A profit-cost ratio maximization approach for a manufacturing inventory model having stock-dependent production rate and stock and price-dependent demand rate

Abstract

This paper discusses an optimal managerial approach regarding stock control in a manufacturing-inventory scenario. The selling price and inventory level in showrooms may impact customers’ demand. The fall in selling price creates additional demand, while shown inventory also positively enhances demand. In this paper, demand is influenced by the selling price during the productive phase and the displayed stock in idle time. The significance of selling price and stock on profit goal may not be inherited from that of the demand function. The production rate varies negatively against the inventory on hand. Instead of taking cost minimization or the profit maximization objective, this paper executes an optimization approach on the profit-cost ratio function, sharpening the manufacturer’s goal. The numerical solution and sensitivity analysis on optimal outcomes succeed the analytical solution in Mathematica software. Numerical results indicate that the profit-cost ratio rises with selling price, suppressing the negative impact of the selling price on demand. Also, the profit-cost ratio shows a concave curve for the production cycle, ensuring a global maximum for the objective function.

Keywords

• Production inventory
• Stock dependent production rate
• Selling price-dependent demand
• Stock-dependent demand
• Profit cost ratio optimization