Essays on the Newsboy Problem

Abstract

The newsboy problem is about minimizing the penalty associated with demand-supply mismatch of an item with uncertain demand by suitably deciding the stocking quantity. Newsboy problem arises in a variety of situations like inventory management of perishable products, supply chain coordination, revenue management, etc. In this dissertation, we address three issues associated with the newsboy problem. 1. Sensitivity analysis of the newsboy model Decision .making .in .optimization .models .requires .knowledge .of .certain .parameters. .Due to parameter estimation error, actual decision deviates from the optimum. We study the impact of sub-optimal .decisions .on .inventory .cost .in .the .classical .newsboy .model. .In .particular, .we identified conditions for symmetry/skewness of cost deviation, i.e., deviation of expected cost from .its .minimum, .and .studied .its .magnitude .by .establishing .a .lower .bound. .We .found .the newsboy model to be sensitive to sub-optimal order quantities. 2. Multi-product newsboy problem with satiation objective Achieving a profit target is often preferred over maximizing expected profit in uncertain business environments. Newsboy problem with satiation objective, i.e., maximization of the probability of achieving .the .given .profit .target, .has .not .received .adequate .attention .from .researchers, particularly in the multi-product setting. We study the multi-product satiating newsboy problem using .a .discrete .formulation. .We .developed .computational .method .for .solving .the .problem optimally. Our algorithms, though inefficient, solve the problem in its general form. 3. Heuristics for the multi-product satiating newsboy problem As .noted .above, .the .multi-product .satiating .newsboy .problem .has .not .been .studied .well. Practically usable solution methods are available only for two-product instances. We developed heuristics for solving larger instances of the problem. Two of our heuristics are search-based, i.e., they search `intelligently' in the solution space. The third heuristic is decomposition-based, i.e., it decomposes the multi-product problem into easily solvable single-product problems. Our heuristics solve the problem in reasonable time with good accuracy.