Analysis and optimization of an EOQ inventory model with promotional efforts and back ordering under delay in payments

In this paper,economic order quantity(EOQ)inventory model is considered subject to promotional efforts.We adopt a demand function which is dependent on sales teams’initiatives in which shortages are allowed which are completely backlogged under the condition of permissible delay in payments with timedependent holding cost.The main objective of this paper is to determine the optimal replenishment schedule and optimal order quantity to maximize the total profit.Expressions for various optimal indices are provided.First,we prove that a unique optimal replenishment schedule exists.Second,we present an effective iterative algorithm to obtain the optimal solution.Furthermore,we establish some useful theorems to characterize the optimal solution to determine the values of replenishment schedule and optimal order quantity.Third,we prove that the total profit is a concave function via differential calculus and present numerical examples using SCILAB 5.5.0 to illustrate the model.Finally,we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss managerial insights.This study suggests to the management of firms to determine the optimal order quantity,optimal inventory cycle length and sales teams’initiatives/promotional effort in order to achieve their maximum profits.

Pricing and inventory decisions for non-instantaneous deteriorating items with price and promotional effort stochastic demand

This study investigates an inventory model for a non-instantaneous deteriorating item with partial backlogging wherein the demand is stochastic in nature and depends on price and promotional effort whereas the deterioration rate is time proportional.Under these settings,a mathematical model is developed with the objective to maximise the expected profit per unit time by determining the optimal price and the length of replenishment cycle.Some useful theoretical results are established to deduce the optimal replenishment schedule.An effective algorithmic procedure is developed to find the optimal solutions to the proposed model.The applicability of the proposed model is illustrated by numerical example.Sensitivity analysis of the optimal solution with respect to key parameters has been carried out and the implications are discussed.The study indicates that though promotional effort stimulates the market demand,it is beneficial in an economic sense when it applies in a conservative manner.