A LINEAR PROGRAMMING TO PLANNING PRODUCTION IN SWINE FARM Sara V. Rodríguez, Luis M. Plá Departament of Mathematics, University of Lleida, Spain Victor Albornoz Departament of Industrias, Universidad Técnica Federico Santa María, Chile
Outline 1. Introduction - Overview of swine industry - Swine production system - Literature review 2. Description problem - Lifespand of the sow - Reproductive cycle 3. Linear programming model - Formulation of the problem - Numerical test - Sensitivity analysis - Dealing with the weakness of LP - Stochastic model extension 4. Further research and conclusions
Introduction Description problem LP model Stochastic programming Further research Overview to Swine Industry Probabilistic System UNCERTAINTY DECISION VARIABLES CONSTRAINTS
Introduction Description problem LP model Stochastic programming Further research Overview to Swine Industry In Europe the decreasing in the profit margin during the last years has motivated the use of operation reseach methods to make better decisions. PROFITABILITY MARGIN
Introduction Description problem LP model Stochastic programming Further research Swine Production System
Introduction Description problem LP model Stochastic programming Further research Danish Swine Production System
Introduction Description problem LP model Stochastic programming Further research Spanish Production System Slaugtherhouse
Introduction Description problem LP model Stochastic programming Further research Literature Review Pla, L.M., 2007. Review of mathematical models for sow herd management. Livestock Science 106, 107–119. • Simulation Models • Optimization Relevant aspects: • Strategic decisions • Infinite horizon • Dynamic Programming; Markov models
Introduction Description problem LP model Stochastic programming Further research SIMULATION MODELS • Allen, M.A., Stewart, T.S., 1983. A simulation model for a swine breeding unit producing feeder pigs. Agricultural Systems 10, 193–211. • Marsh, W.E., 1986. Economic decision making on health and management livestock herds: examining complex problems through computer simulation. Ph.D. thesis, University of Minnesota, St. Paul. • Jalving, A.W., 1992. The possible role of existing models in on-farm decision support in dairy cattle and swine production. Livestock Production Science 31, 351–365. • Plà, L.M., Pomar, C., Pomar, J., 2003. A Markov decision sow model representing the productive lifespan of sows. Agricultural Systems76, 253–272.
Introduction Description problem LP model Stochastic programming Further research OPTIMIZATION MODELS • Dijkhuizen, A.A., Morris, R.S., Morrow, M., 1986. Economic optimisation of culling strategies in swine breeding herds, using the “PORKCHOP computer program”. Preventive Veterinary Medicine 4, 341–353. • Huirne, R.B., Dijkhuizen, A.A., Van Beek, P., Hendriks, Th.H.B., 1993. Stochastic dynamic programming to support sow replacement decisions. European Journal of Operational Research 67, 161–171. • Kristensen, A.R., Søllested, T.A., 2004b. A sow replacement model using Bayesian updating in a three-level hierarchic Markov process II. Optimization model. Livestock Production Sciences 87, 25–36.
Introduction Description problem LP model Stochastic programming Further research Aim a) Formulate a linear optimization model. b) Formulate a linear stochastic extension. Linear Tactical Finite horizon decisions Stochastic two stage.
Introduction Description problem LP model Stochastic programming Further research Swo farm
Introduction Description problem LP model Stochastic programming Further research Swine Production System ENTRY CYCLE INSEMINATION LACTATION GESTATION NEXT CYCLE
Introduction Description problem LP model Stochastic programming Further research Identification of the problem • How many sows the farmer should replace? • How many sows the farmer should buy? • How many insemintions the farmer should accept? • What is the optimal cycle in which the sow should be replace? • What is the optimal reproductive state in which the sow should be replace?
Introduction Stochastic programming Further research Description problem LP model Linear Programming Model
Introduction Stochastic programming Further research Description problem LP model Linear Programming Model • Objective Function Max c T x s.a. Ax ≤ b • Constraints x ≥ 0 Reference Dantzig, G.B. y Thapa, M.N., 1996. Linear Programming. Introduction. Springer Series in Operations Research, Springer.
