Abstract
In this article two multi-stage stochastic linear programming models are developed, one applying the stochastic programming solver integrated by Lingo 17.0 optimization software that utilizes an approximation using an identical conditional sampling and Latin-hyper-square techniques to reduce the sample variance, associating the probability distributions to normal distributions with defined mean and standard deviation; and a second proposed model with a discrete distribution with 3 values and their respective probabilities of occurrence. In both cases, a scenario tree is generated. The models developed are applied to an aggregate production plan (APP) for a furniture manufacturing company located in the state of Hidalgo, Mexico, which has important clients throughout the country. Production capacity and demand are defined as random variables of the model. The main purpose of this research is to determine a feasible solution to the aggregate production plan in a reasonable computational time. The developed models were compared and analyzed. Moreover, this work was complemented with a sensitivity analysis; varying the percentage of service level, also, varying the stochastic parameters (mean and standard deviation) to test how these variations impact in the solution and decision variables.
Highlights
Carrying out an aggregate plan is important in manufacturing industries, especially those where it is planned in periods of 3 to 18 months, or medium term
The main objective of this article is to develop a multi-state stochastic optimization model applied to an aggregate production plans (APP) of a local company, where the production periods are defined as the states, the randomness of production capacity and demand are modeled through a continuous probability distribution using the stochastic programming solver integrated by Lingo
The novelty of this work could be summarized in five points,1) this study provides a mathematical programming model that has been adapted for real needs of a company, which incorporates a service level constraint that it is not found in the literature, usually a confidence percentage is used
Summary
Carrying out an aggregate plan is important in manufacturing industries, especially those where it is planned in periods of 3 to 18 months, or medium term. The production plan seeks to determine the optimal levels of production, hiring, layoffs, inventories, subcontracting, etc. This work presents an aggregate plan that was made for a company that manufactures furniture in the State of Hidalgo. A first approach to the solution of the problem was made in [1]. Only the production capacity was considered as a random variable using two models, one with a continuous probability distribution and the other with a discrete one.
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