A dynamic lot-sizing model with demand time windows

One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real life applications, the customer offers a grace period - we call it a demand time window - during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If shortages are not allowed, the complexity of the proposed algorithm is of the order T square. When backlogging is allowed, the complexity of the proposed algorithm is of the order T cube.dynamic programming;lot-sizing;time windows

Media planning by optimizing contact frequencies

In this paper we study a model to estimate the probability that a target group of an advertising campaign is reached by a commercial message a given number of times. This contact frequency distribution is known to be computationally difficult to calculate because of dependence between the viewing probabilities of advertisements. Our model calculates good estimates of contact frequencies in a very short time based on data that is often available. A media planning model that optimizes effective reach as a function of contact frequencies demonstrates the usefulness of the model. Several local search procedures such as taboo search, simulated annealing and genetic algorithms are applied to find a good media schedule. The results show that local search methods are flexible, fast and accurate in finding media schedules for media planning models based on contact frequencies. The contact frequency model is a potentially useful new tool for media planners.optimization;contact frequency;effective reach;media planning

A Note on "Stability of the Constant Cost Dynamic Lot Size Model" by K. Richter

In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution

Sensitivity Analysis of the Economic Lot-Sizing Problem

In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovered that faster algorithms than the Wagner-Whitin algorithm exist to solve the economic lot-sizing problem. Moreover, these algorithms reveal that the problem has more structure than was recognized so far. When performing the sensitivity analysis we exploit these newly obtained insights

Media planning by optimizing contact frequencies

In this paper we study a model to estimate the probability that a target group of an advertising campaign is reached by a commercial message a given number of times. This contact frequency distribution is known to be computationally difficult to calculate because of dependence between the viewing probabilities of advertisements. Our model calculates good estimates of contact frequencies in a very short time based on data that is often available. A media planning model that optimizes effective reach as a function of contact frequencies demonstrates the usefulness of the model. Several local search procedures such as taboo search, simulated annealing and genetic algorithms are applied to find a good media schedule. The results show that local search methods are flexible, fast and accurate in finding media schedules for media planning models based on contact frequencies. The contact frequency model is a potentially useful new tool for media planners

Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic lot-sizing model, adding stationary production capacities at the manufacturer, as well as multiple intermediate storage levels (including the retailer level), and transportation between these levels. Allowing for general concave production costs and linear holding costs, we provide polynomialtime algorithms for the cases where the transportation costs are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. The running times of the algorithms are remarkably insensitive to the number of levels in the supply chain

Integrated market selection and production planning: Complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances

Bodembiologie sleutel landbouw van de toekomst

De bodem is de motor van de landbouw. Naast de bekende chemische en fysische aspecten speelt de biologie een bepalende rol in de gezondheid van de bodem en daarmee het omringende milieu. Een nieuw geluid in ‘bodemland’ biedt kansen voor een toekomstbestendige landbouwsector: de bodembiologie