Alf Kimms

Lot sizing and scheduling — Survey and extensions

This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both approaches that are well-established and approaches which may represent tomorrows state of the art. Two research directions are discussed in more detail: continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.

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.

A genetic algorithm for multi-level, multi-machine lot sizing and scheduling

Abstract This contribution introduces a mixed-integer programming formulation for the multi-level, multi-machine proportional lot sizing and scheduling problem. It also presents a genetic algorithm to solve that problem. The efficiency of that algorithm is due to an encoding of solutions which uses a two-dimensional matrix representation with non-binary entries rather than a simple bitstring. A computational study reveals that the proposed procedure works amazingly fast and competes with a tabu search approach that has recently been published. Scope and purpose The logic of Manufacturing Resource Planning (MRP II) is implemented in most production planning software packages. In the short-term scope, where lot sizing and scheduling has to be done, MRP II systems basically pass three phases: First, lot sizes are computed while disregarding capacity constraints. Multi-level product structures are taken into account in a level-by-level manner starting with end items. Second, lot sizes are adapted to meet capacity restrictions. This time, precedence relations among items are not taken into account. Finally, sequence decisions are made. Following this strategy is reported to result in high work-in-process and long lead times. To cure these shortcomings, an approach for simultaneous lot sizing and scheduling is required where multi-level product structures and several scarce capacities are taken into account. Unfortunately, such methods have not been presented yet. To close this gap is our aim.

Optimization guided lower and upper bounds for the resource investment problem

The resource investment problem deals with the issue of providing resources to a project such that a given deadline can be met. The objective is to make the resources available in the cheapest possible way. For each resource, expenses depend on the maximum amount required during the course of the project. In this paper we develop two lower bounds for this NP-hard problem using Lagrangean relaxation and column generation techniques, respectively. Both procedures are capable of yielding feasible solutions as well. Hence, we also have two optimization guided heuristics. A computational study consisting of a set of 3210 instances compares both approaches and allows insight into the performance.

Network decomposition-based benchmark results for the discrete time-cost tradeoff problem

In project management, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time–cost tradeoff problem which has been extensively studied in the past. However, the discrete version of the problem which is of great practical relevance, did not receive much attention so far. Given a set of modes (time–cost pairs) for each activity, the objective of the discrete time–cost tradeoff problem is to select a mode for each activity so that the total cost is minimized while meeting a given project deadline. The discrete time–cost tradeoff problem is a strongly -hard optimization problem for general activity networks. In terms of what current state-of-art algorithms can do, instances with (depending on the structure of the network and the number of processing alternatives per activity) no more than 20–50 activities can be solved to optimality in reasonable amount of time. Hence, heuristics must be employed to solve larger instances. To evaluate such heuristics, lower bounds are needed. This paper provides lower and upper bounds using column generation techniques based on “network decomposition”. Furthermore, a computational study is provided to demonstrate that the presented bounds are tight and that large and hard instances can be solved in short run-time.

Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem

This paper introduces an evolutionary algorithm as a procedure to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot-sizing and scheduling of raw materials in tanks and soft drinks in bottling lines, where setup costs and times depend on the previous items stored and bottled. A multi-population genetic algorithm approach with a novel representation of solutions for individuals and a hierarchical ternary tree structure for populations is proposed. Computational tests include comparisons with an exact approach for small-to-moderate-sized instances and with real-world production plans provided by a manufacturer.

Stability Measures for Rolling Schedules with Applications to Capacity Expansion Planning, Master Production Scheduling, and Lot Sizing.

This contribution discusses the measurement of (in-)stability of finite horizon production planning when done on a rolling horizon basis. As examples we review strategic capacity expansion planning, tactical master production schedulng, and operational capacitated lot sizing.

Multi-level, single-machine lot sizing and scheduling: With initial inventory

Abstract This paper presents a mixed-integer program for the dynamic lot sizing and scheduling problem in a multi-level, single-machine environment. It turns out that in contrast to single-level problems the integration of initial inventory is a crucial aspect if generality should not be lost. It is shown how problem instances can efficiently be solved to suboptimality by using a so-called randomized regret based heuristic.

Pattern-based evacuation planning for urban areas

The population of an urban area may be in danger due to disasters like floods, hurricanes, chemical or nuclear accidents. This requires decisions to protect the affected population. One decision may be to evacuate the affected area. For the exceptional case of an evacuation an approach to reorganize the traffic routing of the endangered area is developed. In this paper a two-stage heuristic solution approach for a pattern-based mixed integer dynamic network flow model is presented. The model restructures the traffic routing such that the evacuees leave the evacuation area as safe as possible and as early as possible within the considered time horizon.

Revenue management for broadcasting commercials: the channel's problem of selecting and scheduling the advertisements to be aired

We describe a planning problem at a broadcasting company (e.g. a TV or radio channel). Advertisers place orders for commercials. Typically, each order consists of multiple spots, and the airdates of the spots are not fixed by the advertiser. Therefore, the channel has to decide simultaneously which orders to accept or to reject and when spots from accepted orders should be scheduled. We formally describe this problem in a mathematical model, present five heuristics, develop a rigorous method to generate a test bed and evaluate the performance of the heuristics on over 10,000 instances of various sizes.