Dynamic lot sizing with multiple suppliers, backlogging and quantity discounts

This paper studies the dynamic lot sizing problem with supplier selection, backlogging and quantity discounts. Two known discount types are considered separately, incremental and all-units quantity discounts. Mixed integer linear programming (MILP) formulations are presented for each case and solved using a commercial optimization software. In order to timely solve the problem, a recursive formulation and its efficient implementation are introduced for each case which result in an optimal and a near optimal solution for incremental and all-units quantity discount cases, respectively. Finally, the execution times of the MILP models and forward dynamic programming models obtained from the recursive formulations are presented and compared. The results demonstrate the efficiency of the dynamic programming models, as they can solve even large-sized instances quite timely. © 201

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Optimizing lot sizing model for perishable bread products using genetic algorithm

This research addresses order planning challenges related to perishable products, using bread products as a case study. The problem is how to effi­ci­ently manage the various bread products ordered by diverse customers, which requires distributors to determine the optimal number of products to order from suppliers. This study aims to formulate the problem as a lot-sizing model, considering various factors, including customer demand, in­ven­tory constraints, ordering capacity, return rate, and defect rate, to achieve a near or optimal solution, Therefore determining the optimal order quantity to reduce the total ordering cost becomes a challenge in this study. However, most lot sizing problems are combinatorial and difficult to solve. Thus, this study uses the Genetic Algorithm (GA) as the main method to solve the lot sizing model and determine the optimal number of bread products to order. With GA, experiments have been conducted by combining the values of population, crossover, mutation, and generation parameters to maximize the feasibility value that represents the minimal total cost. The results obtained from the application of GA demonstrate its effectiveness in generating near or optimal solutions while also showing fast computational performance. By utilizing GA, distributors can effectively minimize wastage arising from expired or perishable products while simultaneously meeting customer demand more efficiently. As such, this research makes a significant contri­bution to the development of more effective and intelligent decision-making strategies in the domain of perishable products in bread distribution.Penelitian ini berfokus untuk mengatasi tantangan perencanaan pemesanan yang berkaitan dengan produk yang mudah rusak, dengan menggunakan produk roti sebagai studi kasus. Permasalahan yang dihadapi adalah bagaimana mengelola berbagai produk roti yang dipesan oleh pelanggan yang beragam secara efisien, yang mengharuskan distributor untuk menentukan jumlah produk yang optimal untuk dipesan dari pemasok. Untuk mencapai solusi yang optimal, penelitian ini bertujuan untuk memformulasikan masalah tersebut sebagai model lot-sizing, dengan mempertimbangkan berbagai faktor, termasuk permintaan pelanggan, kendala persediaan, kapasitas pemesanan, tingkat pengembalian, dan tingkat cacat. Oleh karena itu, menentukan jumlah pemesanan yang optimal untuk mengurangi total biaya pemesanan menjadi tantangan dalam penelitian ini. Namun, sebagian besar masalah lot sizing bersifat kombinatorial dan sulit untuk dipecahkan, oleh karena itu, penelitian ini menggunakan Genetic Algorithm (GA) sebagai metode utama untuk menyelesaikan model lot sizing dan menentukan jumlah produk roti yang optimal untuk dipesan. Dengan GA, telah dilakukan percobaan dengan mengkombinasikan nilai parameter populasi, crossover, mutasi, dan generasi untuk memaksimalkan nilai kelayakan yang merepresentasikan total biaya yang minimal. Hasil yang diperoleh dari penerapan GA menunjukkan keefektifannya dalam menghasilkan solusi yang optimal, selain itu juga menunjukkan kinerja komputasi yang cepat. Dengan menggunakan GA, distributor dapat secara efektif meminimalkan pemborosan yang timbul akibat produk yang kadaluarsa atau mudah rusak, sekaligus memenuhi permintaan pelanggan dengan lebih efisien. Dengan demikian, penelitian ini memberikan kontribusi yang signifikan terhadap pengembangan strategi pengambilan keputusan yang lebih efektif dan cerdas dalam domain produk yang mudah rusak dalam distribusi roti

A GENETIC ALGORITHM APPROACH FOR DYNAMIC SUPPLIER SELECTION

Supplier selection has a great impact on supply chain management. This decision considers many factors such as price, order quantity, quality, and delivery performance. We address a dynamic supplier selection problem (DSSP) which a buyer should procure multiple product from multiple supplier in multiple periods. Furthermore, transportation cost has significant impact in the procurement decision. However, only a few researchers consider transportation cost in their model. This paper proposes a dynamic supplier selection problem considering truckload shipping. A mixed integer non-linear programming (MINLP) model is developed to solve dynamic supplier selection problem. The purpose of model is to assign the best supplier that will be allocated products and to determine the right time to order that can minimize total procurement cost. In addition, constraints such as suppliers’ capacity, truck capacity, inventory balance, service level, and buyer storage are taken into consideration in the model. Due to the complexity of the problem, the formulated problem is NP-hard in nature so a genetic algorithm (GA) is presented to solve dynamic supplier selection problem. Finally numerical example has been solved by the proposed GA and the classical method using Lingo 16. The results illustrate an understandable slight errors in total cost when GA is compared to commonly used classical method

The stochastic lot-sizing problem with quantity discounts

This paper addresses the stochastic lot-sizing problem with quantity discounts. In particular, we examine the uncapacitated finite-period economic lot-sizing problem in which the parameters in each period are random and discrete. When an order is placed, a fixed cost is incurred and an all-unit quantity discount is awarded based on the quantity ordered. The lead time is zero and the order is delivered immediately. First we study the case with overstocks by which the excess inventory incurs a holding cost. The objective in this case is to minimize the expected total cost including ordering and holding costs. The stochastic dynamics is modeled with a scenario tree. We characterize properties of the optimal policy and propose a polynomial time algorithm with complexity O ( n 3 ) for single discount level, where n is the number of nodes in the scenario tree. We extend the results to cases allowing stockout and multi-discount levels. Numerical experiments are conducted to evaluate the performance of the algorithm and to gain the man- agement insights

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

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

Multisupplier procurement under uncertainty in industrial fishing environments

viii, 51 leaves : ill. ; 28 cm.Includes abstract.Includes bibliographical references (leaves 44-51).In this paper we address the issue of multi supplier sourcing as a tool for hedging against supply yield uncertainty. Our work was motivated by the problems in the fishing industry whereby fish processing firms are constantly faced with the problems of random supply yields. We formulated a mathematical programming model that can be used to determine the quantities to be ordered from two or more suppliers so as to minimize annual expected procurement cost while attempting to satisfy demand requirements and operating constraints. The cost included are purchasing cost, inventory related cost and ordering cost. We assume that at the beginning of a planning horizon comprised of 12 periods a firm enters into minimum contractual agreement with two suppliers, and in return each supplier offers a discounted price schedule. In our numerical analysis we solved the model for both the 2-supplier case and the single supplier case and compared the cost of using a single supplier versus two suppliers under varying levels of yield variability. We compared deterministic solutions for the single and two-supplier case and use Monte Carlo simulation to assess the robustness of the solutions under varying levels of yield uncertainty. Results show that as the variability of the yield rate increases it becomes cost effective to use two suppliers as a means for hedging against uncertainty. We compared the results from our model to that of a heuristic procedure proposed by Parlar and Wang, an alternative approach for solving the 2-supplier inventory problem. The results indicated that our model provides superior solutions to that of the heuristic procedure