Analysis of multi-stage production/inventory system with an acceptable response time

This paper describes a method to decide the inventory levels of semifinished and finished products so as to realize the target service rate by shipping the finished products within a specified time which we call the acceptable response time. We analyze the substitution relation between the acceptable response time and the inventory levels of semifinished and finished products. As a result, inventory levels required according to the length of the acceptable response time under the condition of satisfying the target service rate are obtained. The validity of our method is also demonstrated through simulation experiments with the conditions given by the analysis.     

A bimodal scheme for multi-stage production and inventory control

This study considers a multi-stage multi-item production plant with its supply chain and customer environment. The production, supply and inventory plan is optimized on a dual-mode basis, under two different information patterns. The short-term plan relies on firm orders received from customers. On the contrary, the long-term plan is based on predicted demands represented by random sequences. In this study, the role of the long-term plan is mainly to impose a final condition set to the short-term plan.     

Production inventory with service time and interruptions

This paper considers an (s,S) production inventory system with positive service time, with time for producing each item following Erlang distribution. Customers arrive according to a Poisson process. A customer who arrives when there is no inventory in the system is considered lost. On the other hand, a customer who finds a busy server with at least one inventory in the system joins a queue of infinite capacity. When the inventory level falls to s, production process is switched on, and it is switched off when the inventory level reaches back to S. Service time to each customer also follows an Erlang distribution. The service of a customer may be interrupted, where the time for such a phenomenon follows an exponential distribution, whenever it occurs. An interrupted service, after repair, resumes from where it was stopped. The correction/repair time follows an exponential distribution. We assume that the service of a single customer may encounter any number of interruptions and that the customer being served waits there until his service is completed. Moreover, at a time the server is subject to at most one interruption. We also assume that no inventory is lost due to a service interruption. Like the service process, the production process also is subject to interruptions, where the duration to an interruption follows an exponential distribution. However, in contrast to the service interruption, in the case of interruption to production process, we assume that the item being processed is lost because of interruption. That is, the production process, on being interrupted, restarts from the beginning, after repair. The repair time of an interrupted production process follows exponential distribution. Few of the last service phases are assumed to be protected in the sense that the service will not be interrupted while being in these phases. The same is assumed for the production process also.

The model is analysed as a level-independent quasi-birth–death process. We apply a novel method to obtain an explicit expression for the necessary and sufficient condition for the stability of the system under study. This method works even if we assume general phase-type distributions for the production as well as the service processes, and hence can be used to characterise the stability of inventory systems where the assumption of disallowing the customers to join the system, when there is a shortage of inventory has been made. Under stability, we apply matrix analytic methods to compute the system state distribution. In consequence to that, several system performance measures have been derived, and their dependence on the system parameters has been studied numerically.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

Optimal policy for set-up time reduction in a multistage production inventory system

A batch production-inventory system consisting of multiple stages with an optimal policy of set-up time reduction and a fixed increment cost are discussed. The ratio of set-up time reduction as a decision variable under various cases of demand in the batch production-inventory model is considered. The ratio of set-up time reduction and lot size are solved simultaneously to obtain an optimal value of the total annual cost. A numerical example is presented to demonstrate the accuracy of the proposed method.     

Multi-echelon inventory production system solution

The multi-echelon inventory problem can be examined from the points of view of dynamic programming. The difficulty is that the number of possible states will be exceptionally large. The authors avoid this difficulty by using some formulation. An introductory section surveys what Clark and Clark-Scarf formulated, the problem of a single product carried at an arbitrary number of activities arranged in a series structure. Subsequent sections provide the researches on analytic consideration and numerical consideration. The final section discusses the production planning in a multi-echelon inventory production system.     

A perishable inventory system with service facilities and retrial customers

In this article, we present a continuous review perishable (s, S) inventory system with a service facility consisting of finite waiting room and a single server. The customers arrive according to a Markovian arrival process (MAP). The individual customer’s unit demand is satisfied after a random time of service which is assumed to have phase-type distribution. The life time of each item and the lead time of reorders are assumed to have independent exponential distributions. Any arriving customer, who finds the waiting room is full, enters into the orbit of infinite space. These orbiting customers compete for service by sending out signals the duration between two successive attempts are exponentially distributed. The joint probability distribution of the number of customers in the waiting room, number of customers in the orbit and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated.     

Improved inventory models with service level and lead time

This paper explores the mixed inventory backorder and lost sales problem in which both the lead time and order quantity are treated as decision variables. In a recent paper on Computers and Operations Research, Ouyang and Wu considered this problem. However, their algorithms might not find the optimal solution due to flaws in their solution procedure. We develop some lemmas to reveal the parameter effects and then present two complete procedures for finding the optimal solution for the models. The savings are illustrated by solving the same examples from Ouyang and Wu's paper to demonstrate the superiority of our revised algorithms.     

