Several Intelligent Techniques to Solve Various Warehouse Problems in Uncertain Environment

Abstract

AbstractIn this chapter, several intelligent techniques to solve several warehouse problems have discussed in uncertain environment. In first model, analogous to chance constraints, real-life necessary and possibility constraints in the context of two warehouses multi-item dynamic production-inventory control system with imprecise holding and production costs are defined and defuzified following fuzzy relations. Hence, a realistic two warehouse multi-item production-inventory model without shortages and fuzzy constraints has been formulated and solved for optimal production with the objective of having maximum profit. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the present system produces some defective units alongwith the perfect ones and the rate of produced defective units is stochastic in nature. Here demand of the units is stock dependent and known and the defective units are selling with reduced prices. The space required per unit item, available storage space are assumed to be imprecise. The budget constraints is also imprecise. The space and budget constraints are of necessity and/or possibility types. The model is reduced to an equivalent deterministic model using necessary and possibility constrained and solved for optimum production function using Pontryagin’s Optimal Control policy, the Kuhn-Tucker conditions and mathematica software 9.0. The engineering students in Optimization engineering and M.B.A.s in the business curriculum can used the model easily. In second model, a three layer supply chain production inventory model (TLSCPIM) under conditionally permissible delay in payments is formulated in fuzzy-rough and Liu uncertain environment. Supplier’s supply the item at a finite rate. Manufacturer has also purchased the said item from supplier and produced the item in a certain rate which is the decision variable. Manufacturer sale his product to the retailer and also give the delay in payment to the retailer. Retailer purchase the item from manufacture and to sale the customers. Ideal costs of supplier, manufacturer and retailer have been taken into account. Also using expectation of fuzzy rough number and Liu uncertain number, the fuzzy rough inventory parameters and Liu uncertain inventory parameters are converted into equivalent crisp problem. Then the problem is solved by Mathematica software 9.0. The model is illustrated through numerical examples and results are presented in tabular and graphical form. In this chapter, various type of warehouse/supply chain problems have been developed where some warehouse parameters are fuzzy/fuzzy-rough/Liu-uncertain in nature. Then several intelligent techniques are used to convert the uncertain warehouse problems into crisp problems and to solve the problems. In addition, this chapter has also included several uncertain techniques/soft computing techniques which are used in seminar classes in industry and teaching an introductory production planning and control or an operations management course for M.B.A. students.KeywordsImperfect production with reworkTwo warehousesThree layers supply chainOptimal control theoryUncertain variables