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

Integration and coordination in after-sales service logistics

Maintenance and after-sales service logistics are important disciplines that have received considerable attention both in practice and in the scientific literature. This attention is related to the often high investments and revenues associated with capital-intensive assets in technically advanced business environments. Different maintenance services such as inspections and preventive maintenance activities are executed with the goal to maximize the availability of these expensive assets. However, unavoidable failures may still happen, which means that, in addition to preventive maintenance and services, repair actions (corrective maintenance) are necessary. Spare parts, service engineers and tools are typically the main resources for executing the repair actions and their availability has a major impact on overall system downtime. In this dissertation, we analyze a multi-resource after-sales service supply chain consisting of a service provider and an emergency supplier. The service provider is contractually responsible for the timely repair of some randomly failing capital intensive assets. To execute a repair, the service provider needs both service engineers and spare parts to replace the malfunctioning parts. In case of spare parts stock out, the service provider can either wait for the regular replenishment of parts or decide to hand over the entire repair call to an emergency supplier. For the latter case, a contract between the service provider and the emergency supplier is necessary to specify the compensation. In the first part of this dissertation, we focus on the optimal integrated planning of spare parts and engineers, considering an asset availability constraint. We evaluate the system performance using Markov chain analysis and queueing models, and employ different optimization algorithms to jointly determine the optimal capacity of the resources. This integrated planning results in considerable cost savings compared to the separate planning of spare parts and engineers. In the second part, we investigate the best contract the supplier can offer to the service provider. Furthermore, we propose different coordinated contracts to achieve optimal revenues for both partners in this after-sales service supply chain, under both full and asymmetric information scenarios. Cooperative games, the dominance of one party over the other (Stackelberg game), and information sharing aspects are the tools included in the second part of this dissertation

Approximation algorithms for capacitated stochastic inventory systems with setup costs

We develop the first approximation algorithm with worst-case performance guarantee for capacitated stochastic periodic-review inventory systems with setup costs. The structure of the optimal control policy for such systems is extremely complicated, and indeed, only some partial characterization is available. Thus, finding provably near-optimal control policies has been an open challenge. In this article, we construct computationally efficient approximate optimal policies for these systems whose demands can be nonstationary and/or correlated over time, and show that these policies have a worst-case performance guarantee of 4. We demonstrate through extensive numerical studies that the policies empirically perform well, and they are significantly better than the theoretical worst-case guarantees. We also extend the analyses and results to the case with batch ordering constraints, where the order size has to be an integer multiple of a base load.National Science Foundation (U.S.) (CMMI-1362619)National Science Foundation (U.S.) (CMMI-1131249)National Science Foundation (U.S.) (DMS-0732175)National Science Foundation (U.S.) (CMMI-0846554)National Science Foundation (U.S.) (FA9550-08-1–0369

OPTIMAL INBOUND/OUTBOUND PRICING MODEL FOR REMANUFACTURING IN A CLOSED-LOOP SUPPLY CHAIN

The paper presents a model for optimizing inbound and outbound pricing for closed-loop supply chains that remanufacture reusable products. Remanufacturers create reusable products from returned used products and sell the products “as new” to manufacturers or consumers. By implementing a return subsidy, remanufacturers can encourage the consumer to return used products. Demand for the as-new components often depends on the selling price and inventory. The available inventory increases as the subsidy increases and as the price decreases. Our model can determine the optimal subsidy and selling price for used and remanufactured products, respectively. Our model uses the Karush–Kuhn–Tucker conditions to solve its nonlinear problem. Sensitivity analysis reveals how different parameters affect profit under model-optimized conditions

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

Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering

The situation where serviceable products are sold together with a proportion of deteriorating products to consumers is rarely discussed in the literature. This article proposes an inventory model with disparate inventory ordering policies under a situation where a portion of serviceable products and a portion of deteriorating products are sold together to consumers (i.e. mixed sales). The ordering policies consider a hybrid payment strategy with multiple prepayment and partial trade credit schemes linked to order quantity under situations where no inventory shortage is allowed and inventory shortage is allowed with full backorder. The hybrid payment policy offered by a supplier is introduced into the classical economic ordering quantity model to investigate the optimal inventory cycle and the fraction of demand that is filled from the deteriorating products under inspection policy. Further, a new solution method is proposed that identifies optimal annual total profit with mixed sales assuming no inventory shortage and inventory shortage with full backorder. The impact of an inspection policy is investigated on the optimality of the solution under hybrid payment strategies for the deteriorating products. The validation of the proposed model and its solution method is demonstrated through several numerical examples. The results indicate that the inventory model along with the solution method provide a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider inclusion of an inspection policy in the mixed sales of products, as the inspection policy significantly increases the net annual profit

Supply chain contracting coordination for fresh products with fresh-keeping effort

Purpose – Fresh product loss rates in supply chain operations are particularly high due to the nature of perishable products. This paper aims to maximize profit through the contract between retailer and supplier. The optimized prices for the retailer and the supplier, taking the fresh-keeping effort into consideration, are derived. Design/methodology/approach – To address this issue, we consider a two-echelon supply chain consisting of a retailer and a supplier (i.e., wholesaler) for two scenarios: centralized and decentralized decision-making. We start from investigating the optimal decision in the centralized supply chain and then comparing the results with those of the decentralized decision. Meanwhile, a fresh-keeping cost-sharing contract and a fresh-keeping cost- and revenue-sharing contract are designed. Numerical examples are provided, and managerial insights are discussed at end. Findings – The results show that (a) the centralized decision is more profitable than the decentralized decision; (b) a fresh product supply chain can only be coordinated through a fresh-keeping cost- and revenue-sharing contract; (c) the optimal retail price, wholesale price and fresh-keeping effort can all be achieved; (d) the profit of a fresh product supply chain is positively related to consumers’ sensitivity to freshness and negatively correlated with their sensitivity to price. Originality/value – Few studies have considered fresh-keeping effort as a decision variable in the modelling of supply chain. In this paper, a mathematical model for the fresh-keeping effort and for price decisions in a supply chain is developed. In particular, fresh-keeping cost sharing contract and revenue-sharing contract are examined simultaneously in the study of the supply chain coordination problem

An inventory system with time-dependent demand and partial backordering under return on inventory investment maximization

Producción CientíficaIn this article, we study an inventory system for items that have a power demand pattern and where shortages are allowed. We suppose that only a fixed proportion of demand during the stock-out period is backordered. The decision variables are the inventory cycle and the ratio between the initial stock and the total quantity demanded throughout the inventory cycle. The objective is to maximize the Return on Inventory Investment (ROII) defined as the ratio of the profit per unit time over the average inventory cost. After analyzing the objective function, the optimal global solutions for all the possible cases of the inventory problem are determined. These optimal policies that maximize the ROII are, in general, different from those that minimize the total inventory cost per unit time. Finally, a numerical sensitivity analysis of the optimal inventory policy with respect to the system input parameters and some useful managerial insights derived from the results are presented.Ministerio de Ciencia, Innovación y Universidades - Fondo Europeo de Desarrollo Regional (project MTM2017-84150-P

A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems