A Multi-item EPQ Model with Variable Demand in an Imperfect Production Process

Nowadays, to survive and promote the market competition, multi-item business strategy is more effective for any production/manufacturing sector. Here, an attempt has been made to develop a multi-item production inventory model, especially for seasonal products for a finite time horizon. Production process is not 100% reliable, and for this reason some imperfect quality items are produced, and these items are immediately remanufactured incurring some cost to get back its originality. Both demands and production rate of the items are time-sensitive. It is also assumed that production cost per unit varies with defective rates as well as production rates. Imposing two constraints, space and investment, profit maximization model is formulated. Incorporating inflation and time value of money into the model, total profit is represented as a definite integral with time period as its upper limit. The profit function becomes an optimal control problem. The defective rates of the production process are determined by variational calculus. As today’s competitive business transaction is full of uncertainty, another model is considered with fuzzy constraints and solved. Fuzzy constraints are converted to the crisp one, following fuzzy possibility. For the illustration of the developed models, numerical experiments and also some sensitivity analyses are performed and presented.