OPTIMIZING THE OUTPUT OF PRODUCT BATCHES AND INTENSITY OF THEIR MANUFACTURE UNDER RANDOM DEMAND

The problem of optimizing the output of multi-product batch and the intensities of its items manufacture in the production line over a number of time intervals is considered. The line has a linearly ordered multiple positions without buffers. Workpieces of the input sequence composed of cyclically repeated identical subsequences (batches) are processed consecutively one by one in each working position in the order of their location in the line. Only a single workpiece is disposed in each position at each time point. The operation of the line consists of takts of simultaneous processing of all workpieces located in respective positions by the sets of tools corresponding to workpieces and positions. The composition of a batch does not vary from interval to interval. The ranges of possible demand quantities for each product and the probability distribution of the demand in these ranges are assumed known for each time interval. The sum of manufacturing cost, costs of storage and/or penalties for unmet demand on products is used as objective function. Manufacturing cost depends on processing intensities to be defined and increases with an increase in the number of batches produced in the current interval. Storage cost of unclaimed product units as well as penalty for product units not supplied to the customer do not decrease with the increase of number of such units. A two-level decomposition method for solving the problem based on the ideas of multi-step optimization is proposed.

batch of products, lot size, processing intensity, random demand, cost minimization, decomposition method

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