The classical economic lot-scheduling problem (ELSP) involves the batch sizing and scheduling of multiple products in a single facility under deterministic conditions over an infinite planning horizon. It is assumed that the products are delivered to customers at continuous rates. In today's supply chains, however, often employing complex delivery networks, the finished goods are usually transported in discrete lots to succeeding stages along the distribution process, in order to take advantage of economies of scale in transportation. In this paper, we formulate mathematical models that attempt to integrate the production lot scheduling problem with outbound shipment decisions. The optimization objective is to minimize the total relevant costs of a manufacturer, which distributes a set of products to multiple retailers. In making the production/distribution decisions, the common cycle approach is employed to solve the ELSP, for simplicity. Two different shipping scenarios, i.e. periodic full truckload (TL) peddling shipments and less than truckload (LTL) direct shipping, are integrated with and linked to the multiproduct batching decisions. We consider these two shipment policies for both coordinated and uncoordinated scenarios. The resulting mixed-integer, non-linear programming models (MINLPs) are solved by the BONMIN solver. Finally, a set of numerical examples illustrate and evaluate the relative efficacies of these policies.

Studiens syfte är att undersöka optimala orderstorlekar på kaffeproducenten Zoégas förpackningslinjer i Helsingborg. Bakgrunden är att företaget är omedvetna om hur dagens orderstorlekar påverkar produktionen, med hänsyn till produktivitet samt ställ- och lagerhållningskostnader. Fallföretaget har dessutom en vilja att på längre sikt att införa ”pull planning”, vilket understödjer vetskap om förpackningslinjernas förutsättningar. Studien är i huvudsak uppdelad i två distinkta moment; ett som jämför historisk produktivitet i förhållande till orderstorlek och ett som beräknar optimal orderstorlek med hjälp av schemaläggningsverktyget ”Economic lot scheduling problem” (ELSP). Ena förpackningslinjen utmynnar i ett klassiskt fall av ”basic period approach”, som frekvent har behandlats inom litteraturen för ELSP. De andra linjerna har ställtider som beror på ordning, vilket komplicerar tillvägagångssättet. Huvuddelen av datainsamlingen har möjliggjorts genom tillgång till data från företagets produktions- och affärssystem. ELSP-resultatet genererar orderstorlekar och tillverkningsscheman för samtliga förpackningslinjer; optimerade med kostnadsminimering. Studien fann även statistiskt signifikanta samband mellan orderstorlek och produktivitet på Zoégas; samband som resulterade i gränsvärden för mest produktiva orderstorlekar. Majoriteten av ELSP-storlekarna placerade sig innanför dessa gränser. Slutligen fann studien att företaget, vid implementering av studiens förbättringsförslag, kan öka sin produktomsättning och på så sätt vara bättre förberedda för införande av ”pull planning”. / The purpose of this thesis is to investigate optimal order quantities at the coffee producer Zoéga’s packaging lines in Helsingborg. The company is currently unaware of how order quantities affect their production; with regards to productivity as well as setup- and holding costs. With a long-term vision of incorporating “pull planning”, the case company also needs to evaluate the capabilities of their current production system. The case study mainly addresses two areas; one comparing historical productivity in relation to order quantity, and one determining optimal order quantity with the scheduling-tool known as “Economic lot scheduling problem”. One of the packaging lines results in a classic case of “Basic period approach”, a problem frequently reviewed in ELSP-literature. The other lines have sequence dependent setup times, which required a more complex model. The primarily data collection has been from internal production- and management systems. The ELSP-results generated optimal order quantities and production schedules for all packaging lines. The study also found statistically significant correlations between order quantity and productivity for Zoéga’s. These correlations compiled upper and lower limits for the most productive order quantities; where most of the ELSP-quantities placed inside these limits. Finally, the study shows that by implementing these suggestions, Zoéga’s could speed up their product turnover and be better prepared for “pull planning” implementation in the future.

