Process mean selection and price differentiation in an imperfectly segmented market for a risk-averse firm

In this paper we propose an integrated model for optimising the process mean, the price of products, and the production quantity. This optimisation is conducted considering the impact of price differentiation in an imperfectly segmented market where demand leakages are common. The products that are produced by the production process are assigned to two market segments using sampling inspection. For optimisation of the process mean, pricing, and production quantities, a multi-objective model is formulated that maximises (i) The expected total risk-adjusted profit across segments for a risk-tolerant firm, (ii) The satisficing level, that is, the probability of exceeding a target set for total risk-adjusted expected profit, and (iii) The two conflicting objectives, expected total risk-adjusted profit and satisficing level. Depending on the complexity of models, either derivative-based closed form solutions or heuristic solution procedures are developed. The problem finds applications in process industries. A detailed numerical simulation is performed to corroborate the models, and it shows that a higher risk aversion results in a lower total expected risk-adjusted profit but a higher probability of achieving the target profit.