Mixed Integer Programming Solution Research Articles

A loading and dispatching problem in a random flexible manufacturing system

A scheduling problem in a flexible manufacturing system (FMS) is considered to be a composite of two interdependent tasks: loading and sequencing. Formulations are presented for the loading problem with two objectives: (i) minimization of the system workload unbalance, and (ii) minimization of system unbalance and the number of late jobs; including constraints such as the number of tools slots with duplications, unique job routing, nonsplitting of jobs and machine capacity. For both the objectives, heuristic methods are developed and performance is compared with the exact mixed integer programming solutions. A simulation model is developed for investigating the system performance for the problem of minimizing the system unbalance using heuristic and sequential loading methods in conjunction with four—FIFO, SPT, LPT and MOPR—dispatching rules.

Two Methods of Including the Extra-Caloric Effect of Fat in Minimum Cost Feed Formulations

The apparent metabolizable energy from fat appears to decrease as its level of usage increases. However, functional relationships of this type cannot be directly introduced into common minimum cost programming for use by industry. The data could be directly used in mixed integer programming models, but these are not readily available on industry computers. In this paper the observed relationship is transformed into a marginal energy function that can be used in ordinary linear programming by feed formulators and, furthermore, is equivalent to mixed integer programming solutions. Data from a function developed by Mateos and Sell (1980) from experiments with mature laying hens were introduced into the data bank of one of the largest broiler integrators. Methods and equivalence of solutions were demonstrated and, based on exact simulation of the firm's formulation, savings on the order of 2.00 dollars per ton, or one million dollars per year for the firm, were forecast by use of the marginal energy function. The reliability of this forecast is dependent on the confirmation of the Mateos and Sell function with other sources of fat and with broiler chickens.