Optimal payment time for retailer's inventory system

A retailer's inventory control system for the optimal delay in payment time for initial stock-dependent consumption rate when a wholesaler permits delay in payment is developed. Shortages are not allowed in the inventory system. The effect of inflation rate, deterioration rate, initial stock-dependent consumption rate and a wholesaler's permissible delay in payment is discussed. A mathematical model is derived when a wholesaler permits that the credit period is less than or equal to the retailer's optimal payment time, and that the retailer's optimal payment time is less than or equal to the cycle time for settling the account. Besides, an expression for a retailer's inventory system's total cost derived for this case and five special cases will be discussed. Moreover, a computational procedure is proposed to obtain the optimal cycle time, retailer's payment time and order size. The results could help retailer's managers to determine the optimal total cost and strive for the wholesaler's permission to delay the payment period. Thus, a retailer can attempt to gain two very big advantages: (1) that the retailer will have more money to run in that period because of the extension of the optimal payment time and (2) that extra interest will be earned in that period. Finally, a numerical example demonstrates the applicability of the proposed model and a sensitivity analysis is also discussed.     

A periodic review inventory model involving variable lead time with a service level constraint

In this study, we consider a mixture periodic review inventory model in which both the lead time and the review period are considered as decision variables. Instead of having a stock-out term in the objective function, a service level constraint is added to the model. In our paper, we first assume that the protection interval (i.e. the review period plus the lead time) demand follows a normal distribution, and then we relax this assumption and only assume that the first two moments of the protection interval demand are given. For each case, we develop an algorithm to find the optimal review period and optimal lead time. Furthermore, a sensitivity analysis is also performed.     

A vector space model approach to production planning for a multi-product,multi-cell and multi-stage manufacturing system

This paper develops a formal mathematical approach to aggregate production planning for a multi-product, multi-cell and multi-stage manufacturing system. The model, based upon a vector space approach, includes all the important variables relating to the demand for individual items, inventory levels, the availability of machines taking into account any breakdowns, subcontracting of orders and overtime working. The computational procedure for determining the production planning strategies, in terms of overtime/undertime working and increase/decrease in the number of orders subcontracted, are presented. Three numerical examples are presented showing the use of the model developed. This approach makes it possible to develop realistic models of practical manufacturing systems. It is particularly applicable to flexible manufacturing systems.     

A simulation-based decision support system for a multi-echelon inventory problem with service level constraints

In this paper, we present a simulation-based decision support system for solving the multi-echelon constrained inventory problem. The goal is to determine the optimal setting of stocking levels to minimize the total inventory investment costs while satisfying the expected response time targets for each field depot. We derive new decision support algorithms to be applied in different scenarios, including small-sample and large-sample cases. The first case requires that the set of alternative solutions is known at the beginning of the experiment, and the number of evaluated solutions may depend on the simulation budget (i.e., the time available to solve the problem). In the second case, the alternative solutions are generated sequentially during the searching process, and we may terminate the algorithm when the specified sampling budget is exhausted. Empirical studies are conducted to compare the performance of the proposed algorithms with other conventional optimization approaches.     

Production scheduling and inventory control for multi-stage manufacturing systems

In this paper, singular perturbation methods are used to synthesize high-gain error-actuated production control policies for a class of multi-stage manufacturing systems in which each manufacturing sub-system comprises either one or several production facilities. It is shown that when the manufacturing sub-systems are connected in cascade, each sub-system can be controlled in isolation, but that production control policies based on this approach lead to undesirable transient behaviour if the value of the feedback gain parameter is small. An alternative approach whereby production control policies are synthesized for the composite system leads to improved transient behaviour. However, if the value of the feedback gain parameter is large, both approaches are shown to yield good transient behaviour. In addition, it is demonstrated that trade-off between rapid adjustments in production rates and large inventory-level deviation can be achieved by selecting an appropriate value for the feedback gain parameter.     

