Outline Advanced Herd Management Course introduction Anders Ringgaard Kristensen Preconditions Outcome: What are you supposed to learn? The framework and definition of herd management The management cycle Objectives of production, utility theory Classical production theory Classical replacement theory Limitation of classical theories Outline of the course Teachers The concept of uncertainty Slide 1 Slide 2 Preconditions Courses Animal production: Husdyrproduktion Mathematics: Matematik og modeller / Matematik og planlægning Statistics Statistisk dataanalyse 2 Mandatory first year (economics etc) Brush-up courses The course will start up with brush-up courses of Probability calculus and statistics Linear algebra Slide 3 Slide 4 Learning outcome After attending the course students should be able to participate in the development and evaluation of new tools for management and control taking biological variation and observation uncertainty into account. Outcome - knowledge After completing the course the student should be able to: Describe the methods taught in the course Explain the limitations and strengths of the methods in relation to herd management problems. Give an overview of typical application areas of the methods. Slide 5 Slide 6 1
Outcome - skills After completing the course the student should be able to: Construct models to be used for monitoring and decision support in animal production at herd level. Apply the software tools used in the course. Outcome: Competencies: After completing the course the student should be able to: Evaluate methods, models and software tools for herd management. Transfer methods to other herd management problems than those discussed in the course. Interpret results produced by models and software tools. Slide 7 Slide 8 A pig (an animal) Pig production = N a pig? Medicine Medicine Meat Piglets Manure Meat Piglets Manure Feed Milk Feed Milk Slide 9 Slide 10 Pig production = N a pig? Medicine Pig production Pigs: Ages Groups Individuals Meat Piglets Manure Buildings Fields Neighbors, society, consumers Feed Milk Owner Slide 11 Slide 12 Feed Farm hands 2
Elements of production I The factors (input to production) Animals Feed Buildings, inventory Labor Management Veterinary services Energy Elements of production II Objectives: Maximization of the farmer s welfare: Income (personal) Leisure time (personal) Animal welfare (animals) Working conditions (farm hands) Environmental preservation (future generations) Prestige (personal) Product quality (consumers) Slide 13 Slide 14 Elements of production III Constraints limiting production Physical (land, housing capacity, storage capacity) Economical (capital, prices) Legal (laws) Personal (skills, education) Definition of herd management Having discussed the three key elements: Factors (input to production) Objectives (farmer s welfare) Constraints (limitations) we are now able to define what we mean by Herd Management: Herd management is a discipline serving the purpose of concurrently ensuring that the factors are combined in such a way that the welfare of the individual farmer is maximized subject to the constraints imposed on his production. A dynamic optimization problem under constraints. Decisions! We decide how to combine the factors. Slide 15 Slide 16 The management cycle: A never ending story The management cycle: Classical theories Utility Theory, Ch. 3. (Scarce Resources) Basic Production Monitoring, Ch. 5. Neo-classical Production Theory, Ch. 4. (Animal science, Production function) Slide 17 Slide 18 3
Slide 6 Herd Management Science Utility theory Basic level: As we define the basic level, it consists of Utility theory Neo-classical production theory Basic production monitoring (Animal nutrition, animal breeding, ethology, farm buildings) What any animal scientist should know about management The starting level of this course Briefly revised today We need a criterion for comparison of plans ( ways to produce). Several concerns: The farmer The staff Consumers The animals Environment Who decides the weighting? My answer: The farmer! Farm buildings Land Feed Animals Neighbors, society, consumers Farm hands Owner Slide 19 Slide 20 Farmer s preferences The farmer has/defines a list of concerns: Own direct concerns: Income, u 1 Leisure time, u 2 Prestige, u 3... Indirect concerns (because he cares for others) Animal welfare, u 4 Working conditions, u 5 Environment, u 6 Product quality, u 7 The farmer knows/decides the weighting The items on the list (u 1, u 2,, u k ) are called attributes of the farmer s utility. When is