Optimizing multi-stage production with constant lot size and varying number of unequal sized batches

This paper describes a model for a multi-stage production/inventory system in which a uniform lot size is produced through all stages with a single setup and without interruption at each stage. Partial lots, called batches, may be transported to the next stage upon completion. The number of the unequal sized batches may differ across stages. Considering setup costs, inventory holding costs, and transportation costs, an optimization method is developed to determine the economic lot size and the optimal batch sizes for each stage. The method is illustrated by a computational example and further numerical simulations.     

Optimizing lot size and setup time in a JIT environment: a multiple objective application

The just-in-time (JIT) system has been studied extensively and implemented by a number of US firms as an ell'ective production system. The core of JIT involves determination of lot size and setup time reduction so as to increase manufacturing flexibility while minimizing the inventory level. This decision problem usually involves multiple conflicting objectives and mixed-model production. In this paper, goal programming (GP) is applied to a real-world JIT problem involving fabrication of different automotive and industrial rubber composite belts. The model results provide new insights concerning the conflicting nature of several goals, especially between meeting demand and reducing setup or idle time. Also, the GP solution is superior to the current JIT practice of the company.     

Simultaneous determination of production lot size and process parameters under process deterioration and process breakdown

The purpose of this study is to combine production-inventory management with process-quality design for determining production lot size and process parameters under the possibility of process deterioration and breakdown. The total cost of such an integrated model includes: the combined setup cost (production setup and process resetting), the costs of quality loss, tolerance and mean costs for processes established, a penalty cost for process breakdown and carrying costs for cumulated inventory. The quadratic quality loss function is introduced to assess quality loss within the system. Decision variables include the initial setting (process mean) and process tolerance for process parameters determination, and production lot size for production-inventory management. The cycle time for production-inventory management is assumed to be the same as the resetting cycle for the new process-quality system. The contribution of this study lies in its development of an integrated model that enables process parameters, production lot size, and cycle time to be determined concurrently for quality and economic considerations, and at an earlier time in the process design and production management stage. An example is presented to demonstrate the proposed model.     

The effects of learning and forgetting on the optimal lot size quantity of intermittent production runs

This paper studies the effects of learning and forgetting on the production lot size problem with infinite and finite planning horizons. It is assumed that the determination of the economic manufactured quantity (EMQ) in the succeeding production run is dependent on: (1) the maximum inventory accumulated prior to interruption; (2) the length of the interruption period which incurs total forgetting; and (3) the level of experience in equivalent units remembered at the start-up of the next production run. The optimum operating inventory doctrines is obtained by trading off procurement cost per unit time and the inventory carrying cost per unit time, so that their sum will be a minimum. A numerical example is presented to demonstrate the application of learning and forgetting to the determination of the EMQ.     

Production lot sizing model with insufficient production capacity

A mathematical model is developed for determining the optimal number of batches for the production lot sizing problem where the production capacity is lower than the annual demand requirement. Setup time is included and it is assumed that consumption begins only after the entire batch is produced. The model is illustrated through an example.     

Scheduling a multi-stage production system with startup delays

The problem treated is that of multi-stage scheduling as affected by the interdependence of successive stages. An algorithm is developed which incorporates startup delays as analytical functions of cycle times and production rates at adjacent stages. This is accomplished in part by imposing integer multiple restrictions on the relationship between the cycle times at adjacent stages. Total cost is then minimized for a given set of integer multiples.     

Determination of economic production quantity in a multi-stage production system

In this paper two models have been suggested for determining economic production quantity in a multi-stage production system. The demand for the product is assumed constant and it is supplied by manufacturing the product in equal production runs. The production lot is transported in a number of sub-batches of equal sizes. Each sub-batch is processed on the production stages without wait during process. As a result of processing the sub-batches without wait during process, the processing on the production stages is interrupted. Expressions have been derived for the manufacturing cycle time, the total process inventory and the finished product inventory and then total variable cost models have been suggested and manipulated for obtaining the economic production quantity.     

Modelling and analysis of dynamic capacity complexity in multi-stage production

The uncertainty associated with managing dynamic capacity problem is the main source of its complexity. This article presents a system dynamics approach to model and analyse operational complexity of dynamic capacity in multi-stage production. The unique feature of this approach is that it captures the stochastic nature of three main sources of complexity associated with dynamic capacity. These are the demand, internal manufacturing delay and capacity scalability delay. The developed model was demonstrated by an industrial case study of multi-stage printed circuit board assembly line. The analysis of simulation experiments showed that ignoring complexity sources can lead to wrong decisions concerning both scaling levels and backlog management decisions. In addition, a general trade-off between the controllability and complexity of the dynamic capacity was illustrated. Finally, comparative analysis of the effect of each of these sources on the complexity level revealed that internal delay has the highest impact on dynamic capacity efficiency. Guidelines and recommendations for better capacity management and reduction of its complexity are presented.     

