Workload-dependent capacity control in production-to-order systems (original) (raw)
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1Workload-dependent capacity control in production-to-order systems
2016
The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. We present two analytical approaches to evaluate the policies ’ due-date performance based on stationary analysis. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. We compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results can be used by manufacturing and service industries when e...
Workload-dependent capacity control
The development of job intermediation and the increasing use of Internet allow companies to carry out quicker and quicker capacity changes. In many cases, capacity adaptation can be driven according to the present workload to minimize idle capacity. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. In our analysis we assume exponential interarrival and service times, although the model permits extension to phase-type distributions. We present two analytical approaches to stationary analysis in order to evaluate the policies due-date performance. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. Eventually, we compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results and tools can be used by manufacturing and service industries when declaring a static policy for dynamic capacity planning.
Capacity planning and lead time management
International Journal of Production Economics, 1996
In this paper we discuss a framework for capacity planning and lead time management in manufacturing companies, with an emphasis on the machine shop. First we show how queueing models can be used to find approximations of the mean and the variance of manufacturing shop lead times. These quantities often serve as a basis to set a fixed planned lead time in an MRP-controlled environment. A major drawback of a fixed planned lead time is the ignorance of the correlation between actual work loads and the lead times that can be realized under a limited capacity flexibility. To overcome this problem, we develop a method that determines the earliest possible completion time of an~y arriving job, without sacrificing the delivery performance of any other job in the shop. This earliest completion time is then taken to be the delivery date and thereby determines a workload-dependent planned lead time. We compare this capacity planning procedure with a fixed planned lead time approach (as in MRP), with a procedure in which lead times are estimated based on the amount of work in the shop, and with a workload-oriented release procedure. Numerical experiments so far show an excellent performance of the capacity planning procedure. the time-phasing, i.e. to determine when exactly to start each phase. At each phase production quantities are principally determined by the demand for MPS items multiplied by an explosion factor. These quantities may be adjusted due to lot sizing and inventory considerations (netting), see e.g. Ref. El].
Periodic capacity management under a lead-time performance constraint
OR Spectrum, 2011
In this paper, we study a production system that operates under a leadtime performance constraint which guarantees the completion of an order before a predetermined lead-time with a certain probability. The demand arrival times and the service requirements for the orders are random. To reduce the capacity-related operational costs, the production system under study has the option to use flexible capacity. We focus on periodic capacity policies and model the production system as a queuing system that can change its capacity periodically and choose to operate in one of the two levels: a permanent capacity level and a permanent plus contingent capacity level. Contingent capacity is supplied if needed at the start of a period, and is available during that period, at a cost rate that is decreasing in period length in different functional forms. Next, we propose a search algorithm that finds the capacity levels and the switching point that minimizes the capacity-related costs for a given period length. The behaviour of the capacity-related costs changes drastically under different period lengths and cost structures. In our computational study, we observe that the periodic capacity flexibility can reduce the capacity-related operational costs
Inventory management in supply chain with stochastic inputs
2010
This thesis studies and proposes some new ways to manage inventory in supply chains with stochastic demand and lead time. In particular, it uses queuing principles to determine the parameters of supply chain stations with delayed differentiation (typical assemble-to-order systems) and went on to apply some previously known results of steady state of some queuing systems to the management of flow and work in process inventory in supply chain stations. Consideration was also given to the problem of joint replenishment in partially dependent demand conditions. The first chapter introduces the important concepts of supply chain, the role of inventory in a supply chain, and developing stochastic models for such system. It then went on to review the pertinent literature that has been contributed to the inventory management, especially using stochastic models. Chapter two presents a perishable inventory model with a multi-server system, where some services, having an exponentially distributed lead time, have to be done on the product before it is delivered to the customer. Customers whose demands are not met immediately are put in an orbit from where they send in random retrial requests for selection. The input stream follows a Markov Arrival Process, , and another flow of negative customers (typical of a competitive environment with customer poaching), also following an , takes customers away from the orbit. An (,) replenishment policy was used. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of ii stationary system performance are computed and the total expected cost per unit time is calculated. Numerical illustrations were made. Chapter three is also a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers are assumed to arrive following a quasi-random distribution. Items demanded are also made available after some service, exponentially distributed, has been done on the demanded item. Customers with unsatisfied orders join an orbit from where they can make retrials only if selected following a special rule. Replenishment follows an (,) policy and also has an exponentially distributed lead time. The intervals separating two successive repeated attempts are exponentially distributed with rate ߠ + ݅ߥ, when the orbit has ݅ customers ݅ ≥ 1. The joint probability distribution of the number of customers in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. Chapter four is a two-commodity continuous review inventory system, with three customer input flows, following the ; one for individual demand for product 1; another for bulk demand for product 2; and the third for a joint individual demand for product 1 and bulk demand for product 2. The ordering policy is to place orders for both commodities when the inventory levels are below prefixed levels for both commodities, using (,) replenishment. The replenishment lead time is assumed to have phase type distribution and the demands that occur during stock out period are assumed to be lost. The joint probability distribution for both commodities is obtained in the steady state case. Various measures of system performance and the total expected cost rate in the steady state are derived. Numerical illustrations were then done. Chapter five is a model that shows how the steady state parameters of a typical queuing system can be used in the dynamic management of flow and buffer in a Theory of Constraints () environment. This chapter is in two parts, and the typical ∞/1/ܯ/ܯ production environment with 0 < ߩ < 1 was assumed. The optimal feed rate for maximum profit was obtained. In the first part, the model was considered without consideration for shortage cost. This model was then extended in the second part to a case where a fixed cost is charged for every unit shortage from the desired production level. Part A result was iii shown to be a special case of part B result; the unit shortage cost has been implicitly taken to be zero in part A. Chapter six is the concluding chapter, where the various possible applications of the models developed and opportunities for possible future expansions of models and areas of research were highlighted. The main contributions of this work are in the Supply Chain area of delayed differentiation of products and service lead time. Others include management of joint replenishment and optimisation of flow in a TOC environment. The key contributions to knowledge made in this thesis include: • A model of a multi-server retrial queue with arrival and negative arrival, and deteriorating inventory system in which inventory items are made available only after some work has been done on the inventory item before it is delivered to the customer. No previous model is known to have considered any queuing system with such multi-server system ahead of this chapter. • A model of a retrial queuing system with multi-server rule based in which the arrival pattern is quasi-random, the calling population is finite, and an exponentially distributed system service is done on the inventory item before being delivered to the customer. It has not been found in literatures that such models have been developed elsewhere. • A stochastic model of joint replenishment of stocks in which two products are being ordered together; one of such is ordered in bulk and the other in single units, but both could be ordered together and unfilled order during the replenishment leadtime is lost. No published work is known to have also addressed such systems. • The management of flow in a theory of constraint environment, which explicitly utilises the holding cost, shortage cost, product margin, the level of utilisation of the resource and the effect of such on the stocks (inventory) build up in the system. Such flows are then explicitly considered in the process of buffering the system. Most works have been known to focus on buffer and not the flow of the products in order to optimise the system profit goal. iv Some of the insights derived include • An understanding of how the system cost rate is affected by the choice of the replenishment policy in systems with arrival pattern so that controlling policies (reorder point and capacity) could be chosen to optimise system profit • The effect of correlated arrival in input system on the cost rate of the system • How the nature of input pattern and their level of correlation affect the fraction of the retrials in a retrial queue in a competitive environment that are successful and how many of such customers are likely to be poached away by the randomly arriving competitors. This has direct effect on the future market size. • The nature of utilisation, blocking and idleness of servers in typical retrial queues, such that there could be yet-to-be-served customers in the orbit while there are still idle serves in such systems • Management of utilisation of resources in stochastic input and processing environment with respect to the throughput rate of such systems. It was shown that it may not be profitable to strive to always seek to fully utilise the full capacity of a Capacity Constrained Resource, even in the face of unmet demands. Increase in utilisation should always be considered in the light of the effect of such on the throughput time of the