something an attribute? When it directly influences the subjective welfare of the farmer. May NOT be an attribute: Average milk yield of cows Average daily gain of slaughter pigs Animal welfare, because animals at a high level of welfare also produce at a higher level. May be an attribute: Monetary gain Leisure time Animal welfare, if the farmer is willing to accept that it to some extent decreases the levels of other attributes. Slide 21 Slide 22 Consequences measured by attributes Aggregation of attributes: Utility function Stage Attribute 1 2 T 1 u 11 u 12 u 1T 2 u 11 u 22 u 2T The utility function Aggregation over time Monetary gain Animal welfare Aggregation over attributes k u 11 u k2 u kt At any stage, the attributes will depend on the production Y t and the factors x t. The relation is given by the attribute function h: Expected Utility Theorem: Maximization of U is all we need to care about! Refer to Chapter 3 for details! Slide 23 u t = h(y t, x t ) Slide 24 4
Production function Production function In classical production theory, the uncertainty represented by the e s is ignored. Slide 25 Slide 26 Neo-classical production theory Answers 3 basic questions: What to produce. How to produce. How much to produce. Marginal considerations Basic principle: Continue as long as the marginal revenue, MR, exceeds marginal costs, MC. At optimum we have MR = MC. How much to produce One factor x and one product y Prices p x and p y A production function y = f(x). Profit u(x) = yp y xp x = f(x)p y xp x Problem: Find the factor level that maximizes the profit Slide 27 Slide 28 How much to produce How much to produce Maximum profit where u (x) = 0. u(x) = f(x)p y xp x u (x) = f (x)p y p x u (x) = 0 f (x)p y = p x Maximum profit where: Marginal revenue = Marginal cost! 1 0,8 0,6 0,4 0,2 Total revenue, f(x)p y Average revenue, f(x)p y /x 0-0,2 Marginal revenue, f (x)p y Slide 29 Slide 30 5
How much to produce, optimum How much to produce, logical bounds 1 1 0,8 Total revenue, f(x)p y 0,8 Total revenue, f(x)p y 0,6 0,6 0,4 0,4 0,2 Average revenue, f(x)p y /x 0,2 Average revenue, f(x)p y /x 0 0 Price of factor p x -0,2 Marginal revenue, f (x)p y -0,2 Marginal revenue, f (x)p y Slide 31 Slide 32 Classical replacement theory The replacement problem in a broad sense is one of the most important decision problems in animal production. Dynamics: What we decide at this stage (keep/replace) may influence production in many future stages. Many other decision problems relate to the replacement problem: Insemination Treatment for diseases Feeding level A correct handling of the other problems implies that the question of replacement must be taken into account. Definition Replacement: When an existing asset is substituted by a new one with (more or less) the same function. Examples: Light bulbs Cars Sows Milking robots Slide 33 Slide 34 Replacement problems in animal production Female production animals: (Ewes, mink, goats) Sows Dairy cows Two levels: Optimal lactation to replace Optimal stage of lactation to replace Repeatability of milk yield over lactation rather high (as opposed to litter size in sows). Replacement problems in animal production Technical: Examples: Farm buildings Equipment & machinery Very similar to the sow replacement problem, except for the biological variation Technological improvements probably more important than the corresponding genetic improvement in cows. Marginal/average considerations apply well Slide 35 Slide 36 6
Replacement problems in animal production A chain of assets Slaughter calves: If housing capacity is limited and replacements are available, the problem is in agreement with classical theory. Marginal/average considerations Slaughter pigs: Two levels: When to deliver individual pigs (animal level) When to deliver the remaining pigs (batch level) Broilers: At batch level (no animal level) in agreement with classical theory. Contracts may limit the decisions of the farmer Asset 1 t r Asset 2 Asset 3 How do we determine an optimal value for t r - the length of the period to keep each asset in the chain? Asset n Slide 37 Slide 38 Optimal time for replacement Assume that the price of a new asset is S The salvage value of the asset at time t is s t The net returns from the asset in stage (time step) t is r t The total net revenue T(t) from the asset if it is replaced at stage t is then Optimal time for replacement Average net revenue, if replaced at time t: Marginal net revenue at time t Optimal replacement time where Slide 39 Replace where: marginal revenue = average revenue Slide 40 Graphical illustration Marginal revenue 300 200 The replacement problem Typically decreasing because of decreasing productivity and increasing maintenance costs. The net returns adjusted for change in salvage value. The marginal curve crosses the average curve where the average is maximal. Revenue 100 0 0 5 10 15 20-100 -200 Time Marginal Average Slide 41 Slide 42 7