Introduction Stochastic programming Further research Description problem LP model PERIOD= WEEK I 1 INSEMINATION WEEK L L L L 1 2 3 4 LACTATION WEEK
Introduction Stochastic programming Further research Description problem LP model GESTATION GESTATION BREEDING- CONTROL G G ZR ZR ZR G r ={1,2,3} 15 16 1 2 3 4 k ={1,2,3} WEEK
Introduction Stochastic programming Further research Description problem LP model PERIOD= WEEK ZR G G L L L L Z 1 15 16 1 2 3 4 ZR G G L L L L Z 1 15 16 1 2 3 4
Introduction Stochastic programming Further research Description problem LP model C={1, 2, 3, ...} Set of number of cycles. Sg={1, 2, ..., 16} Set of number of gestation week Sl={1, 2, 3, 4} Set of number of lactation week T={1, ... 52} Set of periods Nr={1,..3} Set of repetitions of insemination Sr={1,..,3} Set of insemination waiting week α (t,c,g) = Survival rate of gestation of the period t , cycle c and gestation week g . β (t,c,r) = Survival rate of insemination of the period t , cycle c , waiting the reinsemination r . γ (t,c) = Number of weaned piglets at period t and cycle c .
Introduction Stochastic programming Further research Description problem LP model Y(t,c,l) Number of sows in lactation state at period t , cycle c, lactation week l . X(t,c,g) Number of sows in gestation state at period t , cycle c, gestation week g . Z(t,c) Number of sows in insemination state at period t , cycle c . ZR(t,c,r,k) Numer of sows in breedig-control state at period t , cycle c, waiting the reinsemination r, waiting week k. UL(t,c) Number of replaced sows at the end of lactation state. UZ(t,c,r) Number of replaced sows at the end of insemination state, waiting the reinsemination r.
Introduction Stochastic programming Further research Description problem LP model Objective Function ∑ ∑ ∑∑ ∑∑∑ ∑∑ γ + + + * * * * * rl Y ru UL ru UZ ru AB , , , , , , * t c t c , , t t c t t c r t t c t c l ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ t T c C t T c C t T c C r Nr t T c C
Introduction Stochastic programming Further research Description problem LP model Objective Function
Introduction Stochastic programming Further research Description problem LP model Objective Function BREEDING- GESTATION INSEMINATION LACTATION CONTROL ∑ ∑ ∑ ∑ ∑ ∑ + + * * rz Z rzr ZR rz t,1 , , , , , , , , t c t c t c k t c r k ∈ ∈ ∈ ∈ ∈ ∈ t T c C t T c C r Nr k Sr ∑ ∑ ∑ ∑ ∑ ∑ + * * rx X rl Y , , , , , , , , t c g t c g t c l t c l ∈ ∈ ∈ − ∈ ∈ ∈ t T c C g Sg Sr t T c C l Sl
Introduction Stochastic programming Further research Description problem LP model Objective Function ∑ ∑ ∑∑ ∑∑ ∑ ∑∑ γ + + + * * * * * rl Y ru UL ru UZ ru AB , , , , , , * t c t c t t c t t c r t t c , , t c l ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ t T c C t T c C t T c C r Nr t T c C ∑ ∑ ∑ ∑ ∑ ∑ + + * * rz Z rzr ZR , , , , , , , , t c t c t c k t c r k ∈ ∈ ∈ ∈ ∈ ∈ t T c C t T c C r Nr k Sr ∑ ∑ ∑ ∑ ∑ ∑ + * * rx X rl Y , , , , , , , , t c g t c g t c l t c l ∈ ∈ ∈ − ∈ ∈ ∈ t T c C g Sg Sr t T c C l Sl
Introduction Stochastic programming Further research Description problem LP model Constraints = ∈ − 0 { 1 } … ( 1 ) Z Z c C 1 , c c = ∈ ∈ ∈ 0 … ( 2 ) Z ZR r Nr k Sr c C 1 , , , , , c r k c r k = ∈ ∈ 0 … ( 3 ) X X g Sg c C 1 , , , c g c g = ∈ ∈ 0 … ( 4 ) Y Y l Sl c C 1 , , , c l c l
Introduction Stochastic programming Further research Description problem LP model LACTATION INSEMINATION 4 Z = − ∈ − ∈ − { 1 } { 1 } … ( 5 ) Z Y UL t T c C − − , 1 , 1 − − * t c 1 , 1 , t c t c l
Introduction Stochastic programming Further research Description problem LP model ZR ZR ZR Z 1 2 3 1- β (t,c,r) UR ZR ZR G ZR 1 2 3 = ∈ − ∈ { 1 } … ( 6 ) ZR Z t T c C − , , 1 , 1 1 , , t c t c = − β − ∈ − ∈ ∈ − ( 1 ) { 1 } { 1 } … ( 7 ) ZR ZR UZ t T c C r Nr − − − − − − , , , 1 1 , , 1 1 , , 1 , 3 1 , , 1 t c r t c r t c r t c r = ∈ − ∈ ∈ ∈ − { 1 } { 1 } … ( 8 ) ZR ZR t T c C r Nr k Sr − − , , , 1 , , , 1 t c r k t c r k
Recommend
More recommend
