Ordering and pricing strategies for single and two-period inventory problems

Inventory management and choosing the right price are key elements in optimizing the profit of yourbusiness or personal project. The biggest obstacle when determining the quantities one wants to havein stock and for which price to sell these is the unpredictability of the demand. When the exact demandis known, everyone can maximize their profit by ordering the exact demand for a given price. However,in general, this is not the case and there are only previous demands to rely on. In this thesis, we willdiscuss two models, that describe approximations of real-world problems, concerning inventory man-agement.The first model is a single-period model for perishable products with a price-dependent demandDwith known probability density function?D. After a brief review of existing literature, which is donein Chapter 1, the single-period model will be analyzed in Chapter 2. This analysis consists of provingthe existence of a unique optimal ordering quantityq?1and optimal pricep?and of...Show moreInventory management and choosing the right price are key elements in optimizing the profit of yourbusiness or personal project. The biggest obstacle when determining the quantities one wants to havein stock and for which price to sell these is the unpredictability of the demand. When the exact demandis known, everyone can maximize their profit by ordering the exact demand for a given price. However,in general, this is not the case and there are only previous demands to rely on. In this thesis, we willdiscuss two models, that describe approximations of real-world problems, concerning inventory man-agement.The first model is a single-period model for perishable products with a price-dependent demandDwith known probability density function?D. After a brief review of existing literature, which is donein Chapter 1, the single-period model will be analyzed in Chapter 2. This analysis consists of provingthe existence of a unique optimal ordering quantityq?1and optimal pricep?and of finding, if possible,an explicit expression for them. Because of the complexity of the model, it is not possible to obtainan expression for general demand distribution, so multiple demand distributions are considered inSection 2.2. To determineq?andp?we will use the following roadmap:1. Determine the general profit function, which has parametersq,pandD.2. Determine the expected profit function, since the demandDis a random variable.3. Assumepto be given and maximize the expected profit function forq?. This will give an expres-sion forq?, which depends only onp.4. Use the found expression forq?to determine the expected profit function, given the optimalordering quantity and maximize forpto findp?.The second model we will discuss is a two-period model for stable products, i.e., non-perishableproducts. As with the first model, this model considers a price-dependent demandDwith a knownprobability density function?D. Here we add the assumption that unsatisfied demand from the firstperiod can be met in the second period. Another important assumption is that the pricepis the samein both periods. Again, specific probability density functions are assumed to solve this problem, whichis analyzed in Chapter 4. The same roadmap as above can be used to determine the optimal quantitiesq?1,q?2for the first and second period respectively, and the optimal pricep?, with the only differencethe parametersq1andq2instead ofq.Show less

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Ordering and pricing strategies for single and two-period inventory problems