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Simulation in the Dairy Industry

- a case study using SIMUL8

by Christine Campbell and Norman Thomson

High software costs have been a barrier to the wider use of simulation in British industry. A number of packages have been created with the explicit goal of providing on PCs something akin to the power of larger products, only at an affordable cost. The following article describes how SIMUL8 was used to analyse vehicle congestion in an industry with rapidly perishable raw materials, and outlines some of its underlying concepts.

-oo0oo-

Current barriers to simulation

Many pages have been written in the Operational Research and other journals extolling the merits of simulation, and deploring the absence of its wider use in industry and commerce as a whole. Much of the reason for this can be attributed to the hesitation of companies to pay large sums to invest in software which, at the least, requires skills to operate beyond those likely to be found within company resources, and over which there is bound to be doubt as to whether the investment can be recouped. Currently, most of the twenty or so simulation packages available in the market-place can be installed on desktop computers, yet companies selling into the simulation market are still organised to sell individually through high-cost sales people. While price is not the only issue of concern, it is undoubtedly an important factor which must be addressed if knowledge is to be spread and momentum created in this sphere. Readers of the Operational Society Newsletter may already have read an item in the October 1997 issue in which Nigel Cummings compares SIMUL8 with WITNESS and MODSIM III. This article relates how SIMUL8, which is the most recent of the three, was purchased by a client, and used to simulate vehicle movements in the receiving area of a Scottish dairy company, thereby helping the client to focus on the fundamental causes of what was increasingly perceived as a matter of some irritation in day-to-day operations.

A modelling scenario

It takes appreciable time to observe and understand by questioning and discussion the workings of any large company. In the present case, the company’s products are highly perishable, and a significant part of the core operation consists of the movements of a variety of vehicles performing different functions with intensities varying on both a daily and a weekly cycle. For simulation purposes, an essential step following the initial observation period was to abstract a skeletal process description such as the following which served as the basis for subsequent modelling and experimentation.

Milk is delivered to the dairy each day by two different methods. The first method is by the company’s own tankers who collect milk from farms with which the company has a supply contract. This amount fluctuates broadly with the time of year, but very little on a day by day basis. The second source is by deliveries from an external company, the nature of which are determined by a monthly contract. The ratio of milk supplied from these two sources is about 5:7. In addition, the dairy acts as a buffer, sometimes calling for milk from other dairies, and at other times sending them excess milk.

There are four different sizes of tankers of capacities 9,000 litres, 14,700 litres, 21,700 litres, and 23,000 litres, of which the largest is not used by the external contractor. Tankers arriving at the yard are allowed to enter only if there is parking space available in the yard, which can accommodate a maximum of 18 tankers. They enter via a weighbridge, and must then wait for their cargo to be sampled and passed before being allowed to off-load. Sampling is carried out by laboratory staff as soon as practicable after the tanker arrives in the yard. After a sample has been passed as satisfactory, the tanker proceeds to one of six off-load points, providing one is vacant. The time to off-load varies from 30 minutes to an hour, depending on the amount of milk which the tanker is carrying. (Not all tankers are fully loaded.) After off-loading, the tanker either leaves the yard to pick up another load of milk, or it is washed inside and outside at one of four washing bays when one becomes available. Tankers only wash after their last run of the day, and so the washing facilities are generally used only in the afternoon. After washing, the tankers leave yard after being reweighed on the weighbridge. Figure 1 shows a diagrammatic representation of the yard as rendered by SIMUL8, with obvious abbreviations such as COY for Company and EXT for External.

Schematic diagram of yard
Figure 1: Schematic diagram of yard

After off-loading from the tankers, milk proceeds into one of two storage tanks, and is then pumped into one of eight raw milk silos feeding two pasteurisers, which carry out the first of the production processes.

The above is a description of ‘normal’ operation. Problems can develop within the yard when the silos become full due to subsequent blockages in production and packaging, and so a first model was constructed which followed matters through to the stages of pasteurisation, separation and homogenisation. This model had unsatisfactorily long execution times, and some of the detail covering possible exceptions clearly had to go. Comparison with a model representing just the yard

and the associated off-load and wash areas suggested that an adequate representation of what went on there could be achieved by assuming that the silos provided a sufficient reserve so that any bottle-necks further down the line did not affect the vehicle situation in the yard itself. This was the situation which prevailed anyway under normal conditions.

