Abstract
This paper focuses on the development of a bilevel optimization model with random coefficients for a production-inventory system. The expected value operator technique is used to deal with the objective function, and rough approximation is applied to convert the stochastic constraint into a crisp constraint. Then an interactive programming method and genetic algorithm are utilized to solve the crisp model. Finally, an application is given to show the efficiency of the proposed model and approaches in solving the problem.
Highlights
Production and inventory controls are a complex problem, as these two systems are affected by the number of producers and retailers, as well as the level of customer’s demand
From the retailer’s view, this system is a bilevel programming problem, where the upper level has the objective of achieving maximum profit, while the lower level has the objective of controlling supplier’s production costs
We have discussed a bilevel programming model with random coefficients and its application to productioninventory systems. We converted it into a crisp model using an expected value operator and rough approximation
Summary
Production and inventory controls are a complex problem, as these two systems are affected by the number of producers and retailers, as well as the level of customer’s demand. (ii) Methods based on Kuhn-Tucker conditions: these methods apply Kuhn-Tucker to deal with the following levels and convert the multilevel model into the single level. This is referred to in [20, 21]. This paper applies an interactive programming technique to convert the bilevel model into a single-level and uses genetic algorithm to solve the complicated nonlinear programming problem.
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