Admission policies for the customized stochastic lot scheduling problem with strict due-dates (original) (raw)
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International Journal of Production Economics, 1999
This paper surveys the current research literature on the stochastic lot scheduling problem which deals with scheduling production of multiple products with random demand on a single facility with limited production capacity and signi"cant change-overs between products. The deterministic version of this problem has received signi"cant coverage in the literature; however, the stochastic problem has been addressed only recently. Furthermore, a range of distinctly di!erent analytical methods have been applied to this problem. This paper provides a unifying framework for discussing these approaches and o!ers some explanation and clari"cation of the di!erent analytical methods for this problem. After discussing some of the modeling and managerial implications of this problem, a detailed review of both continuous and discrete time control strategies is given, and areas for further research are outlined.
Stochastic lot-sizing: Solution and heuristic methods
International Journal of Production Economics, 1996
We consider a single item stochastic lot-sizing model motivated by a Dutch company operating in a make-to-order environment. Since there is no possibility for having stocks on hand, every customer's order receives a fixed delivery date upon arrival. The objective is to determine the optimal size of production lots so that delivery dates are met as closely as possible at the expense of minimal costs. These include set-up costs, holding costs for orders that are finished before their delivery date and penalty costs for orders that are not satisfied on time and therefore backordered. We model this problem as a Markov Decision Process. Given that the optimal production policy is likely to be too complex, attention is focused on the development of heuristic procedures. In this paper three lot-sizing rules are proposed for both the uncapacitated and capacitated versions of the problem. The first one is a simple production strategy where the orders for a certain number of periods are produced whenever the demand for the current period is above a given value. The second lot-sizing strategy is based on the well-known Silver Meal algorithm for the case of deterministic time-varying demand. The third rule is a fixed cyclic strategy. Numerical results are presented for some test problems with demand distributions close to real situations. The performance of the lot-sizing rules is analysed considering several capacity levels.
Pesquisa Operacional
This research addresses a lot sizing and scheduling problem inspired by a real-world production environment where the customers make advanced orders and the industry need to decide which orders will be accepted with the aim of maximizing the profit respecting the production capacity constraints. Orders are composed of different types of items which must be delivered within a given time interval and, moreover, such orders cannot be split. A mixed integer programming (MIP) model is proposed to represent the problem and a MIP-based heuristic is also proposed to deliver good solutions at an acceptable computational time. The heuristic is composed of three phases (construction, deterministic improvement and stochastic improvement phases) and combines relax-and-fix, fix-and-optimize, and iterative MIP based neighborhood search procedures. Computational tests are presented in order to study the efficiency of the proposed approaches.
The stochastic economic lot scheduling problem: A survey
European Journal of Operational Research, 2011
The present literature survey focuses on the stochastic economic lot scheduling problem (SELSP). The SELSP deals with the make-to-stock production of multiple standardized products on a single machine with limited capacity under random demands, possibly random setup times and possibly random production times. The main task of a production manager in this setting is the construction of a production plan for the machine. Based on the critical elements of such a production plan, we present a classification and extensive overview of the research on the SELSP together with an indication of open research areas. By doing so, we intend to stimulate the discussion on the important problems concerning the SELSP both from a theoretical and a practical point of view.
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.
Lot scheduling problem for continuous demand
International Journal of Production Economics, 1996
This paper deals with a lot scheduling problem for multi-item continuous demand utilizing a single machine with setup times. The problem involves dynamic determination of lot-sizes to minimize the inventory level. In such systems, the lowest inventory level is realized by maximizing the number of setups under the condition of no stockout. Based on the above fact, first, an analytical solution of lot-sizes for a cyclic schedule is given based on a constant-demand model. Secondly, a stochastic-demand model is developed, and some heuristic setup rules are studied using the concept of time inventory, defined from the solution based on a constant-demand model. These rules realize a stable system with a lower average stockout level and a lower inventory level. Effects of the setup rules on the system are revealed by Monte Carlo simulations.
International Journal of Production Economics, 2000
This paper deals with lot sizing and scheduling for a single-stage, single-machine production system where setup costs and times are sequence dependent. A large-bucket mixed integer programming (MIP) model is formulated which considers only e$cient sequences. A tailor-made enumeration method of the branch-and-bound type solves problem instances optimally and e$ciently. The size of solvable cases ranges from 3 items and 15 periods to 10 items and 3 periods. Furthermore, it will become clear that rescheduling can neatly be done.
Make-to-order policies for a stochastic lot-sizing problem using overtime
International Journal of Production Economics, 1998
We address a stochastic single item production system in a make-to-order environment where customer orders receive a promised delivery date upon arrival. Capacity is reserved for the production of the item but can be extended by working overtime. The problem consists of determining the optimal size of a production lot, so that delivery promises are met on time at the expense of minimal average costs. These include setup costs, holding costs for orders that are finished before their promised delivery date and penalty costs for orders that are not satisfied on time and are therefore backordered. Also, the use of capacity beyond the regularly available incurs overtime costs. Given that the optimal policy is likely to be too complex in most practical situations, we propose four different strategies for obtaining production lot sizes. Three of the rules are based on the well-known (s, S) and (R, S) policies for make-to-stock problems while the fourth strategy is motivated by a rule originally derived for a similar problem with unlimited production capacity. An extensive numerical study indicates the conditions under which each lot-sizing rule shows the best performance. 0 1998 Elsevier Science B.V. All rights reserved.
International Journal of Production Economics, 1994
If the shop capacity is tight, it may not be possible to make a schedule that leads the completion times of all the parts processed in the shop to be exactly at their due dates. As a result, the shop may have to incur a holding cost for the parts finished earlier. This paper addresses a multi-due-date heterogeneous machine batch-scheduling problem to minimize the holding cost under the condition that parts to be processed should arrive at the production line just-in-time and that completed parts should be delivered just-in-time. The procedure to solve the problem is an algorithm that divides the whole planning horizon into a number of partitions of periods, distributes the parts to the partitions, distributes the resulting distributions to the available machines, and solves the problem of batch scheduling on each machine. Numerical experience showing the characteristics of the problem is also presented.