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In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.

Cost reduction for setup and improvement of processes quality are the main target of this research along with free minimal repair warranty for an imperfect production System. This paper deals with the effect of setup cost reduction and process quality improvement on the optimal production cycle time for an imperfect production process with free product minimal repair warranty. Here the production system is subject to a random breakdown from an controlled system to an out-of-control state. Shortages are fully backlogged. The main target to minimize the total cost by simultaneously optimizing the production run time, setup cost, and process quality. A solution algorithm with some numerical experiments are provided such as the proposed model can illustrate briefly. Sensitivity analysis section is decorated for the optimal solution of the model with respect to major cost parameters of the system are carried out, and the implications of the analysis are discussed.Mathematics Subject Classification. 90B05, 90B06.

The concept of advanced sustainable inventory manage- ment, where demand pattern stock level and advertising dependent under trade-credit policy is taking account in this present study. Opti- mal credit period and cycle time are the main objective of this advanced system. A developed solution methodology is derived to show the exis- tence of global optimality under optimum credit period and cycle time. The main concern of this advanced system is to maximize the annual total system pro t of retailer with nite replenishment rate. Numerical illustration are carry forward for di erent cases to prove the stainabil- ity along with real impact of this model. Sensitive analysis for the key parameters is discussed in sensitivity analysis section along with some real \managerial insights".