Project 3.1 ~ Total Resource Management
Mission

To develop a tactical decision-making framework for optimising profitability in a beef supply chain. For this project, the core of the supply chain is defined as the breeding, growing and finishing components of the beef industry.

Specific Objectives

·  Develop and implement a program to optimise some key management factors (such as mating dates, patterns of feeding and stock purchases) to maximise an objective function that includes consistent supply to retailers.

·  Extend development to optimise management at the individual-animal or subdivided cohort level.

·  Extent development to accommodate individual group member business autonomy.

·  Develop a framework useful for developing supply chain decision-support tools for other supply chains.

Progress

Required function of the TRM software

The problem scenario to be solved is as follows:

At any given stage, at any time of year, the members of the industry partner group (the Ebony Hills Quality Beef (EHQB) alliance) are faced with present and/or upcoming decisions on a range of management issues (stock purchase, stock movements, stocking rates, supplementary feeding, sending stock to feedlot, sending stock to slaughter, breed choice, sire choice, mating dates, use of genetic markers, drafting groups to target different market end points, etc.)

The planned function of the prototype was to address a good number of these issues in a tactical decision framework. What drives the recommendations is a function based largely on the need for consistent supply of the branded product, but also minimization of costs and handling of logistical constraints.

The result is a recommendation of actions to be taken now, and also actions to be taken in the future. We need to plan future actions, as the best thing to do now depends on what you think you will do in the future. However, the program is rerun frequently, such that planned actions change in the face of changing conditions – climatic, market, financial etc.

Structure of the problem tackled

The structure of the problem tackled relates to the Ebony Hills scenario. Reference to the figures in the results section may help.

Groups of cattle are referred to as lines. There are three types of line:

  1. Existing lines. These are the separately managed groups of cattle on each property, for example grouped by sex and year of birth.
  1. Future lines to be mated for on members’ properties
  1. Future lines of cattle to be bought in to help ensure consistency of supply

Management decisions are derived throughout a period (of say 2 years). These currently relate to the following:

·  Mating dates (for lines of type 2)

·  Levels of feeding when at pasture (this has still to be related to stocking rate and/or other management options)

·  Dates of transfer to feedlot

·  Projected dates of buying in extra lines of stock

·  Target body weights of extra lines of stock projected to be bought in

The predicted effect of these decisions on the components of an objective function are found. This function, described in more detail below, considers factors such as target body weight, food costs, and adherence to a targeted pattern of branded product supply over the period considered.

Components required

Animal Growth

We need to be able to predict the consequences of taking any set of management decisions. Central to this is prediction of the manner in which animals will be conceived and grow to eventually deliver product, as a function of the environment that we create for them.

This means we need a model of feeding and growth. We need to plan mating dates, and so this model must work sufficiently well from conception to maturity. No model with the required attributes could be found, so one was developed.

The model of Professor James Oltjen (University of California, Davis) had been used previously, as noted below, and in Bindon et al. (2001), but had some constraints that made it simply not workable for our task:

·  Unable to handle animals below about 130kg

·  Infinite growth rate upon infinite food offered means optimization can result in unrealistic recommendations

·  No distinguishing between animals of the same weight (say 200Kg) but different age (say 6 months versus a stunted 2yr old)

James Oltjen is developing a different model now because of some problems in the previous model, mostly in prediction of fat gain. This new model handles muscle and viscera as two separate protein pools. Mature size can now be varied. The new model is being designed and calibrated on the basis of sheep data, which provide more scope than available cattle data. This appears to be a ‘higher level’ model, that does not consider pools of DNA. The model will operate from zero weight, but when we invoked this, growth rate per day at conception was similar to maximal growth rate (about 400g/day). This may not be a problem for James’ objectives:

·  Better composition prediction for compensating cattle

·  Precisely track changes in composition as cattle near slaughter endpoint.

… but it is a considerable problem for the TRM project, which needs to model growth from conception. It is a problem that may come to be resolved. It is also possible that good performance of James’ model in relation to his objectives above could mean seeking permission to use it in specific roles in older animals nearer to slaughter age.

In the meantime the BK model continues to be used to underpin prototype code, as reported on below. A number of models are now being calibrated against CRCI and other data by PhD student Brad Walmsley.

Pasture growth

Various models of pasture growth have been considered, and work on one of these, from Joyce Macala has been taken up for prototyping purposes. However, the SGS model of Ian Johnson, which was used in project TRM.002, looks most promising for production use.

Before that time, the strategy under consideration is to calibrate the feed input portion of the animal growth model according to the predictions of the member producers on what growth is expected of the prevailing cattle under favourable, neutral and unfavorable conditions. This will capture practitioner experience and give them more “ownership” of the final results/recommendations. The potential downside of course is lack of ability to make predictions of any value.

Drafting and re-constitution of groups

The prototype code developed by BK in 1999 gives an illustration of how we can split groups to help achieve adherence to multiple product end-points, or multiple contracts. Here is a brief example. (For more detail see: Bindon et al. 2001).

The introduction of drafting and group reconstitution is the subject of goal 2 (see Milestones, above).

The objective function

A solution to the prevailing problem is a set of decision recommendations (stock purchase, stock movements, stocking rates, etc, as mentioned above.)