Limitations of neo-classical theory Static approach: Immediate adjustment Only one time stage Deterministic approach Ignores risk Biological variation Price uncertainty Knowledge representation (knowledge considered as certain): Unobservable traits Production functions Detached from production: No information flow from observations. No updating of knowledge. Limitations of classical replacement theory Uncertainty: The classical replacement theory assumes full certainty about the marginal profit function, the investment costs and all prices. As discussed in details in Chapter 2, uncertainty is an inherit property of the decision making process in herd management. The uncertainty is partly a consequence of imperfect knowledge, and partly of random variation. Uniqueness: The general theory implicitly assumes that the marginal and average profit functions are as shown in Figure 4.5 with a uniquely determined intersection. For several applications the intersection is not unique. This is, for instance, the situation in dairy cows, where the average and marginal profits are as shown in Figure 4.7. Availability: The theory assumes that a new asset for replacement is always available. Slide 43 Slide 44 Background for course Structural development in the sector Increasing herd sizes Decreasing labour input Technological development Sensors, automatic registrations Computer power Networking Methodological development Statistical methods Operations Research Outline of course - I Part I: Brush-up course on Probability calculus and statistics Linear algebra Advanced topics from statistics Basic production monitoring Registrations and key figures Analysis of production results Slide 45 Slide 46 Outline of course - II Part II: The problems to be solved From registrations to information, value of information, information as a factor, sources of information Decisions and strategies, definition and knowledge foundation Consequences of decisions and states Visualisation and user interfaces Outline of course - III Part III: The methods to be used State of factors Monitoring and data filtering Bayesian networks Decision support Decision graphs Simulation (Monte Carlo) Linear programming (low priority) Markov decision processes (dynamic programming) Mandatory reports Slide 47 Slide 48 8
Teachers Anders Ringgaard Kristensen Cécile Cornou Mandatory reports 4 minor reports must be handed in Based on the exercises At least 3 must be approved in order to attend the oral exam The 4 reports are distributed over the following methods: Bayesian networks Monitoring and data filtering Linear programming Markov decision processes Slide 49 Slide 50 The web Absalon Home page of the course http://www.prodstyr.ihh.kvl.dk/vp/ Course description Plan Pages for each lesson with a description of the contents, literature, exercises, software to use etc. Exercise, uncertainty Production function: f ( x, x, x ) = 1 2 3 2 2 2 c x + c x + c x + c x + c x + c x + c x x + c x x + c x x 11 1 22 2 33 3 1 1 2 2 3 3 12 1 2 13 1 3 23 2 3 - milk yield given energy, protein and fat Adding uncertainty, the actual milk yield is Y = f(x 1,x 2,x 3 ) + e Slide 51 Slide 52 Uncertainty, II Uncertainty - III Adding uncertainty to production function: Considerable improvement, BUT Significant uncertainty about true energy, protein and fat content still ignored Example, only considering energy Silage obs.* Silage true Ration Milk yield* Concentr.* Herd size* True energy content of silage is unknown The precision of the observed content depends heavily on the observation method (standard value from table, laboratory analysis etc.) Slide 53 Slide 54 9
Uncertainty - IV Effects of decisions will be over-estimated if uncertainty about true state factor characteristics factor effects is ignored. Wrong decisions may be made. Uncertainty, V Baysian networks with decisions and utilities added (student project). Silage obs.* Method Silage true Concentr.* Ration Herd size* Milk yield* Price Mix Cost Rev. Slide 55 Slide 56 Uncertainty - VI Uncertainty is not the opposite of knowledge Uncertainty is a property of knowledge Reduction of uncertainty is often possible at some cost! Reducing uncertainty is not always profitable. Slide 57 10