Abstract
A polymorphic uncertain linear programming (PULP) model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.
Highlights
For a manufacturer, a favorable production planning involves suitably forecasting the demand of products and translating the demand forecast into a plan of production that maximizes the enterprise’s profit or minimizes its cost
In [5], the production capacities and the customer demands are represented by interval numbers, respectively
In [2, 3], the customer demands, the prices of products, and the production capacities are described as fuzzy subsets
Summary
A favorable production planning involves suitably forecasting the demand of products and translating the demand forecast into a plan of production that maximizes the enterprise’s profit or minimizes its cost It has been viewed as a useful approach to formulate the production planning problem into an optimization model by constructing a function of profit or cost as the objective and employing some equalities and inequalities to describe the constraints in the process of production that include the limitations of production resources, the capacity, and the demand of customers. Since polymorphic uncertainty exists in production planning, different from the existent results, this paper intends to construct a polymorphic uncertain model for the generalized production planning problem, where the amount of production, the amount of inventory, and the unmet demand are the decision variables, the customer demands are represented by interval numbers, and the consumption of raw material and the amounts of all resources available are described as fuzzy subsets.
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