Optimal lot sizing in a non-cooperative material manager–controller game

Determining the optimal probing lot size for the wafer probe operation in semiconductor manufacturing

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...

Influence of lot size and planned lead time on service level and inventory for a single-stage production system with advance demand information and random required lead times

Supply chain management is one of the new approaches that are considered significantly by variety of experts and enterprises in today competitive world. Supply chain refers to the network of facilities, supply centers, production centers and distribution centers which encompass various tasks such as providing raw materials, transforming raw materials to components or finished products and distributing them among customers. Regarding this issue, studying literature indicates on this fact that multi-level, multi-product, multi-period models in multi-sourcing situation by considering the supply capacity have not been taken into account notably and just few mathematical models are proposed for the analysis of such decisions. In this paper, it is attempted to investigate and delve into the supply chain planning issue in multi-level, multi-product, multi-period situation. In the proposed model, simultaneously optimization of two objectives is considered which entails maximizing the service level related to giving agreeable services to customers at each retailer's site and minimizing the overall costs of supply chain. As the proposed mixed integer non-linear model has specific complexity, branch and bound solver is utilized and has been applied for a data set in an automotive supply chain. In this way, a model has been presented which determines the lot size of ordering among various members in a supply chain, the amount of holding inventory at each elements of supply chain's site, optimal combination of selecting potential suppliers and the amount of ordering components to suppliers.

This article develops a game theoretic model of a supply chain with one supplier and two risk-averse retailers competing in price, service and lot size, where the Economic Order Quantity (EOQ) production-inventory policy is adopted. After studying the existence of EOQ equilibrium, we investigate how to adjust their decisions when the economic environment changes. We find that one retailer will decrease its optimal lot size, retail price and service level when it becomes more risk averse or its service investment efficiency decreases. When the supplier's capacity increases, the retailers will reduce retail price and increase service level, which in turn results in a higher lot size. The effect of the risk sensitivity of one retailer on the rival retailer's decisions depends on the relative service cost efficiency of the retailer. When the absolute risk aversion and service investment efficiency of one retailer increase, the supplier's profitability will increase due to a higher total expected demand. We further give the managerial insights for practitioners, which helps managers to make right decisions in an uncertain environment.

We propose a novel joint pricing and lot sizing model to enable manufacturers plan production and pricing. These types of models have proven to be very popular and are collectively known as the Joint Pricing and Lot sizing Models. We include a discount factor in our model to increase profit for the manufacturer. Our proposed model relies on the fact that demand influences production cost indirectly, while it is dependent on price and the discount offered. By considering the form of demand and production cost, it is apparent that the presented model is a Signomial Geometric Programming problem. We obtain optimal solutions for price, lot size and discount factor by applying the modified transformation method of geometric programming. Numerical examples, which include sensitivity analysis of the objective function and parameters, illustrate our model. References C. J. Corbett and X. de Groote. A supplier's optimal quantity discount policy under asymmetric information. Management Science, 46(3):444--450, 2000. R. J Duffin, E. L Peterson, and C. Zener. Geometric programming, Theory and Application. John Wiely and Sons, 1967. J. R. Freeland. Coordination strategies for production and marketing in a functionally decentralized firm. AIIE Transactions, 12:126--132, 1982. Woon J.Lee, Daesoo Kim, and A. Cabot. Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28:941--952, 1996. http://cat.inist.fr/?aModele=afficheN&cpsidt=2490704. Daesoo Kim and Woon J. Lee. Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109(1):212--227, 1998. http://www.sciencedirect.com/science/article/B6VCT-3TMR6M6-H/2/2d166a9b5fc0a9a27e923c495f256663. Woon J. Lee. Determining order quantity and selling price by geometric programming. Decision Sciences, 24:76--87, 1993. doi:10.1111/j.1540-5915.1993.tb00463.x. Woon J. Lee and Daesoo Kim. Optimal and heuristic decision strategies for integrated product and marketing planning. Decision Sciences, 24(6):1203--1213, 1993, doi:10.1111/j.1540-5915.1993.tb00511.x. Seyed J. Sajadi, Maryam Orouge, and M. B. Aryanezhad. Optimal production and marketing planning. Computational Optimization and Applications, 30(2):195--203, 2005. http://portal.acm.org/citation.cfm?id=1062644.1062668. Richard J. Tersine. Principles of Inventory And Materials Management. PTR Prentice Hall, Englewood Cliffs, New Jersey 07632, 1994. S. Viswanathan and Q.Wang. Discount pricing decisions in distribution channels with price sensitive demand. European Journal of Operational Research, 149(3):571--587, 2003. http://ideas.repec.org/a/eee/ejores/v149y2003i3p571-587.html. Prakash L. Abad. Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 3(19):622--634, 1988. Z. Kevin Weng. Channel coordination and quantity discounts. Management Sciences, 41(9):1509--1522, 1995. http://www.jstor.org/view/00251909/di012962/01p03025/0. Prakash L. Abad. Supplier pricing and lot sizing when demand is price sensitive. European Journal of Operational Research, (78):334--354, 1994. http://cat.inist.fr/?aModele=afficheN&cpsidt=3309143. Charles S. Beightler. Applied Geometric Programming. John Wiely and Sons, 1976. C. W. Chiang, J. Fitzsimmons, Z. Huang, and S. Li. A game theoretic approach to quantity discount problem. Decision Sciences, 25(1):153--168, 1994. doi:10.1111/j.1540-5915.1994.tb00521.x.

