Knut Haase

Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities

This paper deals with lot sizing and scheduling for a single-stage production System where setup costs and times are sequence dependent. A large bucket mixed integer programming (MIP) model is formulated which considers only efficient sequences. A tailor-made enumeration method of the branch-and-bound type solves problem instances optimally and efficiently. Furthermore, it will become clear that rescheduling can neatly be done.

Capacitated lot-sizing with sequence dependent setup costs

In this paper we consider a single-stage system where a number of different items have to be manufactured on one machine. Expenditures for the setups depend on the sequence in which items are scheduled on the machine. Holding costs are incurred for holding items in inventory. The demand of the items has to be satisfied without delay, i.e. shortages are not allowed. The objective is to compute a schedule such that the sum of holding and setup costs is minimized with respect to capacity constraints. For this problem which we call capacitated lot-sizing problem with sequence dependent setup costs (CLSD) we formulate a new model. The main differences between the new model and the discrete lot-sizing problem with sequence dependent setup costs (DLSDSD), introduced by Fleischmann, is that continuous lot-sizes are allowed and the setup state can be preserved over idle time. For the solution of the new model we present a heuristic which applies a priority rule. Since the priority values are affected by two significant parameters, we perform a local search in the parameter space to obtain low cost solutions. The solution quality is analyzed by a computational study. The comparison with optimal solutions of small instances shows that the solution quality of our heuristic is acceptable. The Fleischmann approach for the DLSPSD computes upper bounds for our new problem. On the basis of larger instances we show that our heuristic is more efficient to solve the CLSD.ZusammenfassungDieser Beitrag beschäftigt sich mit der Ablaufplanung für eine Engpaßmaschine unter besonderer Berücksichtigung reihenfolgeabhängiger Rüstkosten. Neben Rüstkosten sind von Losgrößen abhängige Lagerkosten entscheidungsrelevant. Die Losgrößen sind dabei unter Berücksichtigung der Maschinenkapazität in einem vorgegebenen Planungszeitraum so zu bestimmen, daß alle Teilebedarfe termingerecht in ausreichender Menge befriedigt werden. Zur Lösung des Planungsproblems entwickeln wir zunächst ein neues Modell. Es unterscheidet sich von dem von Fleischmann eingeführten Modell (the discrete lot-sizing problem with sequence dependent setup costs, DLSPSD) dadurch, daß es statt diskrete kontinuierliche Losgrößen zuläßt und daß der Rüstzustand bei Stillstand der Maschine erhalten bleibt. Zur Lösung des Problems wird eine prioritätsregelbasierte Heuristik vorgeschlagen. Die Prioritätswerte und dadurch auch die Lösungsgüte des Verfahrens hängen von zwei Parametern ab. Ein Suchverfahren zur Bestimmung geeigneter Parameterwerte wird vorgestellt. Anhand kleinerer optimal gelöster Datensätze wird gezeigt, daß die Lösungsgüte der Heuristik akzeptabel ist. Für größere Datensätze wird ein Vergleich mit dem von Fleischmann für das DLSPSD vorgeschlagenen Verfahren durchgeführt. Das Verfahren von Fleischmann liefert, bedingt durch die diskrete Losgrößenbildung, nur eine obere Schranke für die hier betrachtete Problemstellung. Der Vergleich zeigt, daß die prioritätsregelbasierte Heuristik dem Verfahren von Fleischmann hinsichtlich der betrachteten Problemstellung überlegen ist.

Proportional Lotsizing and Scheduling

Abstract Two multi-item capacitated dynamic lotsizing and scheduling models with a finite horizon have been established recently: the discrete lotsizing and scheduling problem as well as the continuous setup lotsizing problem. An analysis of the underlying fundamental assumptions provides the basis for introducing a new model, the proportional lotsizing and scheduling problem. We present a new backward-oriented regret-based biased random sampling method which solves the new model efficiently. The model is well suited for the incorporation of some of the extensions relevant for practice: setup times, sequence-dependent setup costs (times), multiple machines as well as multiple stages.

Experiences with fine‐grainedparallel genetic algorithms

In this paper, we present some results of our systematic studies of fine‐grained parallelversions of the island model of genetic algorithms and of variants of the neighborhood model(also called diffusion model) on the massively parallel computer MasPar MP1 with 16kprocessing elements. These parallel genetic algorithms have been applied to a range ofdifferent problems (e.g. traveling salesman, capacitated lot sizing, resource‐constrainedproject scheduling, flow shop, and warehouse location problems) in order to obtain anempirical basis for statements on their optimization quality.

