Assessing the Effects of using Demand Parameters Estimates in Inventory Control

Inventory models need some specification of the distribution of demand in order to find the optimal order-up-to level or reorder point.This distribution is unknown in real life and there are several solutions to overcome this problem.One approach is to assume a distribution, estimate its parameters and replace the unknown demand parameters by these estimates in the theoretically correct model.Earlier research suggests that this approach will lead to underperformance, even if the true demand distribution is indeed the assumed one.This paper directs the cause of the underperformance and quantifies it in case of normally distributed demand.Furthermore the formulae for the order-up-to levels are corrected analytically where possible and otherwise by use of simulation and linear regression.Simulation shows that these corrections improve the attained performance.Unknown Demand Parameters;Inventory Control;Normal Distribution;Service Level Criterion

Assessing the Effects of using Demand Parameters Estimates in Inventory Control

Inventory models need some specification of the distribution of demand in order to find the optimal order-up-to level or reorder point.This distribution is unknown in real life and there are several solutions to overcome this problem.One approach is to assume a distribution, estimate its parameters and replace the unknown demand parameters by these estimates in the theoretically correct model.Earlier research suggests that this approach will lead to underperformance, even if the true demand distribution is indeed the assumed one.This paper directs the cause of the underperformance and quantifies it in case of normally distributed demand.Furthermore the formulae for the order-up-to levels are corrected analytically where possible and otherwise by use of simulation and linear regression.Simulation shows that these corrections improve the attained performance

Milloin ennustetarkkuus on tärkeää vähittäiskaupassa? Tuotteen avainparametrien vaikutus

Accurate forecasting is important for retail companies that want to minimize the capital that is tied in stocks while simultaneously ensuring adequate product availability for their customers. Forecasting processes are typically automated; however, time-consuming and costly manual corrections to forecasts are often made. Therefore, retailers would benefit from clear criteria for selecting products for which forecast accuracy has the greatest impact. In addition, quantifying the business impact of forecast accuracy could help retailers that are considering investments in advanced forecasting solutions. Furthermore, researched and clearly documented evidence about the importance of forecast accuracy could aid communication both within retail companies and with other players in the supply chain. For these reasons, the goal of this thesis is to identify the situations in which forecast accuracy is important and those in which it is not. This thesis utilizes real sales figures from a major European retailer and mathematical simulations to clarify when forecast accuracy is important. Approximately 7 million product locations were included in the thesis, and the data covered sales history for 24 months. With access to real product-specific sales data, the researcher was able to simulate the future using real sales figures from the past. In other words, it was possible to go a few years back in time and test the impact a certain forecast would have had. Using real sales and product data, it was possible to vary the key forecast and product location parameters and then to simulate the business outcome. The results of this study suggest clear principles for prioritizing product locations and quantify how much additional stock is needed to compensate for forecast errors. The results also reveal the impact of different product location parameters on the business importance of forecast accuracy. The sales volume of a product location proved to be the most important parameter, although relative batch size also had some importance. Average time to delivery plays a minor role in some cases, while relative sales standard deviation (STD) had only an insignificant effect. Based on the results of this thesis, retailers should consider focusing their efforts on improving the forecast accuracy of high-selling products and, to some extent, on products with small batch sizes. Average time to delivery deserves closer scrutiny only in cases with systematic forecast errors. Relative sales STD proved so marginal that retail managers could consider ignoring it.Tarkat ennusteet ovat tärkeitä vähittäiskaupan yrityksille, jotka haluavat minimoida varastoihin sitoutuneen pääoman, mutta samalla pitää riittävästi tuotteita saatavilla asiakkailleen. Ennustaminen on tyypillisesti pääosin automatisoitua, mutta ennusteisiin tehdään usein käsin kalliita ja aikaa vieviä korjauksia. Vähittäiskauppa hyötyisi selkeistä kriteereistä, joilla valita ne tuotteet, joille ennustetarkkuus on kaikkein tärkeintä. Ennustarkkuuden vaikutusten kvantifioiminen voisi olla höydyllistä myös silloin, kun vähittäiskauppa harkitsee investointeja edistyneempiin ennustemenetelmiin. Lisäksi selkeästi esitetty tutkimustieto ennustetarkkuuden merkityksestä edistäisi kommunikointia vähittäiskaupan toimitusketjussa. Näistä syistä tämän diplomityön tavoitteena on tunnistaa, milloin ennustetarkkuudella on merkitystä ja milloin ei. Diplomityön tavoitteen saavuttamiseksi hyödynnettiin yhden merkittävän eurooppalaisen vähittäiskauppaketjun myyntitietoja, joiden pohjalta tehtiin simulointeja. Data sisälsi noin 7 miljoonaa tuotelokaatiota, joiden myyntihistoriaa tarkasteltiin 24:n kuukauden ajalta. Toteutuneen myynnin avulla oli mahdollista mennä ajassa taaksepäin ja tutkia, millaisia vaikutuksia erilaisilla ennusteilla olisi ollut. Käyttäen todellista myynti- ja tuotedataa oli mahdollista simuloida ennuste- ja tuoteparametrien vaikutusta liiketoimintaan. Tämän tutkimuksen tulokset tarjoavat selkeän tavan priorisoida tuotelokaatioita ja kvantifioida sitä, kuinka paljon lisää varastoa tarvitaan ennustevirheen kompensointiin. Tulokset kuvaavat myös, miten eri tuotelokaatioparametrit vaikuttavat ennustevirheen liiketoiminnalliseen merkitykseen. Tärkeimmäksi parametriksi osoittautui myyntivolyymi ja verrattain tärkeä oli myös suhteellinen eräkoko. Keskimääräisellä ajalla seuraavaan toimitukseen oli jossain tilanteissa pieni vaikutus, mutta myynnin hajonnalla ei ollut merkittävää vaikutusta. Tulosten perusteella vähittäiskaupan kannattaisi keskittää ennustetarkkuuden parantamiseen tähtäävät panostukset tuotteisiin, joita myydään paljon, sekä jossain määriin tuotteisiin, joilla on pieni eräkoko. Keskimääräinen aika seuraavaan toimitukseen on tarkkailemisen arvoinen vain tilanteissa, joissa ennusteessa on systemaattista virhettä. Myynnin hajonnan vaikutus on niin pieni, että vähittäiskauppiaat voivat harkita sen jättämistä pois tarkastelusta