Tanker flow problems and possible changes

Most company tankers make two runs a day corresponding to the two milkings which are common practice at the farms. This results in two busy periods each day at approximately 10 am and 3 pm when there are a large number of tankers in the yard. The problem is particularly acute in the afternoon when most tankers use the washing facilities, thereby contributing further to congestion in the yard. The main changes which were investigated in the simulation were :

  1. Not allowing external tankers to wash in the yard.
  2. Moving all washing facilities, both company and external, to another yard.
  3. Negotiating collection arrangements with the farmers to bring about a more even distribution of company tankers throughout the day.
  4. Negotiating for a more even distribution of external tankers throughout the day.

Table 1 : Parameters and D statistics for distributions tested for normality

Distribution Mean St. Devn. # observns. D statistic a0.05 = a0.01 =
Weighout 2.1 0.61 42 0.16 0.21 0.25
Cweighin 1.64 0.83 23 0.15 0.27 0.33
Eweighin 0.74 0.21 28 0.1 0.25 0.3
Sample 24.9 6.41 9 0.2 0.43 0.51
Wash 21.2 6.18 9 0.29 0.43 0.51
Coffload1 15.6 3.16 92 0.18 0.14 0.17
Coffload2 27.4 4.4 79 0.21 0.15 0.18
Coffload3 39.4 4.78 39 0.28 0.21 0.26
Coffload4 48.3 1.88 25 0.31 0.26 0.32
Eoffload1 15.5 3.56 61 0.15 0.17 0.21
Eoffload2 25.9 5.12 78 0.23 0.15 0.18
Eoffload3 44.3 2.98 24 0.17 0.27 0.32

 

Table 2 : Parameters and D statistics for distributions tested for exponential

Distribution Time of day Mean #observns D statistic a0.05 = a0.01 =
Ctime1 09:00-10:00 12.4 194 0.12 0.1 0.12
Ctime2 10:00-13:00 28 331 0.09 0.05 0.09
Ctime3 13:00-15:30 13.4 291 0.07 0.06 0.1
Ctime4 15:30-19:30 45.6 172 0.21 0.08 0.12
Etime1 04:30-09:30 34.4 343 0.21 0.05 0.09
Etime2 09:30-12:00 15.8 459 0.07 0.05 0.08
Etime3 12:00-17:00 19.6 224 0.08 0.07 0.11

 

Table 3 : Part of model description

Work Centre In Output Rule Out Resources
OFFLOAD1-6 OFFLOAD QUEUE Percent 50 MILK1-6
50 TANKER1-6
YARDSPACE
Timing Attributes ... set to Batching Replicates
Attribute
UNLOADTIME
    Batch Size:
Fixed 2
1

 

Work Centre In Output Rule Out Resources
CTANKERS CTankers Percent 37 CSIZE1
40 CSIZE2
17 CSIZE3
6 CSIZE4
GATEMAN
Timing Attributes ... set to Batching Replicates
Fixed
0
WASH
TANKER TYPE
DIRECTION
WASH/NOTWASH
1
CWEIGHIN
- 1

      

Storage Bin In Out Capacity
WEIGHBRIDGE QUEUE OUT WASH1-4
TANKER1-6
WEIGHOUT 3

     

Resource Number Shift Dependent
YARDSPACE 18 -
GATEMAN 1 Available 09:00 - 19:30

  

Table 4 : Extract from results tables

  Low 95% range Average Result High 95% Range
ENTRY QUEUE:
Average Queueing Time
Max Queueing Time
St. Devn. Queueing Time
No. non-zero Queueing Time
Average Queue Size
Maximum Queue Size
0.35
3.64
0.77
16.5
0.02
1.9
0.45
4.61
0.97
17.8
0.03
2.06
0.54
5.59
1.16
19.0
0.03
2.22
WASH QUEUE
Average Usage
Maximum Usage
0.02
1.54
0.02
1.70
0.03
1.86
CTANKERS OUT(WASH)
Number Completed
Minimum Time in System
Average Time in System
Maximum Time in System
St. Devn. of Time in System
15.9
53.4
79.9
108
15.3
16.7
54.6
81.6
111
16.0
17.6
55.9
83.3
114
16.8

 

centres. The time spent by work items in these work centres is usually zero, and they would not normally be represented in a Visual Interactive display.

