Optimal Production Lot Size Research Articles

A Decision-making Model for a Two-stage Production-delivery System in SCM Environment

A decision-making model is developed for an optimal production policy in a two-stage production-delivery system that incorporates a fixed quantity supply of finished goods to a buyer at a fixed interval of time. First, a general cost model is formulated considering both supplier (of raw materials) and buyer (of finished products) sides. Then an optimal solution to the problem is derived on basis of the cost model. Using the proposed model and its optimal solution, one can determine optimal production lot size for each stage, optimal number of transportation for semi-finished goods, and optimal quantity of semi-finished goods transported each time to meet the lumpy demand of consumers. Also, we examine the sensitivity of raw materials ordering and production lot size to changes in ordering cost, transportation cost and manufacturing setup cost. A pragmatic computation approach for operational situations is proposed to solve integer approximation solution. Finally, we give some numerical examples.

The effects of learning on the optimal production lot size for deteriorating and partially backordered items with time varying demand and deterioration rates

In this paper the full transmission of learning for the general production lot size problem with an infinite planning horizon is studied under the following assumptions: (1) Items deteriorate while they are produced or stored. (2) Both demand and deterioration rates are (known) functions of time. (3) Shortages are allowed, but are partially backordered. (4) The production rate is defined as the number of units produced per unit time. A closed form for the total relevant cost as well as a rigorous mathematical method that leads to a minimum total cost of the underlying inventory system are introduced. An illustrative example which explains the applications of the theoretical results as well as its numerical verification are also given.

A finite horizon production model with variable production rates and constant demand rate

In this paper we present a finite horizon single product single machine production problem. Demand rate and all the cost patterns do not change over time. However, end of horizon effects may require production rate adjustments at the beginning of each cycle. It is found that no such adjustments are required. The machine should be operated either at minimum speed (i.e. production rate = demand rate; shortage is not allowed), avoiding the buildup of any inventory, or at maximum speed, building up maximum inventories that are controlled by the optimal production lot size.

A mathematical programming model for production planning using CONWIP

Push-based MRP and pull-based Kanban systems are effective planning tools for a wide range of manufacturing production. Both of them, however, have certain limitations when they are implemented in different production environments. In recent years, CONWIP (CONstant Work-In-Process) has been proposed and studied to take advantage of MRP and Kanban systems for optimal work-inprocess (WIP) inventory control. In this paper, an integer nonlinear mathematical programming model was developed to determine an optimal production sequence and lot sizes in a CONWIP production line. The nonlinear programming model was linearized and solved directly for a number of illustrative example problems.

Manufacturing to Order with Random Yield and Costly Inspection

This study considers a situation where a contractor receives an order that it commits to satisfy in full. The fulfillment of the contract requires manufacturing and inspection. Because the number of defective units within a produced lot is not known in advance, it is possible that after examining the lot, it is learned that the number of conforming units is short of the demand. If so, further manufacturing and inspection are required. Once enough conforming units are found, the inspection terminates, and the remaining uninspected units, as well as all defectives, are scrapped. Whereas previous “multiple production runs” studies implicitly assumed that inspection costs are negligible, we include these costs as a key part of the problem. It turns out that the optimal production lot size depends on the inspection cost. Our model is very general: We provide a framework to calculate the optimal batch and the expected number of inspections for any yield pattern, as well as for any inspection procedure. We also provide results and numerical examples concerning specific yield patterns that are common in practice.

Economic lot sizing with the consideration of random machine unavailability time

This paper extends the work of Abboud and Salameh (Production and Inventory Management 28 (1987) 38–45) by assuming random machine unavailability time and where shortages are allowed. In multiple-item intermittent production runs, the machine might not be available to restart the production of the next batch for a specific item. This situation would result in shortages where items are either backordered or lost. The optimum operating inventory doctrine is obtained by trading off procurement cost per unit time, the inventory carrying cost per unit time, as well as the shortage cost per unit per unit time, so that their sum will be a minimum. Examples illustrating the calculation procedure are provided. Scope and purpose There are numerous production situations where a production facility (e.g., a machine) is used intermittently to produce lot sizes of a certain product. Upon the completion of production a run, the facility may not be available for a random amount of time due to several reasons, such as: the facility is being used to produce other items and their production schedules are not known in advance; the facility needs to be maintained and the maintenance time is random due to unforeseen circumstances; or perhaps the facility is leased by different manufacturers and the demand for the facility is random. As a result, the facility may not be available when it is needed, and stockout situations will arise. It is of interest then to determine the optimal production lot size that minimizes the setup cost, inventory carrying cost, and shortage cost per unit time. Furthermore, we need to determine how the overall inventory cost function is influenced by the nature of the random variable that represents the unavailability time of the production facility.

