Production Lot Size Research Articles

Alternative approach for production lot size problem with scrap and cost reduction distribution policy

Conventional approach for solving replenishment lot size problem is by using the differential calculus with the need of applying the first-order and second-order differentiations to the long-run average production-inventory cost. A recent published paper used conventional method to determine optimal lot size for an integrated production-delivery system with scrap and cost lessening distribution policy. This paper uses an alternative algebraic approach to reexamine the aforementioned problem without referring to derivatives. As a result, optimal lot size and a simpler expression for the long-run average cost are derived, and they are identical to what were obtained by using the conventional method. Key words: Lot size, optimization, scrap, multiple distribution policy, algebraic approach, production planning.

Planning for demand failure: A dynamic lot size model for clinical trial supply chains

This paper examines the optimal production lot size decisions for clinical trial supply chains. One unique aspect of clinical trial supply chains is the risk of failure, meaning that the investigational drug is proven unsafe or ineffective during human testing and the trial is halted. Upon failure, any unused inventory is essentially wasted and needs to be destroyed. To avoid waste, manufacturers could produce small lot sizes. However, high production setup costs lead manufacturers to opt for large lot sizes and few setups. To optimally balance this tradeoff of waste and destruction versus production inefficiency, this paper generalizes the Wagner–Whitin model ( W–W model) to incorporate the risk of failure. We show that this stochastic model, referred to as the failure-risk model, is equivalent to the deterministic W–W model if one adjusts the cost parameters properly to reflect failure and destruction costs. We find that increasing failure rates lead to reduced lot sizes and that properly incorporating the risk of failure into clinical trial drug production can lead to substantial cost savings as compared to the W–W model without the properly adjusted parameters.

Assess your business model strategy to sustain

Subject area This case study considers the supply chain redesign of a multinational company, with specific emphasis on production lot sizing, inventory policy and transportation decisions. Study level/applicability The material is intended for senior level students of business administration, logistics and similar departments. An intermediate knowledge of supply chain, purchasing and inventory concepts is required; therefore, the case is better suited for students who have taken one-semester courses on supply chain management and inventory management. This case can be used in graduate courses as part of discussions on physical distribution, supply chain design/redesign, risk pooling through process optimization. Case overview Within the global market, establishing the right business model where cost of operations is optimized has become key for competitiveness. This necessitates the simultaneous consideration and reevaluation of production, inventory and transportation interactivities within the integrated supply chain. We first discuss the business procurement model of a multinational company with emphasis on critical aspects of the current structure. An alternative model brought into consideration by the managers of the company considers consolidation of shipments through supply hubs and distribution to regional manufacturers. We present an analysis based on perspectives of company managers for and against this new business model. We finally provide numeric evidence on relevant costs of both models in order to enhance further discussion on redesign decisions. Expected learning outcomes The discussion regarding the case will provide a better understanding of key concepts of supply chain integration and coordination as well as the significance of the optimization of underlying processes. Supplementary materials Teaching notes.

Analytical modelling of multi stage convergent supply chain system under just-in-time

The main objective of this paper is to develop an analytical model for operational level decisions for convergent supply chain system controlled by kanban under JIT where a product is assembled from a number of components supplied by many multistage supply chains. It integrates production and shipment lot size across the various stages of supply chain so that components travel through the supply chain in a coordinated way without any mismatch and final product reaches the customer in time. A quantitative analytical approach has been followed to develop the non-linear integer program (NLIP) and a generic LINGO program also has been developed for NLIP using branch and bound method for optimisation. This model facilitates integrated supply chain optimisation for system wide inventory, logistic and production setup costs optimisation. The model has been validated using automotive supply chain data. However, it can be applied to any industry.

Determination of production lot size and DC location in manufacturer DC retailer supply chains

Efficiency and responsiveness of global supply chains can no longer be achieved through isolated logistics systems or just production systems. This paper is inspired by an industry project to balance the design, schedule and cost of the production and logistics for a major apparel manufacturer. We model the supply chain as a Manufacturer-DC-Retailer system and explicitly incorporate the interplay between the logistics configuration and production control to support the total optimisation. The analytical and numerical results suggest that the proper co-design of the production and logistics systems could achieve significant cost saving.