The latest generation of semiconductor wafer fabs produce Integrated Circuits (ICs) on silicon wafers of 300mm diameter. In this dissertation, we address the following two types of (new) scheduling problems that are encountered in this generation of wafer fabs: multiple-lots-per-carrier scheduling problem (MLCSP) and integrated automated material handling and lot scheduling problem (IMHLSP). We consider several variations of the MLCSP depending upon the number of machines used, the prevailing processing technology of the machines, and the type of objective functions involved. For the IMHLSP, we study two instances, one with infinite number of vehicles and the other with finite number of vehicles. We begin by introducing a single-machine, multiple-lots-per-carrier with single-wafer-processing-technology scheduling problem for the objective of minimizing the total completion time (MLCSP1). The wafer carrier is a front-opening unified pod (FOUP) that can hold a limited number of wafers. The problem is easy to solve when all the lots are of the same size. For the case of different lot sizes, we first relax the carrier (FOUP) capacity and propose a dynamic programming-based algorithm, called RelaxFOUP-DP, which enables a quick determination of its optimal solution that serves as a lower bound for the problem with limited FOUP capacity. Then, a branch-and-bound algorithm, designated as MLCSP1-B&B, is developed that relies on the lower bound determined by the RelaxFOUP-DP algorithm. Numerical tests indicate that MLCSP1-B&B finds optimal solutions much faster than the direct solution of the MLCSP1 model by the AMPL CPLEX 10.1 Solver. In fact, for the medium and low density problems, the MLCSP1-B&B algorithm finds optimal solutions at the starting node (node zero) itself. Next, we consider a single-machine, multiple-lots-per-carrier with single-carrier-processing-technology scheduling problem for the objective of minimizing total completion time (MLCSP2). As for the case of MLCSP1, the optimal solution for the case in which all the lots are of the same size can be obtained easily. For the case of different lot sizes, we determine a lower bound and an upper bound for the problem and prove the worst-case ratios for them. Subsequently we analyze a two-machine flow shop, multiple-lots-per-carrier with single-wafer-processing-technology scheduling problem for the objective of minimizing the makespan (MLCSP3). We first consider a relaxed version of this problem, and transform the original problem to a two-machine flow shop lot streaming problem. Then, we propose algorithms to find the optimal capacitated sublot sizes for the case of lots with (1) the same ratio of processing times, and, (2) different ratios of processing times on the machines. Since the optimal solutions obtained from the lot streaming problem may not be feasible to the MLCSP3, we develop heuristic methods based on the heuristic procedures for the bin packing problem. We develop four heuristic procedures for lots with the same ratio of processing times, and another four procedures for lots with different ratios of processing times on the machines. Results of our numerical experimentation are presented that show that our heuristic procedures generate almost optimal solutions in a matter of a few seconds. Next, we address the integrated automated material handling and lot scheduling problem (IMHLSP) in the presence of infinite number of vehicles. We, first, propose a new strong hybrid model, which has the advantages of both segregate and direct models. In the segregate model, a job is always transferred to the stocker after its completion at a station, while in the direct model, it is transferred to the next machine in case that machine can accommodate the jobs; otherwise, the job will stay at current station. The decisions involved in the strong hybrid model are the sequence in which to process the lots and a selection between the segregate and direct models for each lot, whichever optimizes system performance. We show that, under certain conditions about the processing times of the lots, the problem can be approximated by the cases of either infinite buffer or zero-buffer at the machines. Hence, we consider all three cases of the IMHLSP in this chapter, namely, infinite buffer, zero-buffer, and limited buffer sizes. For the strong hybrid model with limited buffer size, we propose a branch-and-bound algorithm, which uses a modified Johnson's algorithm to determine a lower bound. Two upper bounds for this algorithm are also determined. Results of our numerical investigation indicate that our algorithm finds optimal solutions faster than the direct solution of the IMHLSP model by the AMPL CPLEX 10.1 Solver. Experimental results also indicate that for the same problem size, the times required to solve the IMHLSP model with interbay movements are larger than those for intrabay movements. Finally, we investigate the IMHLSP in the presence of limited number of vehicles. Due to the complex nature of the underlying problem, we analyze small-size versions of this problem and develop algorithms for their solution. For some of these problems, we can find optimal solutions in polynomial time. Also, based on our analysis on small-size systems, we have shown why some real-time dispatching (RTD) rules used in real fabs are expected to perform well while not the others. In addition, we also propose some new and promising RTD rules based on our study. / Ph. D.

Titel: Planeringsmetoder i processindustrin: En fallstudie för AAK AB Författare: Mirlinda Brahimi och William JonassonHandledare: Peter BerlingExaminator: Helena Forslund  Bakgrund: I dagsläget har AAK svårigheter att finna tillräcklig kapacitet för att kunna möta sina kunders ordrar i vissa fall. Det förekommer att de full belastar sin produktionskapacitet och då de måste tacka nej till vissa kunders beställningsordrar. Studien grundar sig i att undersöka och skapa mer förståelse för cyklisk planering eller schemaläggning, då det finns ett behov av att finna sätt att samproducera och gruppera produkter i planeringen. Olika metoder granskas för att upptäcka en lämplig eller förbättrad planeringsmetod som kan skapa produktionsfokus i cykler som vidare bidrar till att minska kapacitetsproblemen och öka produktionseffektiviteten.  Syfte: Studiens syfte är att kartlägga och fördjupa sig i planeringsmiljön på AAK för att förbättra deras produktionsplanering i verksamheten. Det görs främst genom att förenkla och placera AAK:s planeringsmiljö i vilken miljötyp företaget tillhör samt dess förutsättningar som förekommer i miljön. Utifrån miljötypen så identifieras olika planeringsmetoder för att ta reda om dess tillämpbarhet kan realiseras på praktiken och faktiskt stabilisera planeringsmiljöns komplexitet på företaget såväl som det ska leda till en ökad fabriksproduktion.Metod: Studiens metod består av en kvalitativ studie, men också en kvantitativ då det görs beräkningar av olika modeller för det dataunderlag som erhållits för AAK:s kartongtappning. Den teoretiska referensramen skapades främst genom sökning av litterära källor och vetenskapliga artiklar. Studiens empiriska data har insamlats genom ostrukturerade- och semistrukturerade intervjuer av olika personer i studiens fallföretag. Resultat och slutsats: Studiens resultat visar att AAK:s miljötyp liknar en repetitiv masstillverkning. Powers-of-two beräkningar visade på goda resultat för kartongtappningen, men skulle kunna anpassas utifrån ett Product Wheel för att ta vara på båda metodernas fördelar. Mycket tyder på liknande resultat för andra processindustrier, då miljötypen är vanlig inom processindustrin.