Lot-sizing and pricing decisions under attraction demand models and multi-channel environment: New efficient formulations

The presented paper considers the pricing and lot-sizing decisions for a manufacturer who produces and sells a single product in different selling channels i.e physical stock, website, mobile, etc. The objective is to find the production plan and prices of each channel to maximize the total profit defined from difference between the revenues and the productions, holding and setups costs. The consumers’ demand in each channel is represented by attraction demand models which include the multinomial logit ($MNL$), multiplicative competitive interaction ($MCI$) and linear demand models. The addressed problem is formulated as a non-convex mixed-integer nonlinear program ($MINLP$). Based on properties of attraction functions, an efficient reformulation which transforms the initial non-convex problem into a convex one is presented. Therefore, an optimization approach based on the outer approximation algorithm is presented to solve the problem. Numerical tests based on large benchmark of real inspired instances show the efficiency of the proposed approach to solve the addressed problem compared to the initial non-convex model.