22 European Journal of Operational Research 40 (1989) 22-31 North-Holland Case Study Optimization of management plans with short and long run problems: The case of shrimp production A r y e S A D E H LUZ Industries lsrael, Science Based Industries Campus, 91079 Israel H o v a v T A L P A Z Department of Statistics, The Volcani Center, Bet Dagan, 50250 Israel D a v i d A. B E S S L E R and W a d e L. G R I F F I N Department of Agricultural Economics, Texas A &M University, College Station, TX 77843, U.S.A. Abstract: A management plan of continuous production is specified and optimized. An optimal control framework is used to solve for the decision variables. An economic interpretation of the optimality conditions is provided. The model is applied to the management of a shrimp pond. Results for different runs of the model are given and discussed. Keywords: Decision making, optimal control, shrimp Introduction Decision making processes are defined relative to the frequency of the underlying information signal. Even when a process, say of agricultural production, is continuousthe decision process as- sociated with it is discrete. The decision on irriga- tion scheduling of field crops, is taken at certain points of time by the farmer, though the irrigation This work is a result of a research program that was partially funded by the Texas Advanced Technology Research Program and by the Texas A&M University Sea Grant College Pro- gram, supported by the National Oceanic and Atmospheric Administration, Office of Sea Grant, U.S. Department of Commerce under Grant ~ NA85AA-D-SG128 with the Texas Agricultural Experiment Station. Received July 1987; revised March 1988 process itself and related biological processes are continuous. On the other hand, for analytical pur- poses, it is common to approximate discrete deci- sion processes by continuous functional forms. Decisions might be categorized as short run (tactical) and long run (strategic) within a plan- ning horizon. When considered for the same management plan, the first are approximated as continuous processes while the second as discrete processes, i.e. investment decisions versus mainte- nance decisions. The mixture of discrete and con- tfnuous decision processes makes optimization procedures such as dynamic programming dif- ficult to work with. This study solves a discrete decision problem, which is embedded within a continuous process. The case study is a management model for a one 0377-2217/89/$3.50 © 1989, Elsevier Science Publishers B.V. (North-Holland)