Erik Langelo

• Langelo, Erik; Pettersen, Bård Inge & Rekdal, Per Kristian (2019). The profit-maximizing lot size problem with pricing lag effects. Show summary

  In 1970, Joseph Thomas extended the well-known dynamic lot size model of Wagner and Whitin to include variable prices, as well as variable production costs. This master thesis extends Thomas’ model to include something called the “lag effect”. Formally, this master thesis models a disaggregated, finite-horizon, profit-maximizing dynamic lot size problem with pricing lag effects in demand. This effect models the tendency for customers to stock up on a product when it is offered for cheap, causing demand to increase in the “cheap” time period, while it decreases in the next. In effect, lowering the price causes demand to shift backwards in time, in addition to increasing demand as in most demand functions. The problem is to decide in which time periods to produce, how much to produce in each period, and which price to set in each period. The objective is to maximize the total profit, defined as total revenue minus total setup cost, production cost and inventory holding cost. Three theorems which restrict the amount of possible optimal solutions are proved. A solution is then provided to the production horizon problem, a sub-problem of the main problem. The production horizon problem is then solved with two different models: with and without the lag effect. The optimal solutions of these models are then compared for varying values of some key parameters. Keywords: revenue management and pricing, inventory

• Langelo, Erik; Pettersen, Bård Inge & Rekdal, Per Kristian (2019). The profit-maximizing lot size problem with pricing lag effects. Show summary

  In 1970, Joseph Thomas extended the well-known dynamic lot size model of Wagner and Whitin to include variable prices, as well as variable production costs. This work extends Thomas’ model to include something called the lag effect. Formally, this work models a disaggregated, finite-horizon, profit-maximizing dynamic lot size problem with pricing lag effects in demand. This effect models the tendency for customers to stock up on a product when it is offered for cheap, causing demand to increase in the given time period, while it decreases in the next. In effect, lowering the price causes demand to shift backwards in time, in addition to increasing demand as in most demand functions. The problem is to decide in which time periods to produce, how much to produce in each period, and which price to set in each period. The objective is to maximize the total profit, defined as total revenue minus total setup cost, production cost and inventory holding cost. Three theorems which restrict the amount of possible optimal solutions are proved. A solution is then provided to the production horizon problem, a sub-problem of the main problem. The production horizon problem is then solved with two different models: with and without the lag effect. The optimal solutions of these models are then compared for varying values of some key parameters.

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