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.

Comparison of snail density, standing stock, and body size between Caribbean karst wetlands and other freshwater ecosystems

Synthesizing data from multiple studies generates hypotheses about factors that affect the distribution and abundance of species among ecosystems. Snails are dominant herbivores in many freshwater ecosystems, but there is no comprehensive review of snail density, standing stock, or body size among freshwater ecosystems. We compile data on snail density and standing stock, estimate body size with their quotient, and discuss the major pattern that emerges. We report data from 215 freshwater ecosystems taken from 88 studies that we placed into nine categories. Sixty-five studies reported density, seven reported standing stock, and 16 reported both. Despite the breadth of studies, spatial and temporal sampling scales were limited. Researchers used 25 different sampling devices ranging in area from 0.0015 to 2.5 m2. Most ecosystem categories had similar snail densities, standing stocks, and body sizes suggesting snails shared a similar function among ecosystems. Caribbean karst wetlands were a striking exception with much lower density and standing stock, but large body size. Disparity in body size results from the presence of ampullariids in Caribbean karst wetlands suggesting that biogeography affects the distribution of taxa, and in this case size, among aquatic ecosystems. We propose that resource quality explains the disparity in density and standing stock between Caribbean karst wetlands and other categories. Periphyton in Caribbean karst wetlands has high carbon-to-phosphorous ratios and defensive characteristics that inhibit grazers. Unlike many freshwater ecosystems where snails are key grazers, we hypothesize that a microbial loop captures much of the primary production in Caribbean karst wetlands.