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This paper deals with an economic lot size model when demand follows a power law and changes with time, owing to the fact that this kind of pattern is suitable for so many real situations. Production rate is presumed to be proportional to demand rate. Also since that demand is price sensitive in reality, we suppose that demand decreases linearly with price. With regard to these points, in this article a joint pricing and inventory model is presented where demand depends on time with a power pattern and price linearly, production rate changes pro rata with demand rate and multiple items are considered. The principal consideration of the study is to satisfy the demand and optimize the profit for all items in the system, simultaneously. Setup, holding, backlogging and production costs are involved in the inventory system. The aim is to maximize total profit function and achieve optimum values of scheduling period, reorder point and price. Employing mathematical modelling and optimization methods, the existence of the optimal solutions is proved, and then a simple heuristic algorithm is presented to maximize total inventory profit and determine the best values of variables. A numerical analysis is carried out to illustrate the applications of the proposed models.

The constant demand rate is the most common assumption of the basic economic production quantity model, which is not very frequent in practice. In real world situations, demand usually varies with time. With regard to the widespread necessity of power demand pattern, demand is supposed to follow a power law. Another unrealistic assumption is perfect quality of all items. This paper presents a production system with defective items to determine the optimal replenishment quantity, cycle length and backordered size with a power demand rate dependent production rate. We assume that a manufacturer may be faced with three different cases regarding to the date that defective items are drawn from inventory. The setup , backordering, inspection, and production costs, as well as holding cost of both perfect and imperfect items are accounted in the inventory system. An algorithm is offered to optimize total inventory cost and then numerical analyses are presented to demonstrate the applicability of the proposed models. Finally, some sensitivity analyses and managerial insights are provided.

Today, supply chains have been widely welcomed by industry researchers and the results of applying it may increase throughput, reduce cost, increase speed to meet customers' needs and create competitive opportunities. This paper identifies a scientific method, which operates efficiently and effectively manages supply chain operations. In this paper, a computer simulation model is analyzed for analyzing the supply chain and the results are examined, accordingly. Using Taguchi design of experiment and running the proposed model under L27 scenarios, a two-objective optimization was performed on the estimated response surfaces, leading to a 60% increase in productivity and 40% reduction in waiting time.

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