In this paper, we develop a two-warehouse imperfect production model under two cases: (i) model starts with shortages (ii) model ends with shortages. Most of the researchers proposed the models for perfect items but we develop for imperfect quality items, which is very realistic. Demand is taken as time dependent and dependent on the production. Holding cost in rented warehouse (RW) is greater than own warehouse (OW). Deterioration is taken as Weibull distribution in both OW and RW. Shortages are allowed and partially backlogged. The effect of learning on production cost is also considered. Learning from one cycle to other cycle, improve the efficiency of the organization. A numerical example including the sensitivity analysis is given to validate the results of the production-inventory model.

This paper deals with the development of an inventory model for Weibull deteriorating items with constant demand when delay in payments is allowed to the retailer to settle the account against the purchases made. Shortages are not allowed and the salvage value is associated with the deteriorated units. In this paper, we consider two cases; those are for the case payment within the permissible time and for payment after the expiry of permissible time with interest. Numerical examples are provided to illustrate our results. Sensitivity analysis are carried out to analyze the effect of changes in the optimal solution with respect to change in one parameter at a time.

This paper presents production-inventory models for deteriorating items with increasing-steady-decreasing demand pattern under the effect of inflation and time value of money. This type of demand behavior can be observed in some fashion products or seasonal products in general. Shortages are allowed with partial backlogging of demand and a two-parameter Weibull-distribution function is used for the deterioration of items in order to make the models more generalized and realistic. The models generate optimal values of initial production run time, onset of shortages, production recommencement time, and total production quantity that minimizes the total relevant costs of production and inventory for any given set of system parameters. Various possible production strategies available for items with variable demand pattern are examined to determine the optimal production strategy. The discounted cash flow approach and trust region optimization methods are used to obtain the optimal results. The Numerical examples and sensitivity analysis show that the optimal production strategy may vary with changes in system parameters.

This paper presents an order level inventory system with time
dependent Weibull deterioration and ramp type demand rate where
production and demand are time dependent. The proposed model of this
paper considers economic order quantity under two different cases. The
implementation of the proposed model is illustrated using some
numerical examples. Sensitivity analysis is performed to show the
effect of changes in the parameters on the optimum solution.