However, the overall target of the program needs to be represented in a mathematical formulation or "objective function" that covers key component objectives. These can often be couched in monetary terms. Examples are food conversion efficiency, transport costs, product quality and, important for Ebony Hills, consistency of supply. For the prototype described here, there are 10 component objectives:

  1. FCE: Total growth across lines divided by total food eaten.
  2. Penalty for deviation from target weight achieved in each line.
  3. Penalty for deviation from target body fat achieved in each line (weighting fixed at zero so far, as prediction of fat is not reliable).
  4. Penalties for not making target weight within the time window considered
  5. Total cost (value) of pasture eaten across all lines
  6. Total cost of feedlot feed eaten across all lines
  7. Penalty for breaking a declared limit on funds available
  8. Scaled penalties for exceeding target production level on each day of the target period
  9. Scaled penalties for being below target production level on each day of the target period
  10. Quadratic penalty for deviation of each future line from its nearest ideal mating date.

Each of these components has a weighting that can be manipulated to adjust its influence on the outcome.

The task is to find the solution that gives the biggest value of this objective function, while not breaking any prevailing constraints such as quarantine barriers or numbers of animals available.

How much emphasis should we put on each component in the objective function? There are two approaches to this:

  1. Calculate appropriate weighting values for each component. This is easy for things like feed costs, which relate simply to profit, but more difficult for consistency (8 and 9 above) or mating dates.
  1. Discover appropriate weighting values for each component. For different values of objective function weightings, an optimal solution is found, as described later, with corresponding results for each component of the objective. Graphing these results aids in choosing the most appropriate outcome for the prevailing problem, together with the corresponding weightings.

An economically rational framework to optimize the whole supply chain, including all technical logistical and cost issues, does not really exist. This is what leads to the desired outcomes approach. However, we can aim for good scientific and economic balance between issues or groups of issues for which rational comparisons can be made. For example, there is value in using economically rational treatment of feed costs, transport costs, and stock purchase costs, yet treat supply consistency and engineering of low management requirement over Xmas as desired outcome components. This means adopting a mixture of 1 and 2 above.

Experience with TGRM shows that such a mix of "desired outcomes" and “economically rational” approaches works well for complex problems, and is readily identified with by practitioners.

Finding good solutions (optional reading)

For a given objective function, with set values of weighting factors, the optimal solution was found using an evolutionary algorithm (EA). These algorithms are simple, and yet they can solve very complex problems. The manner in which they work can be readily understood by analogy with biological evolution (Kinghorn et al. 2002):

"In the evolution of life, DNA of a given configuration can express its fitness through the performance of the organism that hosts it. It is not necessary to calculate what is the best configuration of DNA – this can be evolved through expressions of fitness and a system of breeding. Evolutionary and genetic algorithms do the same thing. It is not necessary to calculate what is the best configuration of input parameters – these can be evolved through expressions of fitness (value on an objective function) and a system of breeding (better solutions being selected as parents, to mix and pass on their attributes at random)."

The specific method used was Differential Evolution (DE). As DE is a widely applicable method of general utility for optimization, the reader is directed to (Price and Storn 1997) for detailed description and example computer code. A mere outline of the concept is given here:

A population of candidate solutions is established. Each population member is constituted by a possible set of parameters (in this case, an 8 X 8 matrix of numbers of mating pairs saved, as shown in tables 4 and 5) and is characterized by its fitness (its value on the prevailing objective function).

For each population member, a challenger is constructed. If this challenger has superior fitness, it will replace the population member in the next generation. A challenger is constructed as follows:

Three other population members are chosen at random. We can label these as a, b and c. Each parameter is then addressed in turn. With probability CR, the parameter is simply adopted from the population member that the challenger is challenging. Otherwise, a new parameter value is constructed as the value for member a plus F times the difference of the values for b and c.

Successful challengers replace their respective population members, and, together with surviving members constitute a new generation with higher mean fitness. The process continues over sufficient generations to achieve convergence close to an optimal solution, with the most fit solution being chosen.

One reason that DE works well is that mutation is driven by differences between parameter values of contemporary population members, giving appropriate reduction in magnitude as convergence is approached. If needed, F and CR can be tuned to give fast convergence for the prevailing problem. For the current application, mutation independent of population differences was invoked with a low probability at any instance, to give added security against convergence at local optima.

Problem representation (optional reading)

Some decision areas are complex due to the interactions that they involve. For example, consider migrating animals between management groups to help target “peas in a pod” delivery of consistent product (accounting for animal behaviour and costs!). The number of animals that can be migrated out of a group depends on migrations into that group, if limits on numbers per group are specified. This means that the problem has to be translated in to a simpler format for efficient optimization. This has been a major area of development in TGRM, where it is very difficult to perturb patterns of selection and mating without breaking logistical constraints.

These problems are overcome by development of a filtering mechanism, whereby a simple set of numbers (which the optimization engine operates on) is translated to a set of implementable actions, with no “illegal” sets of recommendations being created. In the case of mate selection across different herds in a practical setting, the filtering mechanism is complex. For problems tackled in the TRM code presented in this milestone, there has been no such complexity – but this will arise later with dynamic drafting.

Parameters in the model

In the example presented here, the number of parameters depends on the numbers of lines of cattle included. The parameters are specified here:

·  For each line a mating date is specified. For existing lines, this is fixed as the known (or estimated) date of conception. For lines to be mated for this is recommended mating date for each line. For lines to be bought in, this is used in conjunction with the projected date of buying in each line to specify the target mean age of stock to buy in at that time.

·  Levels of feeding when at pasture are specified, currently as a single value per line, for illustration. The simple treatment is to specify the proportion of ad libitum feed available, with limits of 0.6 to 0.9 currently applied.