Sensitivity of multi-product two-stage economic lotsizing models and their dependency on change-over and product cost ratio's

This study considers the production and inventory management problem of a two-stage semi-process production system. In case both production stages are physically connected it is obvious that materials are forced to flow. The economic lotsize depends on the holding cost of the end-product and the combined change-over cost of both production stages. On the other hand this 'flow shop' is forced to produce at the speed of the slowest stage. The benefit of this approach is the low amount of Work In Process inventory. When on the other hand, the involved stages are physically disconnected, a stock of intermediates acts as a decoupling point. Typically for the semi-process industry are high change-over costs for the process oriented first stage, which results in large lotsize differences for the different production stages. Using the stock of intermediates as a decoupling point avoids the complexity of synchronising operations but is an additional reason to augment the intermediate stock position. The disadvantage of this model is the high amount of Work-In-Process inventory. This paper proposes the 'synchronised planning model' realising a global optimum instead of the combination of two locally optimised settings. The mathematical model proves (for a two-stage single-product setting) that the optimal two-stage production frequency corresponds with the single EOQ solution for the first stage. A sensitivity study reveals, within these two-stage lotsizing models, the economical cost dependency on product and change-over cost ratio‟s. The purpose of this paper is to understand under which conditions the „joined setup‟ or the „two-stage individual eoq model‟ remain close to the optimal model. Numerical examples prove that the conclusions about the optimal settings remain valid when extending the model to a two-stage multi-product setting. The research reveals that two-stage individually optimized EOQ lotsizing should only be used when the end-product stage has a high added value and small change-over costs, compared to the first stage. Physically connected operations should be used when the end-product stage has a small added value and low change-over costs, or high added value and large change-over costs compared to the first production stage. The paper concludes with suggesting a practical common cycle approach to tackle a two-stage multi-product production and inventory management problem. The common cycle approach brings the benefit of a repetitive and predictable production schedule

Amendment of Heuts-Selen's lotsizing and sequencing heuristic for single stage process manufacturing systems

Productivity;Production Scheduling;Manufacturing;production

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

APLIKASI TEKNIK LOT SIZING PADA PROYEK GEDUNG LABORATORIUM KEBENCANAAN UNIVERSITAS SYIAH KUALA

Abstrak Salah satu faktor mempengaruhi kelancaran dalam pelaksanaan suatu proyek konstruksi adalah pengadaan material ke lokasi. Keterlambatan datangnya material konstruksi yang menyebabkan stockout persediaan material saat akan digunakan membuat pekerjaan menjadi tertunda. Hal ini secara tidak langsung dapat mempengaruhi total waktu pelaksanaan serta biaya proyek. Penentuan tingkat persediaan yang tepat dapat diaplikasikan dengan mengunakan metode Material Requirement Planning (MRP). Tujuan dari penelitian adalah untuk mengetahui ukuran pemesanan dan biaya pengadaan material yang paling efisien dari dua teknik lotsizing yaitu teknik Period Order Quantity (POQ) dan teknik Economic Order Quantity (EOQ) pada Gedung Laboratorium Kebencanaan Universitas Syiah Kuala (USK) di Kota Banda Aceh. Proses yang terdapat dalam MRP meliputi netting, lotting, offsetting, dan explosion. Metode MRP diterapkan pada proyek Gedung Laboratorium Kebencanaan USK, dengan menghitung jumlah kebutuhan material berdasarkan data Rencana Anggaran Biaya (RAB), Analisis Harga Satuan (AHS), dan jadwal pelaksanaan terhadap 28 (dua puluh delapan) material di lokasi proyek. Berdasarkan dari teknik yang dianalisa, teknik lotsizing yang menghasilkan biaya total paling ekonomis untuk semua material adalah teknik Periodic Order Quantity (POQ) dengan biaya sebesar Rp. 9.850.848.30, Sedangkan yang mempunyai biaya pengadaan material sangat tinggi ditunjukkan oleh teknik EOQ, Rp. 9.852.102.40, artinya biaya yang dikeluarkan lebih kecil yaitu Rp. 1.234.00 (97%). Kata Kunci: Gedung Universitas Syiah Kuala, Material Requirement Planning, Lotsizing, Period Order Quantity, Economic Order Quantity  Abstract One of the factors influencing the continuity running of a construction project is material procurement to the site. The delay in the arrival of construction materials which causes a stockout of material supplies when they will be used makes the work delayed. This can indirectly affect the total implementation time and project costs. by using the Material Requirement Planning method. The purpose of this study was to determine the order size and the most efficient material procurement costs from the two lotsizing inventory control techniques, namely the Period Order Quantity (POQ) and the Economic Order Quantity (EOQ) at Disaster Laboratory Building University of Syiah Kuala in Banda Aceh city. The processes contained in MRP is netting, lotting, offsetting, and explosion. The MRP method is applied to the Disaster Laboratory Building University of Syiah Kuala project, by calculating the amount of material needed based on the Budget Plan data, Unit Price Analysis, and the project schedule which includes its 28 materials. Based on the analyzed technique, the lotsizing technique that produces the most economical total cost for all materials is the Periodic Order Quantity (POQ) technique with a cost of Rp. 9,850,848.30, while those who have very high material procurement costs are indicated by the EOQ technique, Rp. 9,852.102.40, meaning that the costs incurred are smaller, namely Rp. 1.234.00 (97%). Keywords: Building University of Syiah Kuala, Material Requirement Planning, Lotsizing, Period Order Quantity, Economic Order Quantit

Sonoco uses a stochastic lotsizing and scheduling model to optimize the production of coreboard

Since several years we have been working together with the European supply chain team of Sonoco, one of the largest global players active in the packaging industry, to solve a variety of supply chain challenges encountered in their industrial products & services division. In this work, we present the result from a pilot project related to production planning for which we developed a novel stochastic lotsizing and scheduling model and a solution approach tailored to their specific business environment

Workforce planning in a lotsizing mail processing problem

The treatment of mail objects in a mail processing centre involves many operations, in particular sorting by destination. Out of the batching problem that we can identify in such a process, there are also staff planning concerns. In this paper, we analyse a treatment area (registered mail) belonging to a mail processing center, where mail objects are treated in a chain production process. The production quantities and the transfer amounts among machines are required to be determined along the daily work period. The objective is to minimize the costs with human resources needed in the process, linked with the lotsizing production plan, by matching staff to work requirements. This leads into a lotsizing and workforce problem, for which we propose an integer programming formulation. A case study of a particular treatment area is also discussed. The formulation is adjusted to the specific constraints of this case study and some computational results are included, considering average, small and high daily amounts of mail arrived to that particular treatment area.http://www.sciencedirect.com/science/article/B6VC5-4CK7RXK-4/1/5986796334d7e593786cb5bf5b7dc4a