products and the consequence on the system's profit goal. This decision is also important in determining the necessity and level of buffers allowable in the production system. v ACKNOWLEDGEMENTS My profound gratitude goes to so many people that have made this study possible. But particular mention needs to be made of some very special people. First and foremost, I would like to thank Professor VSS Yadavalli, who is my promoter. He is actually more than just a promoter, but a reliable mentor, guide, instructor, teacher, listener and guardian, both in official and personal capacities. I am indebted to you. I would also like to thank my family members, especially my loving and understanding wife, Ireti, and my kids who have been denied many valuable moments to share, so that we can rejoice at the realisation of this dream. I thank my parents and siblings for the foundations you all provided for me. It still helps my development. I thank the entire staff members of the department of Industrial and Systems Engineering of the University of Pretoria, for giving me the opportunity to work with this great team, and doing that without prejudice or let. I have been much better with you in my life. I would like to appreciate the efforts of Pastor and Dr (Mrs) Akindele, who encouraged and supported me to quit my comfort zone in the office to pursue this course of life, which actually has become my passion. And most importantly, my Lord and Master, Jesus Christ, who has made a person out of a mere birth that would have been without direction or hope in life. vi
Modelling flow and jobbing shops as a queueing network for workload control
International Journal of Production Economics, 2002
Workload control is an approach for production planning and control that attempts to manage manufacturing lead times rather than treat them as a forecasting problem. It is particularly appropriate for jobbing and #ow shops in the make-to-order sector of industry. It is based on Little's well known formula in queueing theory that the time an arrival spends in the system is the average number in the system divided by the arrival rate. However, the workload control approach treats the jobbing shop as a single entity and thus ignores the complexities caused by competing jobs arriving at a work station at the same time thus forming queues. This paper describes how the job shop environment may be formulated as an open queueing network. It is computationally impossible to solve the model exactly if there are more than three or four work stations. Results for an exact Markov process model for a triangular con"guration of work stations are described. Initial results suggest that treating each work station as an independent queueing system leads to signi"cant underestimation of the manufacturing lead times, even for such a simple manufacturing system. Some initial ideas on deriving an approximation of the exact model to cover larger systems are also discussed.
International Journal of Production Economics, 2003
In this paper we investigate the control of throughput and work-in-process (WIP) in job shops where operations processing times in the work centers depend on the workload in the shop. We assume that production efficiency is high if the workload in the shop is such that the workers experience a stimulating work pressure. For higher and for lower workload we assume that the production efficiency is lower because either the workers experience a too low work pressure, or a too high work pressure. Such production systems are unstable if the arrival rate is exogenous and larger than the order completion rate under high workload. Therefore a high throughput can only be obtained if the order arrival rate can be controlled in response to the workload in the system. In this paper we investigate the effect of a simple workload dependent arrival rate control policy on the throughput and WIP of a simple model of a job shop. We use numerical analysis of a queueing model to investigate the performance of the shop under various combinations of parameter values in the arrival control policy.
The effect of workload constraints in mathematical programming models for production planning
2010
Linear and mixed integer programming models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these eterministic models are the current-state-of-art, it should be recognized that they are used in an environment that is inherently stochastic. This fact should be kept in mind, both when making modeling choices and when setting the parameters of the model. In this paper we study the relation between workload constraints that reflect the finite capacity of the manufacturing system, and the use of planned lead times. It is a common practice in rolling schedule based production planning to limit the periodic output to the average production rate. If lead times are not modeled explicitly, this also implies a restricition on the periodic releases to the average production rate. We demonstrate that this common practice results in inefficient use of the production capacity and show that the use of planned lead times leads to a ...
Managing Capacity and Inventory Jointly in Manufacturing Systems
Management Science, 2002
I n this paper, we develop approximations that yield insight into the joint optimization of capacity and inventory, and how the optimal inventory policy varies with capacity investment in a single-product, single-station, make-to-stock manufacturing system in which inventory is managed through a base-stock policy. We allow for a correlated demand stream as we analyze our models in an asymptotic regime, in which the penalty and holding costs are small relative to the cost of capacity. Although our approximations are asymptotically correct, our Brownian approximation is accurate even under moderate traffic intensity.