Pall Jensson

Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry

The underlying time framework used is one of the major differences in the basic structure of mathematical programming formulations used for production scheduling problems. The models are either based on continuous or discrete time representations. In the literature there is no general agreement on which is better or more suitable for different types of production or business environments. In this paper we study a large real-world scheduling problem from a pharmaceutical company. The problem is at least NP-hard and cannot be solved with standard solution methods. We therefore decompose the problem into two parts and compare discrete and continuous time representations for solving the individual parts. Our results show pros and cons of each model. The continuous formulation can be used to solve larger test cases and it is also more accurate for the problem under consideration.

Procedure for reducing the risk of delayed deliveries in make-to-order production

Make-to-order production is generally operated in a very unpredictable and competitive environment, where the key factors to succeed are to provide high service levels and flexibility while at the same time offering inexpensive products. To receive customers, production companies must often promise short lead-times and the option of adjustable order quantities and delivery dates. Coping with uncertainty and variable demand is a challenging task. With the additional challenge of cutting down the production costs to be able to provide inexpensive products, proper planning and scheduling of the production becomes very difficult and crucial for success. It is therefore of crucial importance to develop systematic methods to address the problem of planning and scheduling under uncertainty in order to create efficient and reliable plans and thereby reduce the risk of delayed deliveries of customer orders. This study introduces the subject of creating robust production plans and schedules in the typical modern production environment characterised by several important sources of uncertainty. We introduce an efficient and practical modelling approach for creating robust production plans under uncertain and varying demand conditions. As an inspiration we have a large real-world problem originating from a complex pharmaceutical enterprise.

A Simulation Model of the Capelin Fishing in Iceland

In the last decade, or since the herring disappeared from the Icelandic fishing waters in 1967–68, the capelin has been by far the most important industrial fish for the production of meal and oil in Iceland.

Impact of the cost of the time resource on efficiency of economic processes

The objective of the paper is to simulate behavior of economic agents with a special emphasis on the use of the time resource in economic processes. The case studied is from the fishing industry. With simulations, the study analyzes the behavior of economic agents as they lead their processes through time. The paper estimates the value of time in a fishery operation, and shows that the time cost is essential in clarifying some phenomena in the economic behavior of agents. Among the conclusions is that the difference in economic efficiency between strong and weak ownership is due to difference in time costs. The secondary goal of the paper is to develop a simulation tool for analyzing a range of problems in the fishing industry, ranging from decision situations onboard fishing vessels to serving as a tool for fishery managers and legislators.

Optimal sequencing of tasks in an aluminium smelter casthouse

This paper examines the problem of determining the sequence in which to cast aluminium ingots such that setup times are minimized. The aluminium ingots are of different size and consist of different alloys; this poses constraints on the allowable ordering of casting jobs. The sequencing problem can be formulated as an asymmetric traveling salesman problem with additional constraints. Two different methods are used to formulate and solve this problem, a genetic algorithm (GA) and an integer programming approach (IP). A new method for detecting sub-tours in the IP formulation is set forth and used. Both the GA and IP approach are implemented in a software tool that is being used in the aluminium production industry. The results show that even though the integer programming formulation can be used to solve the problem to optimality, the size of the problem is a limiting factor for practical implementation. Therefore, the genetic algorithm is used in the industrial implementation with good results.

Integration of multi-scale planning and scheduling problems

Abstract In this paper we propose a multi-scale approach together with integration strategies for a continuous and dynamic planning and scheduling decision problem from the process industry. The decisions have to be made before all data are available in contrast to most sophisticated planning and scheduling approaches for the process industry that consider a fixed time horizon and assume that all data is given at the time of application. The approach is based on a hierarchically structured moving horizon algorithm. On each level we propose optimsation models to provide support for the relevant decisions. The levels are integrated with versatile integration strategies that transfer and implement the decisions at the adjacent levels. The algorithm based on the integration strategies restricts the solution space to eliminate infeasible solutions and uses hard constraints, bounds, shaping methods and penalty functions as guidelines, for obtaining near-optimal solutions. Feasible solutions can still be obtained when the guidelines are violated although they become less optimal. Solution procedures have been developed and the integrated multi-scale approach has been validated and tested with data from the real world problem.