Production and Inventory Control of a Single Product Assemble-to-Order System with Multiple Customer Classes (original) (raw)
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Managing an assemble-to-order system with after sales market for components
European Journal of Operational Research, 2015
In this paper, we consider an assemble-to-order manufacturing system producing a single end product, assembled from n components, and serving an after sales market for individual components. Components are produced in a make-to-stock fashion, one unit at a time, on independent production facilities. Production times are exponentially distributed with finite production rates. The components are stocked ahead of demand and therefore incur a holding cost rate per unit. Demand for the end product as well as for the individual components occurs continuously over time according to independent Poisson streams. In order to characterize the optimal production and inventory rationing policies, we formulate such a problem using a Markov decision process framework. In particular, we show that the optimal component production policy is a state-dependent base-stock policy. We also show that the optimal component inventory rationing policy is a rationing policy with state-dependent rationing levels. Recognizing that such a policy is generally not only difficult to obtain numerically but also is difficult to implement in practice, we propose three heuristic policies that are easier to implement in practice. We show that two of these heuristics are highly efficient compared to the optimal policy. In particular, we show that one of the two heuristics strikes a balance between high efficiency and computational effort and thus can be used as an effective substitute of the optimal policy.
Optimal and near-optimal inventory control policies for a make-to-order inventory–production system
European Journal of Operational Research, 2002
This paper examines several inventory replenishment policies for a make-to-order inventory-production system that consists of a production workshop and a warehouse. Demands arrive to the production workshop according to a Poisson process, and are processed in an FCFS manner. The production workshop requires that the warehouse provides, as needed, raw materials for use in the production process. The warehouse inventory is replenished according to an inventory replenishment policy. The optimal replenishment policy, which minimizes the average total cost per product, is derived using a Markov decision process approach. The structure of the optimal replenishment policy is explored. Simple ''order-up-to'', ''myopic'', and heuristic replenishment policies are introduced. The myopic and heuristic replenishment policies are easy to compute, and yet perform almost as well as the optimal replenishment policy. Ó
Optimal control of a nested-multiple-product assemble-to-order system
International Journal of Production Research, 2008
In this paper, we study an assemble-to-order system consisting of n products assembled from a subset of m distinct components where the products have a modular nested design. i.e., product i has only one additional component more than product i−1. In particular, we study the optimal production and inventory allocation policies of such systems. Components are produced on independent production facilities one unit at a time, each with a finite production rate and exponentially distributed production times. The components are stocked ahead of demand and therefore incur a holding cost per unit per unit of time. Demand from each product occurs continuously over time according to a Poisson process. The demand for a particular product can be either satisfied (provided all its components are available in stock) or rejected. In the latter case, a product-dependent lost sale cost is incurred. In this situation, a manager is confronted with two decisions: when to produce a component and whether or not to satisfy an incoming product order from on-hand inventory. We show that, for the production of a component, the optimal policy is a base-stock type where the base-stock level depends on all other components' inventory. We also show that, for inventory allocation, the optimal policy is a multi-level rationing policy where the rationing levels depend on all other components' inventory. We propose a simple heuristic that we numerically compare against the optimal policy and show that, when carefully designed, it can be very effective.
European Journal of Operational Research, 2010
In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k 0 -Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k l -Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.
Operations Research, 2011
We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At each decision epoch, we must determine whether or not to produce an item and should demand from a particular class arise whether or not to satisfy it from existing inventory, if any is available. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. In contrast to systems with exogenous and deterministic production leadtimes, we show that the optimal production policy for each item is a state-dependent base-stock policy with the base-stock level non-increasing in the inventory level of items that are downstream and non-decreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multi-level state-dependent rationing policy with the rationing level for each demand class non-increasing in the inventory level of all non-end items. We also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory.
International Journal of Production Economics, 2011
We consider the optimal production and inventory allocation of a single-product assemble-to-order system with multiple demand classes and lost sales. Each component is replenished by a dedicated machine that is subjected to unpredictable breakdowns. We find that the machine state not only influences the production and allocation decisions on its own component but also influences the decisions on the other components. Specifically, the optimal component production policy is a basestock policy with the base-stock level non-decreasing in the inventory levels of the other components and the states of the other machines. The optimal component allocation policy is a rationing policy with the rationing level non-increasing in the inventory levels of the other components, the states of the other machines, and its own machine state. We use an exponential distribution to approximate the distribution of the total processing times and propose two heuristic policies to address the production and allocation decisions. The importance of taking machine failures into consideration is revealed through computational experiments.
Operational Research, 2019
In this paper, we examine a single-stage, manufacturing system with setups, which produces a single part type to satisfy demand from two customer classes. We address the problem of coordinating production control, stock rationing, and order admission decisions. The optimal policy, in respect to minimizing holding, backorder, lost sales, and setup costs, is derived by formulating the underlying problem as a Markov Decision Process and solving it by means of Dynamic Programming. The structure of the optimal policy is investigated numerically and, on that basis, a parametric control policy is proposed. The Markov chain model of the single-machine manufacturing system, operating under the proposed policy, is developed. Furthermore, analytical expressions of the steady-state probabilities and of the expected total cost are obtained. The proposed policy is compared to the optimal, as well as to three heuristics, in an extended series of experiments. The numerical results indicate that the proposed policy is a very good approximation of the optimal one, and that it largely outperforms the alternative control policies.
Optimal control of an assembly system with demand for the end-product and intermediate components
IIE Transactions, 2012
We consider the production and admission control of a two-stage manufacturing system where intermediate components are produced to stock in the first stage and an end-product is assembled from these components through a second stage assembly operation which may allow backorders. The manufacturing firm faces two types of demand. The one directed at the end-product is satisfied immediately if there are available products in inventory, and the firm has the option to accept the order for later delivery or to reject the order if no inventory is available. The second type of demand is for any of the intermediate components and the firm again has the option to accept the order or reject it to keep the components available for assembly purposes. We provide structural results for the demand admission, component production and product assembly decisions. We also extend the model to take into account multiple customer classes based on revenue and a more general revenue collecting scheme where only an upfront partial payment for an item is received if a customer demand is accepted for future delivery with the remaining revenue received upon delivery. Since the optimal policy structure is rather complex and defined by switching surfaces in a multidimensional space, we also propose a simple heuristic policy for which the computational load grows linearly with the number of products and test its performance under a variety of example problems.
Optimal control of price and production in an assemble-to-order system
Operations Research Letters, 2008
ABSTRACT We study the optimal control of an assembly system that produces one assembled-to-order final product with multiple made-to-stock components and sells it at variable price. It is shown that a threshold control on component production, product price, and product orders maximizes total discounted profit over an infinite horizon.