Linking herbivory and pollination: Costs and selection implications in Centrosema virginianum Bentham (Fabaceae: Papilionoideae)

This research first evaluated levels and type of herbivory experienced by Centrosema virginianum plants in their native habitat and how florivory affected the pollinator activity. I found that populations of C. virginianum in two pine rockland habitat fragments experienced higher herbivory levels (15% and 22%) compared with plants in the protected study site (8.6%). I found that bees (Hymenoptera) pollinated butterfly pea. Furthermore, I found that florivores had a negative effect in the pollinators visitation rates and therefore in the seed set of the population. ^ I then conducted a study using a greenhouse population of C. virginianum. I applied artificial herbivory treatments: control, mild herbivory and severe herbivory. Flower size, pollen produced, ovules produced and seeds produced were negatively affected by herbivory. I did not find difference in nectar volume and quality by flowers among treatments. Surprisingly, severely damaged plants produced flowers with larger pollen than those from mildly damaged and undamaged plants. Results showed that plants tolerated mild and severe herbivory with 6% and 17% reduction of total fitness components, respectively. However, the investment of resources was not equisexual. ^ A comparison in the ability of siring seeds between large and small pollen was necessary to establish the biological consequence of size in pollen performance. I found that fruits produced an average of 18.7 ± 1.52 and 17.7 ± 1.50 from large and small pollen fertilization respectively. These findings supported a pollen number-size trade-off in plants under severe herbivory treatments. As far as I know, this result has not previously been reported. ^ Lastly, I tested how herbivory influenced seed abortion patterns in plants, examining how resources are allocated on different regions within fruits under artificial herbivory treatments. I found that self-fertilized fruits had greater seed abortion rates than cross-fertilized fruits. The proportion of seeds aborted was lower in the middle regions of the fruits in cross-fertilized fruits, producing more vigorous progeny. Self-fertilized fruits did not show patterns of seedling vigor. I also found that early abortion was higher closer to the peduncular end of the fruits. Position of seeds within fruits could be important in the seed dispersion mechanism characteristic of this species. ^

The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.