Duty-period-based network model for crew rescheduling in European airlines

Airline rescheduling is a relatively new field in airline Operations Research but increasing amounts of traffic will make disturbances to the original schedule more frequent and more severe. Thus, the need to address the various problems arising from this situation with systematic, cost-efficient approaches is becoming more urgent. One such problem is crew rescheduling where after a disturbance in the crew schedule the aim is to determine new crew assignments that minimize the `impact’ on the original schedule.In this work we present a new duty-period-based formulation for the airline crew rescheduling problem that is tailored to the needs of European airlines. It uses a new type of resource constraints to efficiently cover the various labor regulations. A solution method based on branch-and-price is tested on various rescheduling scenarios, each with several distinct cases. Results show that the solution method is capable of providing solutions within the short period of time available to a rescheduler after a disturbance occurs.

An Exact Branch and Cut Algorithm for the Vehicle and Crew Scheduling Problem

We present a new model for the vehicle and crew scheduling problem in urban public transport systems by combining models for vehicle and crew scheduling that cover a great variety of real world aspects, including constraints for crews resulting from wage agreements and company regulations. The main part of the model consists of a set partitioning formulation to cover each trip. A column generation algorithm is implemented to calculate the continuous relaxation which is embedded in a branch and bound approach to generate an exact solution for the problem. To improve the lower bounds, polyhedral cuts basing on clique detection and a variant of the column generation algorithm that suits the cuts were tested.

Optimizing Railway Crew Scheduling at DB Schenker

Freight railway crew scheduling consists of generating crew duties for operating trains on a schedule at minimal cost while meeting all work regulations and operational requirements. Typically, a freight railway operation uses thousands of trains and requires thousands of crew members to operate them. Because of the problems large size, even moderate percentage savings in crew costs translate into large monetary savings. However, freight railway operations are complex, and a crew-scheduling problem is difficult to solve. We describe the development and implementation of crew-scheduling software at DB Schenker, the largest European railway freight carrier. The software is based on a column-generation solution technique. Computational results demonstrate that high-quality solutions can be obtained using reasonable run times, even for large problem instances. We implemented all of DB Schenkers major requirements to ensure that the software is operationally viable. Management also uses this software as a decision support tool for strategic planning.

Capacitated Lot-Sizing with Linked Production Quantities of Adjacent Periods

One of the most important tasks operations manager are confronted with is to determine production quantities over a medium-size planning horizon such that demand is met, scarce production facilities are not overloaded and that the sum of holding and setup costs is minimized. For the single machine case the well-known Capacitated Lot-Sizing Problem (CLSP) has been proposed to determine minimum cost solutions. The CLSP is based on the assumption that for each lot produced in a period setup cost is incurred. But in practice the machine setup can be preserved over idle time very often. In such cases the setup cost of a CLSP solution can be reduced by linking the production quantities of an item which is scheduled in two adjacent periods. Therefore we propose the CLSP with linked lot-sizes of adjacent periods. The problem is formulated as a mixed-integer programming model. For the heuristic solution we present a priority rule based scheduling procedure which is backward-oriented, i.e. at first lot-sizes are fixed in the last period, then in the last but one period, and so on. The priority rule consists of a convex combination of estimated holding and setup cost savings. Since the solution quality depends on realisation of the convex combination we perform a simple local search method on the parameter space to obtain low cost solutions. We show by a computational study that our procedure is more efficient than a two stage approach which first solves the CLSP with the Dixon-Silver or the Kirca-Kokten heuristic and performs linking of lots afterwards.

A comparison of linear reformulations for multinomial logit choice probabilities in facility location models

In the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model. Three linear reformulations of the original non-linear model have been proposed so far. In this paper, we discuss these models in terms of solvability. We present empirical findings based on synthetic data.

Insights into clients' choice in preventive health care facility location planning

In this contribution we build on the approach proposed by Zhang et al. (OR Spectrum 34:349–370, 2012) to consider clients’ choice in preventive health care facility location planning. The objective is to maximize the participation in a preventive health care program for early detection of breast cancer in women. In order to account for clients’ choice behavior the multinomial logit model is employed. In this paper, we show that instances up to 20 potential locations and 400 demand points can be easily solved (to optimality or at least close to optimality) by a commercial solver in reasonable time if the problem is modeled by an alternative formulation. We present an intelligible approach to derive a lower bound to the problem. Our paper provides interesting insights into the trade-off between minimum workload requirement (to ensure quality of care) and participation (and thus early diagnosis of disease). We present a general definition of clients’ utility (which allows for clients’ characteristics, for example) and discuss some fundamental issues (and pitfalls) concerning the specification of utility functions.