A computational model to design plastic food packaging is proposed. The model minimizes the cost of the multi-layer structure satisfying the specific product requirements, using a heuristic optimization algorithm. The product requirements are defined by the expected shelf life, the storage conditions, the water sorption isotherms of foods and the maximum allowable gain or loss of gases (O2, CO2, N2, etc.) and moisture for the packaged food. In order to assure the food shelf life, these product requirements should be fulfilled to estimate the maximum permeance values of the plastic package. The computational algorithm automatically generates different multi-layer film structures that satisfy the product requirements. This algorithm combines different polymeric materials taking into account the barrier properties and cost of each layer, the compatibility between layers, the maximum number of layers and the minimum and maximum film thickness for each layer. Temperature and relative humidity corrections for the permeance calculations are considered.
Permeance calculations of several barrier films are compared with oxygen transmission rate (OTR) and water vapor transmission rate (WVTR) measurements. The optimization model algorithm is evaluated by means of standard numerical routines and numerical benchmarking.
RobertsonGL. Food packaging: Principles and practice, New York, NY: Marcel Dekker, 1993.
2.
Hernandez RJ, Selke SEM, and Culter JD. Plastics packaging: Properties, processing, applications, and regulations. Hanser Gardner Publishers, 2000.
3.
StoffersNH. Certified reference materials for food packaging specific migration tests: Development, validation and modelling, Wageningen, the Netherlands: Wageningen University, 2005.
4.
Solvay Plastics sector. Major markets in 2001. Looking at Solvay Differently, June 2002.
5.
Harte BR and Gray JI. The influence of packaging on product quality. In: Gray JI, Mils J and Harte BR (eds). Food product-package compatibility proceedings. : Technomic Publishing Co, 1987.
6.
RobertsonG. Food packaging: Principles and practice, Taylor & Francis/CRC Press, 2006.
7.
KulchanRBoonsupthipWSuppakulP. Shelf life prediction of packaged cassava-flour-based baked product by using empirical models and activation energy for water vapor permeance of polyolefin films. J Food Eng2010; 100: 461–467.
8.
CárdenasFCGiannuzziLZaritzkyNE. Mathematical modelling of microbial growth in ground beef from Argentina. Effect of lactic acid addition, temperature and packaging film. Meat Sci2008; 79: 509–520.
9.
Peychès-BachAMoutounetMPeyronS. Factors determining the transport coefficients of aroma compounds through polyethylene films. J Food Eng2009; 95: 45–53.
10.
PiringerOGBanerAL. Plastic packaging materials for food, Wiley, 2000.
11.
Van BreeIDe MeulenaerBSamapundoS. Predicting the headspace oxygen level due to oxygen permeability across multi-layer polymer packaging materials: A practical software simulation tool. Innov Food Sci Emerg Technol2010; 11: 511–519.
12.
Rodriguez-AguileraROliveiraJCMontanezJC. Mathematical modelling of the effect of gas composition and storage temperature on the gas exchange rate of soft cheese. J Food Eng2009; 95: 82–89.
13.
GenkawaTUchinobTMiyamotoS. Hamanaka. Development of mathematical model for simulating moisture content during the re-wetting of brown rice stored in film packaging. Biosyst Eng2008; 101: 445–451.
14.
ScheichlRKlopfferM-HBenjelloun-DabaghiZ. Permeability of gases in polymers: Parameter identification and nonlinear regression analysis. J Membr Sci2005; 254: 275–293.
15.
MastromatteoMDel NobileMA. A simple model to predict the oxygen transport properties of multi-layer films. J Food Eng2011; 102: 170–176.
16.
López ID, Estrada O, Noriega M del P, et al. Optimization model based on a heuristic method for barrier films design. In: ANTEC, 2005. Nashville: Society of Plastic Engineers.
17.
Noriega M, Estrada O and Vargas C. Design of plastic multi-layer structure that fit the requirements of a specific food or beverage. In: ANTEC, 2003, Nashville: Society of Plastic Engineers.
18.
Dennis JE and Lewis RM. A comparison of nonlinear programming approaches to an elliptic inverse problem and a new domain decomposition approach. CRPC-TR94468. Center for Research on Parallel Computation. Rice University, August 1994.
19.
AlottoPNerviMA. An efficient hybrid algorithm for the optimization of problems with several local minima. Int J Numer Methods Eng2001; 50(4): 847–868.
20.
WrigthMH. Interior methods for constrained optimization. Acta Numerica-1992, New York, NY: Cambridge University Press, pp. 341–407.
21.
Nelder JA and Mead R. A simplex method for function minimization. Comput J 1965: 7, New York, NY: Wiley.
22.
GabrieleGARagsdellKM. Large scale nonlinear programming using the generalized reduced gradient method. ASME J Mech Des1980; 102(3): 566–573.
23.
MintonSJohnstonMDPhilipsAB. Minimizing conflicts: A heuristic repair method for constraint satisfaction and scheduling problems. Artif Intell1992; 58: 161–205.
24.
DIN. Determination of water vapor transmission (density of moisture flow rate) of plastics films, elastomer films, paper, board and other sheet materials. DIN 53122, Part 2.
25.
DIN. Determining the gas transmission rate of plastic film, sheeting and mouldings by the carrier gas method. DIN 53380-3.
26.
ASTM Standards. Standard test methods for water vapor transmission of materials. ASTM E-96.
27.
ASTM Standards. Standard test method for oxygen gas transmission rate trough plastic film and sheeting using a coulometric sensor, ASTM D-3985-95.
28.
EVALCA. Gas barrier properties of resins. Technical Bulletin No. 110, 1996.
29.
Wah BW and Chen YX. Optimal anytime constrained simulated annealing for constrained global optimization. In: Sixth international conference on principles and practice of constraint programming, September 2000, Springer-Verlag.
30.
WahBWWangT. Simulated annealing with asymptotic convergence for nonlinear constrained global optimization. Principles and practice of constraint programming1999, pp. 461–475.
31.
JohnstonMJMintonS. Analyzing a heuristic strategy for constraint-satisfaction and scheduling. Intelligent scheduling, Morgan Kaufmann, 1994.
32.
Plastics Europe Market Research Group (PEMRG). Business data and charts, Bruselas: Association of Plastics Manufacturers, 2007.
33.
VernaudJMRoscaLD. Assessing food safety of polymer packaging, Rapra, 2006.
34.
PDL. Plastics and rubbers data collection. PDL Handbook Series, RoverTM Inside, 1997.
35.
KirkpatrickSGelattCDVecchiMP. Optimization by simulated annealing. Science1983; 220(4598): 671–680.
36.
IngberAL. Simulated annealing: Practice versus theory. J Math Comput Model1993; 18(11): 29–57.
Alexandrov NM. Multilevel and multiobjective optimization in multidisciplinary design. AIAA paper 96- 4122, 1996.
39.
AlexandrovNMDennisJEMultilevel algorithms for nonlinear optimization. In: BorggaardJBurkardtJGunzburgerMPetersonJ (eds). Optimal design and control, Birkhauser, 1994, pp. 1–22.
40.
CardosoMFSalcedoRLde AzevedoSF. Nonequilibrium simulated annealing: A faster approach to combinatorial minimization. Ind Eng Chem Res1994; 33: 1908–1918.
41.
FloudasCAPardalosPM. A collection of test problems for constrained global optimization algorithms, Lecture Notes in Computer Science, Vol. 55Springer-Verlag, 1990.
42.
AlexandrovNMDennisJE. A class of general trust-region multilevel algorithms for nonlinear optimization: Global convergence analysis. SIAM J Optim2000. (in revision).
