Optimal decisions on fencing, pricing, and selection of process mean in imperfectly segmented markets

This paper integrates the selection of a process mean, production and marketing decisions at a firm's level. We discussed a manufacturing firm's problem that integrates its manufacturing decisions on production quantities and selection of a process mean with marketing decisions. The marketing decisions include setting prices, and the fencing investment to mitigate the effect of demand leakages between market segments. The manufacturing firm yields products of varied quality based on a single quality characteristic (e.g., amount of fill). The firm operates in a monopoly, and manufacturing process is assumed to follow a normal distribution, and therefore, it produces multi-grade (class) products distinct in their single quality characteristic. Depending upon the quality characteristic, a product with quality characteristic equal to greater than the upper specification limit is classified as grade 1 product, and sold in primary market at a full price. When the quality characteristic falls between the lower and the upper specification limits, it is referred to as a grade 2 product, and sold in a secondary market at a discounted price. Any product with a quality characteristic lower than the lower specification limit is reworked at an additional cost. A 100% error-free inspection is conducted to segregate the products at a negligible cost. Unlike many related studies in literature, this research proposes a novel integration of the pricing and production quantity decisions along with the process targeting in the two markets with pricing decision in the presence of demand leakages due to cross-elasticity. Furthermore, it is assumed that the firm can mitigate the demand leakage at an additional investment on improving fencing. Thus, the firm's optimal decision would also include the pricing in each market segment, and fencing investment along with its decision on the production quantity for each product class. Mathematical models are developed to address this problem assuming the price-dependent stochastic demand. Structural properties of these models are explored and efficient heuristic solution methodologies are developed. Later, we also developed models when the stochastic demand information is only partially known, and proposed Harmony Search algorithm on the problem. Numerical experimentation is reported to highlight the importance of the proposed integrated framework and the impact of the problem related parameters on a firm's profitability and its integrated optimal control decisions on selection of a process mean, pricing, production quantity, and fencing investment.