of fertility.

D corresponds to a 10-days period of oestrous detection, weaning on Thursday, average variability of WOI and 70% of fertility.

† Included the culled gilts.

Effect of weaning day

This analysis concerns the consequences of planning weaning on Wednesday instead of Thursday. Results on productivity and event distribution are presented in Table 3, columns B. No consequences on productivity parameters were found but the occurrence of events during the weekend strongly increases. This mainly concerned oestrus which occurred more frequently during the weekend whereas this shift resulted in a decrease in the number of farrowings occurring during the weekend.

Effect of WOI and fertility

To evaluate if the model is able to respond to a modification of the biological parameters describing the animals, a simulation experiment was performed with an increase in variability of the WOI from 0·9 to 1·1 days. The results for each plan are presented in Table 3, columns C. Differences between the two experiments concerned only the distribution of events with an increase in the number of periodic task events occurring during the weekend when the variability increased.

In the same way, the effect of sow fertility was investigated with the aim of understanding how the different BFS will face a reduction in fertility from 90 to 70%. The results of this experiment are presented in Table 3, columns D. The model was near to maintaining the number of sows at farrowing and variability between replications remained low despite a slight increase. However, this resulted in an increase in the number of sows at service by 20–30%. In the 4-week BFS, many of these sows were replacement gilts resulting in a strong decrease in the mean parity at farrowing. In the other BFS most were non fertilized sows from the previous batch resulting in increase in the WCI. The number of culled sows per batch also increased in all BFS (multiplied by 2 in the 4-week and by around 1·3 in the other BFS) and concerned younger sows. From these different results it can be concluded that the 4-week BFS appears more sensitive to a decrease in fertility than the other two systems. Moreover, the increase in the number of sows at service also increased the number of events to be managed by the farmer but did not change their time distribution.