In the model illustrated in Figure 1, alongside the entry queues there are dummy work centres CTANKERS (see Table 3) and ETANKERS whose purpose is to set the initial attributes of wash, tanker type and direction. The value of the attribute wash determines the direction which a tanker takes when it finishes off-loading. The attribute direction is set to xweighin (as opposed to xweighout ), and tanker type is set to 1 or 2 to indicate company/external tanker.

Storage Bins are objects corresponding to queueing spaces where work items can wait prior to a forthcoming processing stage. In normal modelling practice a storage bin is often provided immediately prior to each ‘non-fictitious’ work-centre. Storage bins may have a maximum capacity, for example WEIGHBRIDGE QUEUE OUT (see Table 3) has a capacity of three because that is the maximum number of tankers which can queue for exit.

Resources typically model operators or high value tools, but dummy resources can also be employed in order to impose shift or other time availability patterns, which are also objects. (Work centres themselves are assumed to be available throughout the entire simulated time.) In the dairy model there is a GATEMAN resource which is used to restrict the arrival of company tankers until after 9am by

which time they have made their first collections from the farms. The model starts running daily at 4.30 am which is the time at which external tankers start arriving. There is a further dummy resource YARDSPACE which is used to give a running count of the number of spaces used within the yard.

Work entry points are where work items enter and leave the model. Each work entry point requires an inter-arrival distribution. Work exit points are suitable gathering points for statistics about throughput and time in system. In Figure 1 separate work exit points COY TANKERS OUT and EXT TANKERS OUT are used to gather statistics about company and external vehicles.

Results gathering

A wide variety of results are available for recording at work centers, storage bins and work exit points. These can be displayed both as tables and as graphs. Table 4, for example, is an extract from a table of results following a run of the dairy model.

The most effective way of demonstrating to the client the effects of the various proposed changes was firstly to have him watch visual displays of various runs as they progress, and secondly to present graphs of YARDSPACE occupancy during the course of a specimen working day from 04:30 to 22:30. The initial situation was as shown in Figure 2. The horizontal axis measures time in minutes, and the dotted line represents the mean occupancy.

Data collection

A large amount of time was spent collecting and analysing data within the yard, with a view to fitting distributions. Record sheets were available for the arrival times of tankers, their sizes, and the amount of milk unloaded, from which the time to unload could be derived reasonably accurately. However there was no information available on sampling times, washing times, and time spent at the weighbridge, all of which had to be observed with a stopwatch.

The Kolmogorov-Smirnov test was used to validate the fitted distributions used within the model. This test has considerable simplicity in use, since it requires only that a few functions, one for each distribution to be considered for fitting, be set up on a spreadsheet or other computing system. Following data entry, a single set of numbers giving the results which can then be compared with tables of the D statistic. Given the relative straightforwardness of such procedures, it seems unfortunate that to the writers’ knowledge this facility is not provided within any of the existing simulation packages.

The D statistics for each of the distributions of times (in minutes) which were expected to be Normal and negative exponential are given in Tables 1 and 2 respectively. In each case other distributional possibilities were explored, but none gave a better overall fit. Prefixes C and E refer to Company and External tankers respectively. The final columns give the 5% and 1% critical values for the Kolmogorov-Smirnov statistic, that is the values which, if the underlying distribution was as postulated (that is Normal or exponential) would be exceeded only 5% or 1% of the time in long run random sampling.

Table 2 reflects the fact that the inter-arrival times for tankers varies throughout the day. It was judged by observation of the records that there were essentially four identifiable time periods appropriate to the company tankers, and three for external tankers. This is modelled as a time-dependent distribution, that is as a distribution of distributions for which time-of-day is the primary parameter.

