Optimal harvesting strategies for a multi-cycle and multi-pond shrimp operation: A practical network model

Abstract

In this paper, we introduce a network formulation of the optimal scheduling model for a multi-cycle and multi-pond shrimp operation grounded on the original optimal harvesting theory for a single production unit. The optimal schedule comprises the harvesting and restocking time that maximizes total profit throughout the planning horizon, bounded by the underlying biological and economic conditions. The model takes into account the information such as harvest size distribution, seasonality of price, temperature and weight-dependent growth, and labor force and market demand constraints. We applied the model to an existing shrimp operation in Hawaii with 40 one-acre ponds and generated the optimal schedule for a year that maximizes overall production. The model schedule is found to be able to increase total production by 5% when compared to the schedule generated using an “educated” trial-and-error procedure currently practiced by this operation. Further insights for this multi-cycle and multi-pond scheduling problem were also generated through several alternate simulations. It is found that labor force and market demand constraints are the key factors in scheduling multi-cycle and multi-pond shrimp operations.

Introduction

The problem of determining the optimal harvest size of farmed fish has first been analyzed and modeled by Bjorndal [2] using an optimal control framework for salmon culture. Arnason [1], Heaps [8], [9], and Hean [7] have extended this model to include optimal feeding schedule, density-dependent growth and mortality and potential culling, and release cost, respectively. Cacho et al. [3] have applied a similar analytical framework to identify the feeding strategies of catfish culture. Springborn et al. [18] have analyzed the optimum harvest time for cultured Nile tilapia using a similar framework. Leung et al. [14] have also employed a similar framework to identify the optimal harvest age for giant clam culture. Recently, Pascoe et al. [15] have applied a similar framework to identify the optimal harvest time for sea bream and tiger prawn. Forsberg [4], [5] has proposed an alternative multi-period linear programming approach to model explicitly the size-structure of farmed fish in determining the optimal stocking and harvesting schedules.

In terms of applications to crustaceans, Leung and Shang [12] have applied Markov process and dynamic programming to model the stocking and harvesting decisions for freshwater prawns. Karp et al. [11] have also applied dynamic programming to determine the optimal stocking and harvesting rates of shrimp in the Southwest U.S. Hochman et al. [10] and Leung et al. [13] have extended the stochastic growing inventory framework to marine shrimp culture for the purpose of identifying the optimal stocking and harvesting schedules. Tian et al. [20] have evaluated the implications of using different shrimp growth functions on optimal harvest size. Purwanto [16] has developed a set of linear and non-linear programming models for optimizing the economic benefits from shrimp farming in Australia and West Java, Indonesia. Tian et al. [19] have also developed a computer simulation model to analyze the economics of shrimp production under different stocking regimes, harvesting schedules and farm sizes.

While the previous research mentioned above has provided the theoretical foundation to model optimal harvesting decisions for finfish and shrimp culture, they are generally not readily applicable to commercial operations for the following reasons. First, most of the models described above used experimental data to model the growth process and they have been shown to differ widely from actual commercial operations. For example, the model by Leung et al. [13] was based on limited data from one growout cycle of marine shrimp in an experimental pond. Second, all of the models are designed primarily as a research inquiry tool rather than an operations management tool for on-farm applications. This is particularly true for the model by Leung et al. [13] where it has been used primarily to investigate the economics of controlled environment. Third, almost all of the models were developed for optimizing the harvest schedule of a single pond or production unit. While it is certainly important to derive and understand the essence of the optimal harvest schedule of a single pond, it is essential to extend this framework into a whole farm setting whereby all the ponds or production units are scheduled in an optimal manner to smooth out production so as to satisfy the labor force and market demand constraints. Against this background, the purpose of this research is to develop, test and operationalize a management model that takes into account the multi-cycle and multi-pond nature of most commercial shrimp farms in order to solve for the optimal growout production schedule of the entire farm.

The paper is organized as follows: Section 2 presents the mathematical representation of the optimal scheduling problem and introduces the underlying biological and economic functions. Section 3 provides the network representation of the optimal scheduling model that is equivalent to the otherwise unsolvable mathematical formulation. Section 4 applies the network model to an existing shrimp farming entity with 40 growout ponds to generate the optimal schedule for a year. Section 5 discusses the results of the optimal scheduling and implications from several alternate simulations. Section 6 concludes the paper.