A production policy considering reworking of imperfect items and trade credit

Making production decisions that will reduce total cost is a goal that most manufacturers pursue actively. However, the traditional production model development assumed that all products are perfect quality, which is far from reality. Since trade credit is a popular payment method in today’s business environment, this paper analyzes the production problem under trade credit and imperfect product reworking conditions. This work extends the traditional production model by considering reworking imperfect items and trade credit to cope with realistic situations. The objective of this study is to determine the optimal production lot size while minimizing the total cost. This paper develops an easy-to-use algorithm to solve the problem described, provides numerical examples to illustrate the proposed solution procedure, and discusses the impact of various system parameters.

Determining optimal lot size problem with rework and multiple deliveries using algebraic approach

This paper presents an algebraic approach for determining optimal lot size for economic production quantity (EPQ) model with rework and multiple deliveries. Conventional methods for solving production lot size are by using diff erential calculus on the longrun average production-inventory-delivery cost function with the need to prove optimality first. This paper shows that optimal lot size and its related costs for the aforementioned EPQ model can be derived without derivatives. As a result, it enables students and/or practitioners who with little knowledge of calculus to understand and handle with ease the realistic EPQ systems

Optimal production schedule in declining market for an imperfect production system

This is a study about economic production in an imperfect production system. The imperfect production system means is a system in which the machine shifts from an ‘in-control’ state to an ‘out-of-control’ state. This may happen at any random time during the production period. The classical economic production lot size model is based on the assumption that the produced items are of perfect quality. However, this is not observed during the production phase. In the long run, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to continuous usage of the machine. The proposed model is developed to study the optimal production when a certain percent of total product is of imperfect quality. These items are reworked to maintain the quality of the products. The production cost per unit item is convex function of production rate. The demand is assumed to be decreasing function of time. The total cost of inventory system per time unit is minimized. The development of the model is validated by numerical examples and its sensitivity analysis is carried out too.

Joint Production and Spare Part Inventory Control Strategy Driven by Condition Based Maintenance

Throughput of a manufacturing process depends on the effectiveness of equipment maintenance, and the availability of spare(service) parts. This paper addresses a joint production and spare part inventory control strategy driven by condition based maintenance(CBM) for a piece of manufacturing equipment. Specifically, a critical unit is continuously monitored for performance degradation during operation. The amount of degradation is utilized to initiate replacement actions in conjunction with spare part inventory control under both production lot size, and due date constraints. A degradation limit maintenance policy is combined with a base stock spare part inventory control policy to manage the manufacturing process. The objectives are to minimize the spare part inventory, and the expected total operating cost. Constrained least squares approximation, and simulation-based optimization are utilized, in a heuristic two-step approach, to determine the optimal base-stock level of spare parts, along with the preventive maintenance threshold. The resulting joint decision ascertains the allowed stockout probability for spare parts, while incurring the minimal operating cost for the required production within a fixed production duration. A case study of an automotive engine manufacturing process is provided to demonstrate the proposed decision-making methodology in practical use.

Improving production policy for a deteriorating item under permissible delay in payments with stock-dependent demand rate

This paper presents a production lot size inventory model in which the production rate constitutes of productions during both regular time and overtime. The demand rate is assumed as stock-dependent and the stock itself is depleted due to demand and deterioration. Supplier’s incentives include price discounts and granting of credit periods for account settlement within time M 1 , or the supplier allows interest-free credit upto an extended period M 2 . This formulation leads to a single objective optimization problem for maximum average profit evaluation through a real-coded genetic algorithm (GA) with rank-based selection and arithmetic crossover. The model is illustrated through a numerical example, and sensitivity analyses have been done with the variation of demand and deterioration parameters on optimal profit.

