In this study, a multi-product, multi-period and non-linear programming model is developed for production planning problem where demand is under uncertainty. The proposed study is designed for a real-world case study of chemicals production factory with 1 production line and 2 manual and automatic technologies. In manual technology, workers are working with 3 amateur, typical and professional skills in 2 typical and overtime working. Automatic technology in this system has n machines in which the repairing and maintenance of the machineries are also included. This system has n products and the products are life-limited and with diversity. The primary goal is to propose a model for improvement of the production planning and minimization of the production system costs. The products in high volume and various types are produced and they are stored in bottles as the final products. For different production periods, the human forces capacities are considered and the level of employment or forces dismissal are considered. The production process is forwarding and backward process is not acceptable; that is, it is not allowable to rework in this system. Delivering final product from stockpiles to the retailers is conducted using vehicles with limited capacity. To solve the model in larger space and because of the complexity of the model, meta-heuristic algorithm is used. Finally, it is concluded that due to covering most of the assumptions in perishable products production, the proposed model is closer to the real-world circumstances and reduces costs in production systems.

In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only), cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same.