Abstract: Synthetic methods for lactone-containing compounds such as the discodermolides are provided, as are compounds which mimic the chemical and/or biological activity thereof, and methods and intermediates useful in their preparation.

Abstract: Synthetic methods for lactone-containing compounds such as the discodermolides are provided, as are compounds which mimic the chemical and/or biological activity thereof, and methods and intermediates useful in their preparation.

Abstract: A method and system for generating an optimized solution for assigning traffic loads to channels in SONET rings in cooperation with a computer having sufficient memory. The method and system utilize a Mixed Integer Program (MIP) having corresponding variables necessary to model the cost of Terminal Multiplexers, Add/Drop Multiplexers and corresponding interface ports necessary to route the desired traffic loads. By routing traffic loads to reduce computation time and imposing mathematical bounds on the MIP variables, the number of possible MIP solutions is reduced. The Mixed Integer Program is minimized in accordance with the traffic routing and imposed mathematical bounds such that an electrical signal is generated which corresponds to the optimized traffic load assignment information. The signal is converted to digital format whereupon it may be retrieved from computer memory and displayed to the user.

Abstract: An improved method and system for translating an optimization problem for use in efficient resource allocation. The improved method of the present invention includes the step of generating an index link record for each of the index variables in the optimization problem so as to eliminate the need for a symbol table and a plurality of temporary data records. The method also includes the step of linking the index link records of the index variables requiring expansion in a reverse order of the order listed in the optimization problem so as to reduce the number of traversals performed during expansion processing. The index link records have a pointer for identifying the next index variable requiring expansion.

Abstract: Methods and systems of traffic routing in a circuit switched communication network having a plurality of switches and a plurality of trunk groups connecting the switches are disclosed. The methods include a step of determining a set of alternate routing paths for each of a plurality of ordered pairs of the switches, wherein the number of alternate routing paths through each of the trunk groups is constrained to be less than a corresponding first predetermined threshold. In one embodiment, the alternate routing paths are determined by computing a solution to a predetermined integer programming problem. In another embodiment, a heuristic technique is used to determine the alternate routing paths.

Abstract: A method for generating an optimized solution for assigning traffic loads to channels in SONET rings in cooperation with a computer having sufficient memory. The method utilizes a Mixed Integer Program (MIP) having corresponding variables necessary to model the cost of Terminal Multiplexers, Add/Drop Multiplexers and corresponding interface ports necessary to route the desired traffic loads. By routing traffic loads to reduce computation time and imposing mathematical bounds on the MIP variables, the number of possible MIP solutions is reduced. The Mixed integer Program is minimized in accordance with the traffic routing and imposed mathematical bounds such that an electrical signal is generated which corresponds to the optimized traffic load assignment information. The signal is converted to digital format whereupon it may be retrieved from computer memory and displayed to the user.

Abstract: A method is disclosed for use in cooperation with a computer having memory in a Synchronous Optical Network (SONET) for generating an optimized transition plan for the placement of Self-Healing Rings (SHR) and the routing of point-to-point demand in accordance with projected customer demand over a selected multi-period time interval. By determining the number of nodes within a SONET, the demand therebetween over selected time interval as well as the discounted add-drop cost for a plurality of selected Add-Drop Multiplexers (ADMs), a set of logical rings as well as a set of physical rings and detailed routing information may be obtained and graphically illustrated. Logical rings may be determined by optimizing discounted fixed and interconnection costs for the plurality of ADMs in accordance with a selected mixed integer program to generate a corresponding electrical signal for receipt by the computer memory.

Abstract: A method and system is provided for use in cooperation with a computer having a memory for generating an optimized transition plan for the placement and interconnection of carrier hubs in a local access network having a plurality of Central Offices (COs), Serving Wire Centers (SWCs) and Point-of-Presence (POP) exchange carriers such that calls may be routed at least cost. In operation, the total number and location of existing SWCs within the network must be determined along with the total switched and special access demand. Thereafter, known tariff rates for selected channel terminals, transport channels and multiplexers must be determined along with the total number of DS3 lines from each SWC to its corresponding POP. By expressing determined network demand as selected mixed-integer program decision variables and determining a corresponding set of logical constraints consistent with these decision variables, the optimized placement of hubs within the local access network may be determined.

Abstract: An improved logistics planning method and system for recommending optimal order quantities and timing, choice of vendor locations and storage locations, and transportation modes, for individual items and for product families. The system is designed for use in cooperation with the computer having memory and incorporates item, customer, supplier, and routing information databases. In operation, the item, customer and supplier databases are accessed in order to provide customer and warehouse demand forecasts. The routing and customer databases are similarly accessed to provide transportation cost forecasts necessary to determine optimized routing modes for selected items, customers and suppliers. The demand and transportation costs are processed in accordance with a dynamic programming model to determine stock and non-stock order/shipment solutions for the selected items and customers, including optimized supplier and routing selection, order timing and quantity.