Dubbel ABC-analys och lagerlayout i reservdelslager

Syftet med mitt slutarbete är att implementera ett system åt Alholmens såg för att kartlägga vilka reservdelar som är kritiska att ha i lager för att produktionen inte skall stanna. Men även att försöka skära ner lagerkostnaden genom att minska på antalet mindre kritiska delar i lagret. Utöver denna uppgift ombads jag även att göra en lager layout för ett nytt reservdelslager. Tidigare har man beställt delar utgående från erfarenheter, men dessa erfarenheter besitter endast en person i lagret. Man vill därför skapa ett verktyg så att nyanställda också ska kunna beställa rätt mängd av delar utan att öka på det bundna kapitalet. Därför valde jag att använda mig av en dubbel ABC-analys som kategoriserar reservdelarna enlig pris och utagsfrekvens. Med hjälp av analysen kan man nu klart se vilka delar som är dyra och används ofta och kräver hög prioritet men också delar som inte används så ofta som man kan överväga att ta bort ur reservdelsregistret.The purpose of my thesis is to implement a system for Alholmens såg to map which spare parts are crucial to have in stock to keep the production line running. Also, trying to cut down warehouse costs by reducing the amount of less crucial parts in stock. In addition to this task I was also asked to do a layout for a new spare parts warehouse. Previously spare parts have been order out of experience, but only one person in the warehouse possesses these experiences. That’s why a creation of tool is wanted, that makes it possible for newly hired personnel to order the right amount of parts whiteout increasing the capital. That’s why I chose to use a double ABC-analysis that will categories the spare parts per price and withdrawal rate. Whit the help of the analysis one can now clearly see which parts that are expensive, are used a lot and demands a high priority, and which parts that are not used so much and maybe considered to take out of stock

A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.

We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e. g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions

Sobolev inequalities with variable exponent attaining the values 1 and n

We study Sobolev embeddings in the Sobolev space W1,p(·) (Ω) with variable exponent satisfying 1 6 p(x) 6 n. Since the exponent is allowed to reach the values 1 and n, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of L∞ at the upper end

Regularity theory for non-autonomous problems with a priori assumptions

We study weak solutions and minimizers $u$ of the non-autonomous problems $\operatorname{div} A(x, Du)=0$ and $\min_v \int_\Omega F(x,Dv)\,dx$ with quasi-isotropic $(p, q)$-growth. We consider the case that $u$ is bounded, H\"older continuous or lies in a Lebesgue space and establish a sharp connection between assumptions on $A$ or $F$ and the corresponding norm of $u$. We prove a Sobolev--Poincar\'e inequality, higher integrability and the H\"older continuity of $u$ and $Du$. Our proofs are optimized and streamlined versions of earlier research that can more readily be further extended to other settings. Connections between assumptions on $A$ or $F$ and assumptions on $u$ are known for the double phase energy $F(x, \xi)=|\xi|^p + a(x)|\xi|^q$. We obtain slightly better results even in this special case. Furthermore, we also cover perturbed variable exponent, Orlicz variable exponent, degenerate double phase, Orlicz double phase, triple phase, double variable exponent as well as variable exponent double phase energies and the results are new in most of these special cases