Solving the economic lot scheduling problem with multiple facilities in parallel using the time-varying lot sizes approach

The conventional Economic Lot Scheduling Problem (ELSP) is concerned with the lot sizing and scheduling of several products so as to minimize the average totalcosts on a single facility. This study is interested in an extension of the ELSP, namely, the ELSP with multiple identical facilities in parallel (which is also called the multi-facility ELSP). In order to solve this problem efficiently, we propose two solution approaches in a two-phase scheme in this study. In the first phase, we use an existing heuristic and a genetic algorithm to search for better product assignments that determine which product should be produced on which facility. Whenan assignment is secured, we employ a Time-Varying Lot Sizes (TVLS) heuristic to obtain a feasible production sequence (or schedule) for each facility inthe second phase. Our numerical experiments show that our approaches outperform an existing heuristic in the literature when the problem size is large and the facility utilization rate is high. On the other hand, we have an interesting observation that was never reported in the literature, namely, the TVLS approach may obtain worse solutions than a well-known upper bound in the literature for some cases.

Impacts of quality and processing time uncertainties in multistage production system

The primary objectives of this research are to develop simulation models for multistage production system under processing time and quality variation, to identify areas of potential bottleneck in production system and to determine the optimum production lot size for each station in a multistage production system under the uncertainties to minimize the WIP level and lead time and thereby the total system cost. A simulation model is developed based on a live case from a Malaysian company. Taguchi approach for orthogonal array is used in designing experiments and these are executed in WITNESS. The models are verified and validated by face validity, the historical data from the company and analytical model. The delivery performances, average lead time and work-in-progress (WIP) in the system, are examined for different experimental scenarios. Interaction effects and confirmation tests are also performed. The optimal batch sizes respectively for polishing unit (PU), quality control (QC) and packing stations are 8, 16 and 3 at minimum WIP and lead time. If the company uses these optimal batch sizes, a total of 24% improvement can be obtained. The simulation models show that Gasketing station is the bottleneck and batch size selection in PU station is the most critical decision in the system. The interaction effects are insignificant. The main contribution of this research is determination of the optimal lot sizes under imperfect quality of product and stochastic processing time. This approach can be generalized to any multistage production system, regardless of the precedence relationships among the various production stages in the system. Key words: Simulation, batch size, lead time, work-in-progress.

An EMQ model in an imperfect production process

The intention of this article is to develop a framework of production policy (resumption and non-resumption) in order to find out optimal safety stock, optimal production rate and production lot size. It encompasses specific versions of the concept of quality and inventory model, stochastic machine breakdown and its correcting and regular repair paths with safety stocks. This framework hopefully serves to simplify answers to the important questions: How much safety stocks, production rate and production lot size are required to minimise the total expected system cost. The optimal production rate, production lot size, production run time and safety stocks are determined numerically and the joint effect of process deterioration, machine breakdown and its repair (correcting and preventive) on the optimal decision is investigated for a numerical example. Such an investigation should also yield logistics directions for the design of products and their manufacturing processes.

A Markov decision model for optimising economic production lot size under stochastic demand

Traditional approaches towards determining the economic production lot (EPL) size in manufacturing applications assume deterministic demand, often at a constant rate. In this paper, an optimisation model is developed for determining the EPL size that minimises production and inventory costs of a periodic review production-inventory system under stochastic demand. Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces an optimal lot sizing policy, as well as the corresponding total production and inventory costs.

Non-cooperative strategies for production and shipment lot sizing in one vendor–multi-buyer system

The supply chain structure examined in this paper consists of a single vendor (or manufacturer) with multiple heterogeneous buyers (or retailers). A continuous deterministic model is presented. To satisfy buyers demands, the vendor will deliver the product in JIT shipments to each buyer. The production rate is constant and sufficient to meet the buyers’ demands. The product is shipped in discrete batches from the vendor's stock to buyers’ stocks and all shipments are realized instantaneously. Special production–replenishment policies of the vendor and the buyers are analyzed. That is, the production batch is transferred to each buyer in several sub-batches in each production distribution cycle (PDC). This paper offers game model without prices, where agents minimize individual costs. It is a non-cooperative (1+ N)-person game model with agents (a single vendor and N-buyers) choosing numbers and sizes of transferred batches. The model describes inventory patterns and cost structure of PDC. It is proved that there exist Nash equilibria in several types of sub-games of the considered game.

