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

Production planning and Order Acceptance: an Integrated Model with Flexible Due Dates

International audienceWe study a tactical problem integrating production planning with order acceptance decisions. We explicitly consider the dependency between the workload (and work-in-process inventory) and lead times. In the new model, orders are accepted/rejected and their processing period is determined. This problem is formulated as a mixed integer linear program for which two relax-and-fix heuristic solution methods are proposed. The first one decomposes the problem based on time periods while the second decomposes it based on orders. The performances of these heuristics are compared with the performance of a commercial solver. The numerical results show that the time-based relax-and-fix heuristic outperforms the order-based relax-and-fix heuristic and the solver solution as it yields better integrality gaps for much less CPU time

Lot Sizing Heuristics Performance

Each productive system manager knows that finding the optimal trade‐off between reducing inventory and decreasing the frequency of production/ replenishment orders allows a great cut‐back in operations costs. Several authors have focused their contributions, trying to demonstrate that among the various dynamic lot sizing rules there are big differences in terms of performance, and that these differences are not negligible. In this work, eight of the best known lot sizing algorithms have been described with a unique modelling approach and have then been exhaustively tested on several different scenarios, benchmarking versus Wagner and Whitin’s optimal solution. As distinct from the contributions in the literature, the operational behaviour has been evaluated in order to determine which one is more suitable to the characteristics of each scenario

DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

Shipping Consolidation with Delivery Deadline and Expedited Shipment Options

Problem definition: Shipment consolidation is commonly used to take advantage of the economies of scale by avoiding some of the shipping costs. However, when pending current orders are consolidated with future orders it may require more expensive expedited shipment in order to meet shorter deadlines. In this paper, we study the optimal consolidation policy focusing on the trade-off between economies of scale and expedited shipping costs. Academic/Practical Relevance: Our work is motivated by the prevalence of consolidation in the supply chain industry and also by its potential application for online and omni-channel retailing, especially with the rise of, so-called, on-demand logistic services. In such situations, sellers, have the flexibility to take advantage of consolidation, by deciding from which warehouse to fulfill the orders and also when to ship the orders, as long as the orders deadlines are met. Methodology: We use Dynamic Programming to study the optimal policy and its structure. We also conduct intensive simulation tests to show the good performance of heuristics which we proposed based on structures of the optimal policy. Results: The optimal policies and their structures are characterized in settings with up to two warehouses, where the impact of expedited shipment on both shipping policy and order fulfillment policy are explored. Utilizing the insights of these structural properties, two easily implementable heuristics are proposed, which perform within 1-2% of the optimal in intensive numerical tests. Managerial Implications: Despite the complexity of the actual optimal consolidation policy, sellers can apply the two simple heuristic policies we proposed to get near-optimal performance in various cases.https://deepblue.lib.umich.edu/bitstream/2027.42/138942/1/1375_Jasin.pd

A review of discrete-time optimization models for tactical production planning

This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation (MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

Multistage stochastic capacitated discrete lot-sizing with lead times: problem definition, complexity analysis and tighter formulations

A stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed. The problem determines the expected cost minimization of satisfying the uncertain demand of a product during a discrete time planning horizon. The supply of the product is made through the purchase of optional distinguishable orders of fixed size with lead time. Due to the uncertainty of demand, corrective actions, such as order cancellation and postponement, may be taken with associated costs and time limits. The problem is modeled as an extension of a capacitated discrete lot-sizing problem with uncertain demand and lead times through a multistage stochastic mixed-integer programming approach. To improve the resolution of the model by tightening its formulation, valid inequalities are generated based on conventional inequalities. Subsets of approximately non dominated valid inequalities are determined heuristically. A procedure to tighten an upgraded formulation based on a known scheme of pairing of inequalities is proposed. Computational experiments are performed for several instances with different uncertainty information structure. The experimental results allow to conclude that the inclusion of subsets of the generated valid inequalities enable a more efficient resolution of the model

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005