The dynamic rate of investment in promotion during different price-ranges and the optimum investment in preservation technology are developed for seasonable or fashionable products through their lifespan. An order level inventory model for deteriorating items with promotional price and trapezoidal-type demand rate is used to maximize the profit of a retailer. The deterioration rate is dependent on the preservation technology i.e., more investment in preservation reduces the rate of deterioration. The aim of this study is to obtain the optimum dynamic investment for the promotion. The optimal control theory is employed to obtain the dynamic investment rates. A modified flower pollination Algorithm is applied to find the optimal pricing scheme, preservation technology investment, and replenishment schedule. An illustrated algorithm based numerical experiment is conducted to validate the dynamic behaviour of the investment. Sensitivity analysis has been carried out with respect to the major parameters to prove the novelty of the algorithm and explored the managerial insights of the proposed model. Numerical studies obtain that dynamical investment is really beneficial for the management of stocks.
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