An integrated production and maintenance planning model with time windows and shortage cost

In this paper, we tackle the problem of integrating production and maintenance. The production problem addresses the issue of determining the production lot sizes of various items. Preventive maintenance is carried out in time windows to restore the production line to an ‘as-good-as-new’ status, and when a production line fails, a minimal repair is carried out to restore it to an ‘as-bad-as-old’ status. The resulting problem is modelled as a linear mixed-integer program. It takes into account demand shortage and the reliability of the production line. Computational experiments are carried out to show the effectiveness of the integrated model compared with a separate classical model for different instances, and the results obtained are analysed in detail.

Erratum to: Production setup-sequencing and lot-sizing at an animal nutrition plant through atsp subtour elimination and patching

This paper considers the usefulness of a production lot sizing and scheduling model at an animal nutrition plant with sequence-dependent setup times. The model covers multiple periods and is based on the asymmetric travelling salesman problem (atsp). It is applied initially to the case where the setup state is zeroed between periods, and then revised to model the carryover of the setup state from one period to the next. An iterative solution procedure based on subtour elimination is applied, and then enhanced by the inclusion of a subtour patching procedure. Case-based tests with actual plant data show that the subtour elimination is practicably fast where the setup state is zeroed between periods, but needs the patching procedure when the setup state is preserved, as is the situation at the plant. In this latter case, the subtour elimination and patching can be very fast, showing the method’s viability for operational lot sizing and sequencing in animal nutrition plants of the kind studied. Tests on perturbed plant data show that further algorithmic development is needed to tackle certain challenging variants found in other plants.

Coordinating a three-level supply chain with learning-based continuous improvement

Learning curve theory has been widely used as a managerial tool to describe and model product and process improvement. This paper investigates a three-level supply chain (supplier–manufacturer–retailer) where the manufacturing operations undergo a learning-based continuous improvement process. Improvements in the manufacturer’s operation are characterized by enhanced capacity utilization, reductions in set-ups times, and improved product quality through the elimination of rework. As a result of these continuous improvements, the manufacturer can justify a production policy that is based on more frequent, smaller lot size production. For this production policy to be practical and not sub-optimal to the supply chain, the manufacturer must integrate its lot-sizing models with the replenishment policies of its upstream raw material suppliers and the demand requirements of its downstream customers (retailers). Mathematical models that achieve chain-wide lot-sizing integration are developed and solution procedures for the models are illustrated by numerical examples. The results demonstrate that learning-based improvements in set-up time and rework allow retailers to order in progressively smaller lot sizes as the manufacturer offers larger discounts and profits and that the entire supply chain benefits from implementing learning-based continuous quality improvements. The results also demonstrate that forgetting effects lead to increases in supply chain costs.

An economic production lot size model in an imperfect production system

The paper investigates an EPL ( Economic Production Lotsize ) model in an imperfect production system in which the production facility may shift from an ‘ in-control ’ state to an ‘ out-of-control ’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘ in-control ’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘ in-control ’ state to the ‘ out-of-control ’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective ( imperfect ), in ‘ out-of-control ’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.

Optimal reliability, production lotsize and safety stock: an economic manufacturing quantity model

Reliability based maintenance provides sound guidance for managers who wish to attain high standards of maintenance at their operating systems. Basically, the amount and the type of maintenance applied for the system depend strongly on the age of components of a machinery system. The present paper describes a production policy (resumption and non-resumption) in order to find out an optimal safety stock, production lotsize and reliability parameters. A production-inventory model with stochastic machine breakdown and its corrective and regular (preventive) repairs with safety stock has been developed incorporating variable reliability parameters. The reliability parameter (θ) is a design variable. Learning effects result in the cost of technology for the design variable which is an decreasing function of (θ) and this, in turn, has an impact on the average cost. Hence the setting of optimal values of reliability parameters and production lotsize with safety stock needs to be considered jointly that achieves the smallest average integrated costs. The Kuhn-Tucker method is used to obtain an optimal solution for reliability parameters, production lotsize and safety stock. Finally, numerical examples with sensitivity analysis of key parameters are given to illustrate the proposed model. Several graphical illustrations of the model are given.