DETERMINISTIC INVENTORY MODELS FOR DELAYED DETERIORATING ITEMS WITH INVENTORY LEVEL DEPENDENT DEMAND RATE

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dc.contributor.authorBARAYA, YAKUBU MAMMAN
dc.date.accessioned2016-04-04T11:22:33Z
dc.date.available2016-04-04T11:22:33Z
dc.date.issued2015-08
dc.descriptionA DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY (Ph.D) DEGREE IN MATHEMATICS DEPARTMENT OF MATHEMATICS AHMADU BELLO UNIVERSITY, ZARIA NIGERIAen_US
dc.description.abstractIn many real-life situations the consumption rate for certain types of consumer goods (such as fruits, vegetables, doughnuts, cassava, yams and so on) is sometimes influenced by the stock-level. In this research, five deterministic inventory models for delayed deteriorating items with inventory level dependent demand rate have been developed. The models are (1) an economic order quantity (EOQ) model with demand rate as a polynomial function of instantaneous inventory level and constant rate of deterioration, (2) an EOQ model with demand rate as a linear function of instantaneous inventory level and shortages, (3) an economic production quantity (EPQ) model with demand rate as a linear function of instantaneous inventory level with linear-time dependent holding cost, (4) an EPQ model with demand rate as a linear function of instantaneous inventory level and time-dependent deterioration rate, and (5) an EOQ model with demand rate as a polynomial function of instantaneous inventory level and linear time-dependent holding cost. In all the models, theoretical control model results for the optimal replenishment policy of the inventory systems have been determined in order to minimize the inventory system cost or maximize profit per unit time. Analytic formulation and analysis of the inventory problems were developed on the framework of the models assumptions. The proposed inventory systems were represented by systems of differential equations including initial and boundary conditions and typical differential and integral calculus were used to analyse the inventory problems. Newton-Raphson method has been used to determine the optimal solutions (optimal order or production quantity and the optimal cycle length) of the developed cost minimization models for the first four models and the profit maximization model for the fifth model. Some numerical examples to illustrate the applications of the models developed are also ix presented. The numerical example presented to demonstrate the fifth model was accompanied by sensitivity analysis. It was shown from the results of the models developed that the impact of stock dependent demand rate, holding cost parameter, deterioration and backlogging rate affect the optimal replenishment policy, and hence should not be left out in developing inventory models for delayed deteriorating items with inventory level dependent demand rate. Finally, the effects of errors in the estimation of various model parameters or even changes in the values of model parameters may occur due to uncertainties surrounding the future of the optimal solutions. In order to examine the implications of these errors or changes, sensitivity analysis was studied based on the given example for the fifth model.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/7588
dc.language.isoenen_US
dc.subjectDETERMINISTIC INVENTORY MODELS,en_US
dc.subjectDELAYED DETERIORATING ITEMS,en_US
dc.subjectINVENTORY LEVEL DEPENDENT DEMAND RATE,en_US
dc.titleDETERMINISTIC INVENTORY MODELS FOR DELAYED DETERIORATING ITEMS WITH INVENTORY LEVEL DEPENDENT DEMAND RATEen_US
dc.typeThesisen_US
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