Single machine lot scheduling with non-uniform lot capacities and processing times

Journal of Combinatorial Optimization - In this paper, we investigate the single machine lot scheduling problem in which each lot contains one or more jobs (or part of jobs). Jobs with different...     

Design of optimal configuration for a multi-stage production system

In this paper the evolution of eBusiness or digital business is analysed. Firstly, a number of definitions are presented. Digital business is then analysed in the context of a clear distinction being drawn between applications and models. Reviews of the enablers and the drivers of eBusiness are also presented. Some conceptual models for understanding eBusiness are then reviewed and finally a new revised model is put forward. This so-called extended SCOR model, developed by combining ideas from the original Supply Chain Operations Reference (SCOR) model and Porter's Value Chain model is offered as a mechanism to map current eBusiness applications and models and may also be used to position and anticipate future eBusiness initiatives.     

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.     

Release of maintenance jobs in a decentralized multi-stage production/maintenance system with continuous condition monitoring

Condition-based maintenance is analyzed for multi-stage production with a separate maintenance department. It is assumed that the conditions of the machines deteriorate as a function of multiple production parameters and that the task of maintenance is to keep up predefined operational availabilities of the individual machines. In this context the problem of determining the optimal machine condition that triggers the release of a preventive maintenance job and the problem of scheduling maintenance jobs at the maintenance department arise. Existing approaches to solve these problems either assume a monolithic production/maintenance system or concentrate on a decentralized system in which the information flow and resource transfer do not cause delays. With our paper we aim at (1) deriving a triggering mechanism that is able to cope with relaxed assumptions and at (2) developing specific priority rules for scheduling maintenance jobs. Therefore, in this paper a specific continuous condition monitoring and a suitable information exchange protocol are developed, factors determining the release situation are operationalized, impacts of choosing the triggering conditions are identified and the components of specific priority rules for scheduling maintenance jobs are clearly elaborated. Finally the performance of the resulting solution approach is analyzed by simulations. Thereby, relevant characteristics of the production/maintenance system, the maintenance task and relevant priority rules are varied systematically. This research contributes answers to the questions on how the exchange of local information can be structured, the parameters of condition-based maintenance can be set and on what maintenance-specific priority rules can be applied in case of incomplete information about deterioration in a decentralized multistage production/maintenance system.     

Multi-product lot scheduling with backordering and shelf-life constraints

In this paper, we revisit the economic lot scheduling problem (ELSP), where a family of products is produced on a single machine, or facility, on a continual basis. Our focus is on the determination of a feasible production schedule, including the manufacturing batch size of each item. We assume that total backordering is permissible and that each of the products has a limited post-production shelf life. Several studies examining this problem have suggested a rotational common cycle approach, where each item is produced exactly once every cycle. To ensure schedule feasibility, we resort to the technique of reducing individual production rates and allow the flexibility of producing any item more than once in every cycle, in conjunction with appropriate timing adjustments. In order to solve this more generalized model, which is NP hard, we suggest a two-stage heuristic algorithm. A numerical example demonstrates our solution approach.     

Optimal batch size and investment in multistage production systems with scrap

In this paper, we study the problem of selecting the optimum production batch size in multistage manufacturing facilities with scrap and determining the optimal amount of investment. We analyse the effect of investment for quality improvement on the reduction of the proportion of defectives, and the effect of this reduction on processing cost, setup cost, holding cost, and profit loss. The quality characteristic of the product manufactured is assumed to be normally distributed with a mean equal to the target value. The purpose of the investment is to reduce the variance of the quality characteristic and hence the proportion of defectives. The model assumes known demand, which must be satisfied completely, scrappage at each stage and profit loss due to scrap. Using this model, the optimal values of the production quantity and the proportion of defectives for minimizing the total cost are obtained. The optimal investment is then obtained using the relationship between the investment and the proportion of defectives.     

A joint economic lot size model for raw material ordering,manufacturing setup,and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.     

Optimal two-stage production-inventory policy with whole lot and split lots

This paper deals with the problem of determining the optimal lot sizes for a two-stage production-inventory system. The first stage has a large lot to be processed in a single batch and is called the ‘whole lot’; this is split in the second stage into smaller lots of equal size called ‘split lots’. The lot in stage 1 is inspected for its conformity to standards before it is passed on to stage 2. We use a single sampling attribute plan for inspection and examine the consequences of rejecting or accepting the lot. The rejected lots are 100 % inspected and defectives are eliminated..The accepted lots contain defectives in the uninspected part which are identified during stage 2 processing. We have combined these aspects of inspection with the usual inventory costs and developed a model to determine the optimal sizes of the whole lot and split lots     

Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having varying order cost, which is a continuous function of the order quantity, and a limit on the total average inventory of all items. Our model is a generalization of that of Gupta and Gupta for unrestricted single-item order quantity model with varying order cost and assumes the same order cost function. This cost function relates well to real-life situations since it increases as the order quantity increases and, at the same time, it is easy to handle when deducing previous work as special cases of our model since it is easily reducible to a constant. An example is solved to illustrate the method.