This paper deals with purchasing inventory replenishment policy for deteriorating items, considering the time-dependent quadratic demand and time-dependent backlogging. Two models were formulated and solved. First, it is for deteriorating items with quadratically time-dependent demand for deteriorating items. Second, quadratically time-dependent demand for deteriorating items and shortages. A mathematical model is developed to the fourth-order equation for each model. The optimal production lot size, which minimizes the total cost, is derived. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system. Numerical examples are taken to illustrate the procedure of finding the optimal inventory cost, cycle time, and optimal lot size. The numerical experiment in this model was coded in Microsoft Visual Basic 6.0.

Optimal production and product inspection policies for a deteriorating production system are considered. In theoretical investigations and practical applications using simplified models, inspection results may be assumed to be perfect. In this study, two kinds of inspection errors are considered. We first show that an inspection policy that does not inspect the first s produced items but inspects only those items from the ( s +1)th till the end of the production run is optimal. Two commonly used inspection strategies, no inspection and full inspection, are discussed. Next, we show how the optimal products inspection policy are incorporated into the determination of optimal lot size. Under the optimal inspection policy, the optimal production lot size is shown to be unique and bounded above by the traditional economic manufacturing quantity. Based on these findings, an efficient solution procedure is provided for the simultaneous determination of the optimal production lot size and its corresponding product inspection policy. Numerical examples are given to illustrate the model. Sensitivity analyses are performed to examine the effect of inspection errors on the solution.

Lot sizes and setup frequency with learning in setups and process quality

Differential Evolution to Solve the Lot Size Problem in Stochastic Production Systems

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.

We propose a decision support approach, called DESMILS, to solve multi-item lot sizing problems with a large number of items by using single-item multiobjective lot sizing models. This approach for making lot sizing decisions considers multiple conflicting objective functions and incorporates a decision maker’s preferences to find the most preferred Pareto optimal solutions. DESMILS applies clustering, and items in one cluster are treated utilizing preferences that the decision maker has provided for a representative item of the cluster. Thus, the decision maker provides preferences to solve the single-item lot sizing problem for few items only and not for every item. The lot sizes are obtained by solving a multiobjective optimization problem with an interactive method, which iteratively incorporates preference information and supports the decision maker in learning about the trade-offs involved. As a proof of concept to demonstrate the behavior of DESMILS, we solve a multi-item lot sizing problem of a manufacturing company utilizing their real data. We describe how the supply chain manager as the decision maker found Pareto optimal lot sizes for 94 items by solving the single-item multiobjective lot sizing problem for only ten representative items. He found the solutions acceptable and the solution process convenient saving a significant amount of his time.

Cycle time reduction is a critical task in semiconductor industries to keep market competitive advantage. Small lot size manufacturing (SLM) is one of the methods to achieve this goal efficiently. Motivated by a new technology of three dimensional integrated circuit (3DIC) and the characteristics of equipments and process flow, we discuss a different lot sizing manufacturing strategy to achieve cycle time reduction in a backend manufacturing. There is rare literature to investigate the overall benefits and impacts of SLM applied for 3DIC manufacturing. This study fills this gap and provides a mathematical model to evaluate the tradeoff among cycle time performance, tool productivity and carrier loading with the objective being to minimize overall costs. A practical case conducted from a semiconductor manufacturer in Taiwan is illustrated in this study. Furthermore, to keep tool productivity, the effects and benefits of lot grouping in batch process tool are discussed. The model proposed helps managers to determine the optimal lot sizing and ensure that it is worthwhile to adopt SLM for 3DIC products in the backend manufacturing.

The classical square-root formula for optimal lot size is a useful tool especially for those manufacturing processes in which labor intensive items are produced in small quantities. There is a class of stationary lot sizing problems to which this formula applies. With learning effects introduced into the production cost of this class of problems the optimal lot size becomes the solution of a transcendental equation. Numerical solutions are presented as well as an approximation which has the structure of the classical formula.

This paper deals with lot sizing decisions in a flexible job shop manufacturing system considering dependencies between lot sizing decisions. A novel mathematical model is developed to optimise lot sizing and scheduling simultaneously using a product-oriented approach as opposed to the job-oriented approach which has been prevalently considered in the literature. Moreover, the proposed model considers further underlying assumptions such as assembly operations, sequence-dependent setup times, initial inventory and safety stock levels, as well as lots with unequal and variable sizes. The objective is to minimise the total production, setup, and tardiness penalty costs of the system. To solve the formulated problem, a self-adaptive Cuckoo Optimisation Algorithm (COA) embedded with three new immigration mechanisms is developed. Numerical experiments are conducted to demonstrate the validity of the model and investigate the efficiency and effectiveness of the employed optimisation algorithm.