A multi-stage learning framework for intelligent system

As information technologies advance and user-friendly interfaces develop, the interaction between humans and computers, information devices, and new consumer electronics is increasingly gaining attention. One example that most people can relate to is Apple’s innovation in human–computer interaction which has been used on many products such as iPod and iPhone. Siri, the intelligent personal assistant, is a typical application of machine-learning human–computer interaction.Algorithms in machine learning have been employed in many disciplines, including gesture recognition, speaker recognition, and product recommendation systems. While the existing learning algorithms compute and learn from a large quantity of data, this study proposes an improved learning to rank algorithm named MultiStageBoost. In addition to ranking data through multiple stages, the MultiStageBoost algorithm significantly improves the existing algorithms in two ways. Firstly, it classifies and filters data to small quantities and applies the Boosting algorithm to achieve faster ranking performance. Secondly, it enhances the original binary classification by using the reciprocal of fuzzily weighted membership as the ranking distance.The importance of data is revealed in their ranked positions. Usually data ranked in the front are given more attention than those ranked in the middle. For example, after ranking 10,000 pieces of data, the top 10, or at most 100, are the most important and relevant. Whether the data after the top ones are ranked precisely does not really matter. Due to this reason, this study has made improvement on the conventional methods of the pair-wise ranking approach. Not only are data classified and ranked binarily, they are also given different weights depending on whether they are concordant or discordant. Incorporating the concept of weighting into the ranking distance allows us to increase the precision of ranking. Results from experiments demonstrate that our proposed algorithm outperforms the conventional methods in three evaluation measures: P@n, MAP, and NDCG. MultiStageBoost was then applied to speech recognition. However, we do not aim to improve the technology of speech recognition, but simply hope to provide evidences that MultiStageBoost can be used in the classification and ranking in speech recognition. Experiments show that the recognition optimization procedures established by this study are able to increase the recognition rate to over 95% in the personal computing device and industrial personal computer. It is expected that in the future this voice management system will accurately and effectively identify speakers answering the voice response questionnaire and will successfully carry out the functions in the choice of answers, paying the way for the formation of a virtual customer service person.     

Two-echelon supply chain inventory model with controllable lead time and service level constraint

This paper considers a two-echelon supply chain inventory problem consisting of a single-vendor and a single-buyer. In the system under study, a vendor produces a product in a batch production environment and supplies it to a buyer facing a stochastic demand, which is assumed to be normally distributed. Also, buyer’s lead time is controllable which can be shortened at an added cost and all shortages are backordered. A model has been formulated for an integrated vendor–buyer problem to jointly determine the optimal order quantity, lead time and the number of shipments from the vendor to the buyer during a production cycle while minimizing the total expected cost of the vendor–buyer integrated system. It is often difficult to estimate the shortage cost in inventory systems. Therefore, instead of having a shortage cost term in the objective function, a service level constraint (SLC) is included in the model that requires a certain proportion of demands to be met in each cycle. An efficient procedure has been suggested to find the bounds on number of shipments and then, an algorithm is developed to obtain the optimal solution of the proposed model. A numerical example is included to illustrate the algorithmic procedure and the effects of key parameters are studied to analyze the behavior of the model. Finally, the savings of buyer and vendor are investigated from implementation of joint optimization model over the model in which they minimize their own cost independently.     

An autonomous decentralized supply chain planning system for multi-stage production processes

In this paper, we propose an autonomous decentralized optimization system for multi-stage production processes. The proposed system consists of a Material Requirement Planning subsystem, a Distribution Planning subsystem and Decentralized Scheduling subsystems belonging to each production stage that constitute the entire plant. In the proposed system, each subsystem repeats both optimization of the schedule at each subsystem and data exchange among the subsystems. Computational results demonstrate that the results of the proposed planning system are superior to those of the hierarchical planning system, despite the fact that the proposed system has wide flexibility for adding the constraints and modifying the criterion of performance evaluation.This revised version was published in June 2005 with corrected page numbers.     

Managing disruption in an imperfect production–inventory system

In this paper, a disruption recovery model is developed for an imperfect single-stage production–inventory system. For it, the system may unexpectedly face either a single disruption or a mix of multiple dependent and/or independent disruptions. The system is usually run according to a user defined production–inventory policy. We have formulated a mathematical model for rescheduling the production plan, after the occurrence of a single disruption, which maximizes the total profit during the recovery time window. The model thereby generates a revised plan after the occurrence of the disruption. The mathematical model, developed for a single disruption, is solved by using both a pattern search and a genetic algorithm, and the results are compared using a good number of randomly generated disruption test problems. We also consider multiple disruptions, that occur one after another as a series, for which a new occurrence may or may not affect the revised plan of earlier occurrences. We have developed a new dynamic solution approach that is capable of dealing with multiple disruptions on a real-time basis. Some numerical examples and a set of sensitivity analysis are presented to explain the usefulness and benefits of the developed model. The proposed quantitative approach helps decision makers to make prompt and accurate decisions for managing disruption.     

Machine assignment policies in a multistage,multifacility and multiproduct production inventory system

In this paper a simulation model is presented to study different machine assignment policies in a multistage, multifacility and multiproduct production inventory system (MS-MF-MP-P1S). The system considered in the present research is the same as reported in the companion paper by Gunasekaran ei al. (1990). The system is modelled based on the ‘discrete event simulation’ approach. The purpose of this simulation model is to enrich the modelling exercise, validate the results of the mathematical model reported in the companion paper and incorporate more realistic decision-making capabilities, such as machine assignment policies, etc. Numerical results are presented to explain the application of the simulation model.