analysis of a two-storage system for advance payment policies with the partial backlogged shortage

Nowadays, due to the highly competitive situation, every business organization faces many shortcomings for smoothly running of his/her own business. so, to survive in the competition, different types of business policies are required (all-unit discount, trade credit etc.). this type of problem is presented mathematically as an optimization problem and solved. in this work, the advance payment facility with n equal instalment before receiving the products is introduced to formulate a two-storage inventory model. this model is studied under the assumptions of price and advertisement’s frequency-dependent customers’ demand, constant deterioration and exponential backlogging rate. deterioration is started in both warehouses at the same time. to solve the proposed model, mathematics and matlab software are used. the concavity of the objective function (average profit) is shown numerically as well as graphically by using mathematica and matlab software for supporting a numerical example. also, it is shown that the objective function is negative definite by using an example. finally, sensitivity analyses are carried out pictorially with the changes of various known parameters.