•An integrated production-inventory model for a single manufacturer-multiple buyers.•Issue of profit division among the partners of a supply chain is discussed.•Four different models of profit sharing have been proposed.•Profit sharing based on Shapley function values turns to be fair and supportive.•GA and TLBO meta-heuristics have also been proposed. This paper undertakes the study of an integrated production-inventory and pricing decision problem for a single manufacturer-multiple buyers supply chain where each buyer faces price-dependent demand. The item manufactured at a finite production rate is shipped to the buyers in multiple equal-sized shipments. Earlier researchers have not studied this problem for maximizing the overall supply chain profit and its allocation among the chain partners. For the allocation of the maximized profit, four different schemes are being proposed, each for a different level of understanding and faith among the partners. Demand, taken as price-sensitive, affects the costs to the manufacturer as the same is dependent upon the sales volume. Since the manufacturer fixes its sales price depending upon the sales volume affected cost, the volume will affect the buyer in terms of its unit purchase cost, and the holding cost which is charged as a percentage of the unit cost. This reality is attempted in this paper in addition to maximization of the chain profit and its allocation among the chain partners for integrated inventory management. Associated problems, formulated as mixed-integer non-linear programming problems, are computationally very hard, and thus evolutionary heuristics as Genetic Algorithm and Teaching-Learning Based Optimization are proposed. The strength of various proposed schemes for profit distributions has been analyzed using numerical experimentation. It is found that a forward contract between manufacturer and buyers will help to generate the maximum profit. It has also been shown that the distribution of profit based on Shapley function values is most fair and logical.