The perceptive reader will observe that the data tested for the Normal distribution fitted it much more comfortably than the data tested for the negative exponential. Pragmatically, there is no compelling theoretical reason why the behaviour of any particular sets of drivers should fulfil the underlying ‘independence of consecutive arrivals’ assumption of the negative exponential distribution. In any case the only times when the negative exponential assumption was totally unsustainable were when the mean inter-arrival time was high, that is in the night and early morning when there was no congestion anyway. It therefore did not matter too much which distribution was used to draw random arrival times from for such periods.

Model construction

Whereas an analysis of this situation could have been achieved using any of the modern software packages, SIMUL8 is the only one for which the client would have been prepared to pay for what is in his perception speculative software. Further, although SIMUL8 is not in itself object-oriented software, the object-oriented style of thinking which it imposes is both distinctive and influential in the rapid achievement of comprehensible models. Although a full technical description of the present model and its variants is not appropriate, Table 3 contains some fragments of the initial model, followed by some notes to support the above contention.

A model is conceived as an aggregate of objects such as Work Centres, Storage Bins, Distributions, Attributes etc, some of which are bound together as nodes in a routing network which is not normally shown as part of a Visual Interactive display. A work centre is an object where transformations are effected on work items, the time to do so being drawn from a distribution object. A work centre can batch work items together, or change them into another work item. It is possible that a resource object is required before any work can be carried out, and the work item may have to wait if one is not immediately available. Work centres can also assign or modify the values of attributes.

For Visual Interaction purposes work centres which correspond to major physical realities such as OFFLOAD stations (see Table 3) would be expected to appear in a simulation window. Some work centres might not correspond to any physical reality, for example if their role was simply to batch items or change attributes. Work centres of this sort can be thought of as dummy or ‘fictitious’ work Figures 3 to 8 show the effect of implementing the changes proposed earlier, singly and in combination.


Figure 2 : Graph of initial situation


Figure 3: Change 1 (no ext tanker wash)


Figure 4: Change 2 (stop all washing)


Figure 5 : Change 3 (even out ext i/a times)


Figure 6: Change 4 (even out all i/a times)


Figure 7 : Changes 1 and 3 combined


Figure 8: Changes 2 and 4 combined

The message of these graphs can be summarised by saying that whereas restricting washing facilities would make little difference to congestion, making tanker arrivals more equally spaced throughout the day would have a much larger effect, potentially halving the maximum number of tankers in the yard. The first of these observations was very pertinent to the company management, since it demonstrated that one of the proposed actions, namely that of denying washing facilities to the external tankers, would have done little or nothing to address the congestion problem but would have almost certainly cost some goodwill with the company’s contractors. The real way of addressing the problem would be to tackle the second issue, namely that of spacing out tanker arrivals more equally equal through the day. That this could be achieved by management directive is not at all obvious given the factor of driver culture, and such a goal could probably only be addressed by more subtle and less direct means.

Project summary

We do not claim in the above to present any significant new developments in simulation theory or practice in the research sense. What we believe we have demonstrated is that it is possible to obtain substantial simulation results within a 15 week time frame which included purchasing the software, observing company operations and abstracting what was important, selecting and statistically verifying best fitting distributions, constructing and modifying models, running these an extensive number of times, and producing a professionally polished report showing in words and graphs that what at the outset was a plausible solution to the problem would have made very little difference but possibly at a human relations cost. The growing power of PCs and the skill of software designers have made this sort of simulation affordable and practicable, thereby confounding previous perceptions of high initial outlay and costly model development times.

CHRISTINE CAMPBELL holds a BEng in Environmental Engineering from Strathclyde University and currently works in the OR Department of the Royal Bank of Scotland in Edinburgh. The case study described was conducted in the course of post-graduate studies at Strathclyde and Glasgow Caledonian Universities.

NORMAN THOMSON is an Honorary Lecturer at Strathclyde University, and prior to retirement worked as a staff statistician for IBM UK Hursley Laboratories and IBM UK manufacturing plant at Greenock

First published to members of the Operational Research Society in OR Insight July- September 1998