WIP inventories in the simultaneous determination of optimal production and purchase lot sizes

This paper studies an integrated production and purchasing lot sizing model with work-in-process WIP inventory. In this model, the single product is made in a multiprocess manufacturing system. The raw materials are procured from outside sources and are converted gradually into the product. A solution procedure is developed to simultaneously find the optimal lot sizes for the product and its raw materials and the corresponding total relevant cost. It is shown that if the cost of WIP inventory is considered in the production lot size computation, the optimal lot sizes of the product as well as those of the raw materials could be altered significantly.

An Algorithm for the Single-item Capacitated Lot-Sizing Problem with Concave Production and Holding Costs

We consider a multi-period single-item production scheduling problem with a deterministic, time-varying demand pattern and concave cost functions. Optimal production lot sizes, so as to minimize the total costs of production, set-up, and inventory, are determined subject to dynamic production capacity and no backlogs. The proposed algorithm was tested extensively by solving several randomly generated problems with varying degrees of complexity. The proposed algorithm appears to perform quite reasonably for practical applications.

Common Cycle Lot-Size Scheduling for Multi-Product, Multi-Stage Production

In this paper we study the Common Cycle Scheduling Problem (CCSP). This classic production problem is concerned with determining optimal production lot sizes for a given set of products using a common facility. CCSP is based on scheduling all products using a common (base) cycle time, so that the lot size for each product is the forecasted demand for that product over the base cycle time. This research provides an optimizing framework for CCSP for a multi-stage, multi-product, flow-shop environment under deterministic and stationary conditions, assuming a fixed sequence is maintained across all processing stages. The framework presented considers the costs of work-in-process inventory and determines a jointly optimal common cycle time and production schedule (start and finish times for each product's production lot-size) for the multi-stage facility in question. The paper also reports some results on the impact of alternative sequencing rules for the CCSP context.

Quality and inventory issues within the newsboy problem

Most inventory models assume that the production lot size does not contain any defectives. Clearly, this assumption does not reflect the reality of most manufacturing systems. The number of defects in a production lot depends on the manufacturing technology implemented by the firm. In this paper we study the decision of a firm seeking to replace its existing manufacturing technology with an improved one. Furthermore, we study the effect the quality of the technology has on the optimal production lot size. In this paper, we formulate a two-stage stochastic programming problem. In the second stage, the optimal production lot size is derived for a given manufacturing technology and a given demand forecast. This derivation is provided under the framework of the one-period inventory problem while maintaining a minimal service level. In the first stage, and using the optimal production lot size of the second stage problem, an optimal manufacturing technology that minimizes the total expected cost to the firm is implemented. An algorithm to find an optimal solution is presented. A numerical example illustrates the results.

Note—The Impact of Inspection Delay on Process and Inspection Lot Sizing

Models in which process quality and lot sizing interact have recently been developed. Lot sizes should be reduced to compensate for poor quality if no effective inspection is possible. This note introduces an inspection delay time, measured in units produced after an inspection is made until results are known. If the inspection delay is negligible, then the problem reduces essentially to two separate lot sizing problems: the classical EOQ lot sizing problem and an inspection lot sizing problem. If the delay is great, then only one inspection should be made and the lot size is as given by Porteus, and Rosenblatt and Lee. This note seeks the optimal production and inspection lot sizes for the full spectrum of inspection delays. The impact of the results is illustrated numerically. The value of automated defect control (with 100% inspection and immediate production stoppage upon detection of a defect) is discussed.

Constrained Optimal Production Lot Sizes for Several Products

SYNOPTIC ABSTRACTThis paper deals with the effect on the {optimal lot sizes, cycle length, and cost} of the system for several products produced on several machines with repetitive common cycle length when the solution is constrained by limited storage space or capital. In order to solve the constrained production lot size problem it is necessary to determine the maximum volume or value of the inventory (MV) required for a given production plan. One simple measure of the storage space or capital required is the sum of the peak values of the individual product inventory levels (SMV). Since the peak inventory levels for all products do not occur simultaneously, SMV is usually much larger than the exact MV and, therefore, would be expected to yield a higher cost solution.In this paper efficient computational procedures are developed to find the exact MV and the corresponding constrained optimal lot sizes and cycle length when the products are made on a single machine. Techniques to determine the MV are explo...

Production Lot Sizing Under A Learning Effect

Abstract Models are developed for determining optimal production lot sizes under a learning effect. These models consider situations in which both bounded and unbounded learning is assumed to occur. Bounded learning occurs when some nonzero lower limit is set on the time allowed to produce one unit of product.