Set Of Optimization Models Research Articles

Manufacturer cooperation in supplier development under risk

Supplier development involves efforts undertaken by manufacturing firms to improve their suppliers’ capabilities and performance. These improvement efforts can be targeted at a variety of areas such as quality management, product development, and cost reduction. Since supplier development requires investments on the part of the manufacturer, it is important to optimally allocate investment dollars among multiple suppliers to minimize risk while maintaining an acceptable level of return. This paper presents a set of optimization models that address this issue. We consider two scenarios: single-manufacturer and multiple suppliers (SMMS) and two-manufacturer and multiple suppliers (TMMS). In the SMMS case, we suggest optimal investments in various suppliers by effectively considering risk and return. The TMMS case investigates whether manufacturers with differing capabilities could gain risk reduction benefits from cooperating with each other in supplier development. Through illustrative applications, we identify conditions in which both cooperation and non-cooperation are beneficial for manufacturers. Under conditions of cooperation, we propose optimal investments for manufacturers to achieve high levels of risk reduction benefits.

Tidal and subtidal flow patterns on a tropical continental shelf semi‐insulated by coral reefs

The present study sets out to describe the tidal and subtidal water motion at the Berau coastal shelf, which represents a tropical continental shelf area of variable width hosting a complex of barrier reefs along its oceanic edge. Moored and shipboard measurements on currents and turbulence were made as part of the multidisciplinary East Kalimantan Research Program. These results and collected data on sea levels, meteorology and bathymetry, were used to setup and calibrate a three‐dimensional barotropic hydrodynamic model in the ECOMSED environment, which is derived from the Princeton Ocean Model. Concurrent profile measurements of flow velocity and Reynolds stress with an acoustic Doppler current profiler were used to infer values of the drag coefficient on locations on the shelf and within the barrier reef environment. The drag coefficients determined from shelf measurements differed less than 20% from optimal model settings. Diurnal and semidiurnal tides have the same character, propagating across the isobaths with amplitudes that increase toward the coast. The tidal amplification is captured in a one‐dimensional model, revealing an analogy with the Amazon Shelf. Regarding the subtidal depth‐mean flow, tidal Eulerian residual currents dominate over monsoon‐driven currents. Lagrangian mean flows reveal freshwater pathways from the coast to the coral reef environment. At a regional scale, the reef complex is established to be semitransparent to tides. The barrier reef influences the tidal phases rather than the amplitudes, especially in the shelf region that is fringed by the reefs. This may explain why tidal phases predicted from hydrodynamic models of tropical continental shelves often feature substantial discrepancies from observations.

Time Budgets and Territory Size: Some Simultaneous Optimization Models for Energy Maximizers

A set of optimization models in two variables of choice, territory size and time spent patrolling for intruders, is presented for energy maximizers. Models vary in the curvilinearity of the relationship between territory circumference and both intrusion rate and cost of expelling a single intruder. Models are analyzed both with and without constraints; constraints are on processing rate and on the time spent patrolling, feeding and actively defending. The models all include the concept of “intruder equilibrium,” an equilibrial density of intruders in a territory resulting from a balance between intrusion rate and expulsion by the defender. This equilibrial density can be considered a measure of territorial exclusiveness. The two-variable models predict effects on territory size and patrol time of variation in food density, intrusion rate, costs of expelling a single intruder in energy and time, food-consumption rate of an intruder, area of detection while patrolling, total time available for territorial and feeding activities, time to eat a unit of food energy, energy cost of patrol per time, and processing-rate capacity. With increasing intruder rate, optimal territory size usually decreases, whereas optimal patrol time behaves much more irregularly. With increasing food density, optimal patrol time usually decreases, whereas optimal territory size behaves irregularly. In particular, when intrusion rate and expulsion costs accelerate sufficiently with increasing territory size and no constraints exist, the higher the food density the smaller the optimal territory size. When food density is large enough for a constraint to be effective, the opposite relation can hold and will always hold for a processing constraint. When a particular parameter changes, optimal territory size and optimal patrol time may covary or one may increase while the other decreases, depending on the parameter and model. A new set of one-variable models is suggested by the two-variable models; models optimizing patrol time while holding territory size constant could correspond to a tightly packed system of territories initially determined by settlement patterns. A unified onevariable analysis suggests that how food density affects territory size when patrol time is constant depends upon whether a constraint is operating: Provided that invasion rate does not vary with density of intruders on the territory, time minimizers and constrained energy maximizers decrease territory size with increasing food density; unconstrained energy maximizers do the opposite. The addition of a second optimization variable to a one-variable model can change qualitative predictions about variation in particular parameters ( e.g. , food density) and can increase the number of parameters predicted to affect optimal territory size and patrol time.