Impacts of memory and impreciseness on inventory policies an exploratory study using integer and fractional order differential equations

Abstract

This thesis aims to address several inventory models under the influence of memory effect and uncertainty of underlying data. In this thesis, the notion of memory has been embedded by useof the theories of fractional calculus. On the other hand, fuzzy and Type 2 interval numbers have been used to capture imprecisenessof underlying decision-impacting parameters. In the existing literature, Newtonian calculus have been used widely to demonstrate and optimize inventory models, which is incompetent to address the memory impacts on the model system. Moreover, the literature concerning EOQ and EPQ models under fuzzy and interval uncertainty abandoned the distinguished characteristics of fuzzy and interval-valued functions. We have organized this thesis into three parts, including two chapters each, to diminish the above-mentioned gaps in existing literature. Memory impacts on inventory models in a crisp environment have been discussed in the first part of the thesis. In this part, Chapter 2 includes two EPQ models of deteriorating products from a generalized point of view.Here, the numerical optimizations are obtained by distinct real pole rational optimization and ABC algorithm. Chapter 3 discusses the impact of memory on an EOQ model with shortage in detail. The second part of the thesis includes two chapters regarding the effects of imprecision on inventory models without memory. Two EPQ models under deterioration using fuzzy differential equations and L-R triangular fuzzy number approaches have been discussed in Chapter 4. Chapter 5explores Type 2 interval-valued calculus and its implication on the EOQ model under interval-described uncertainty. In the third part of this thesis, we have incorporated memory and uncertainty simultaneously while studying inventory models. In chapter 5, we have introduced Type 2 interval-valued fractional calculus and its possible application on the EOQ model considering memory effect and impreciseness of underlying data. Finally, three different inventory models have been discussed in