Inventory control in case of unknown demand and control parameters.

This thesis deals with unknown demand and control parameters in inventory control. Inventory control involves decisions on what to order when and in what quantity. These decisions are based on information about the demand. Models are constructed using complete demand information; these models ensure that a certain service level is achieved. However, in real life the demand information is not known completely. Often, only some historical demand observations are available, and these are used to estimate the information needed in the inventory models. Using these estimates implies that additional uncertainty is introduced in the model and when this extra uncertainty is not taken into account, this could lead to not achieving the desired service level. This thesis shows that this will happen. Furthermore, the size of the underperformance is determined and also methods to reduce it are constructed. However, these methods imply a higher on-hand inventory, which leads to higher inventory costs. So, it might be wiser to address the causes of uncertainty than to treat its symptoms.

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice

Analysis of an inventory system with product perishability and substitution: a simulation-optimization approach

This thesis focuses on some inventory management policies for substitutable and perishable items under demand uncertainty. A set of perishable products with fixed shelf lives is considered under an (R,Si) system of inventory control where demand for a preferred product can be satisfied by a substitute product with a known probability, in the event of a stockout of the preferred product. While taking demand substitution and product expiration into account, the retailer is faced with the decision of determining the order-up-to level, Si, for each product i which maximizes expected total profit, given a common review period, R, determined exogenously.Under demand uncertainty, the problem detailed in this thesis involves stochastic optimization. An exact closed form expression, however, for expected profits becomes difficult for certain parameter values involving product shelf-life, product substitution, and lead time. As an alternative approach, order replenishment, demand consumption, substitution, and product expiration can be effectively modeled using discrete-event simulation. Through a discrete-event simulation model, each realization of the profit function can be evaluated for a selected value of Si, and a mean profit value can be estimated after a number of replications of a simulation run. In order to find the best Si solution, the technique of simulation-optimization is used.This thesis also examines the impact of key parameters such as substitution characteristics, shelf-life, cost structure, lead time, and number of products on the choice of inventory issuing policy on both the optimal Si levels and corresponding mean profit values. Through a factorial experimental design, the effects of these parameters on system performance are analyzed. In addition, heuristics are proposed and tested in order to provide managers with a convenient set of rules for determining near-optimal Si values in practice.Ph.D., Decision Sciences -- Drexel University, 200