• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.206-212
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• 2003

In this paper, we propose a mathematical optimization model with a suitable algorithm to determine delivery and backlogging quantities by minimizing the total cost including the penalty costs for delay. The system has fixed transshipment costs and demands are fulfilled by some delivery units that represent the volume of delivery amount to be shipped in a single time period. Since, backlogging is allowed, demands could be delivered later at the expense of some penalty costs. The model provides the optimal decisions on when and how much to he delivered while minimizing the total costs. To solve the problem, we propose an algorithm that uses the Lagrangian dual in conjunction with some primal heuristic techniques that exploit the special structure of the problem. Finally, we present some computational test results along with comments on the further study.

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.4
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• pp.424-427
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• 2014

In this paper, we consider a production system in which the items are produced by batch. For a production planning of the system, we formulate a lot-sizing problem in which each production should be a multiple of a given unit batch and backlogging is allowed. We propose an optimal dynamic programming algorithm for the plan whose complexity is $O(T^2)$ where T is the maximum number of periods in a plan.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.2
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• pp.5-20
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• 1987

This paper addresses sensitivity analysis for a deterministic multi-period production and inventory model. The model assumes a piecewise linear cost structure, but permits backlogging of unsatisfied demand. Our approach to sensitivity analysis here can be divided into two basic steps; (1) to find the optimal production policy through a forward dynamic programming algorithm similar to the backward version of Zangwill [1966] and (2) to apply the penalty network approach by the author [1986] in order to derive sensitivity ranges for various model parameters. Computational aspects are discussed and topics of further research are suggested.

• Journal of Korean Institute of Industrial Engineers
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• v.36 no.1
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• pp.7-12
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• 2010

This paper considers a dynamic lot-sizing problem with backlogging under a minimum replenishment policy. For general concave production costs, we propose an O($T^5$) dynamic programming algorithm. If speculative motive is not allowed, in this case, a more efficient O($T^4$) algorithm is developed.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.71-79
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• 1993

Dynamic production planning problems are to determine the optimal production times and production quantities of product for discrete finite periods. In previous many researches, the solutions for these problems have been developed through the algorithms using dynamic programming. The purpose of this research is to suggest the new algorithm using linear programming. This research is to determine optimal production quantities of product in each period to satisfy dynamic for discrete finite periods, minimizing the total of production cost and inventory holding cost. Cost functions are concave, and no backlogging for product is allowed. The new algorithm for capacity constrained problem is developed.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.539-552
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• 1999

An order-level inventory model for a perishable product with a time-dependent demand is developed for a fixed planning pe-riod allowing backlogging in all cycles within the said period. The market demand is assumed to decrease exponentially as time elapses. The average system cost is derived and its optimization procedure is illustrated with a numerical example. Sensitivity of the optimal so-lution to changes in the values of different parameters of the system is also analysed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.750-753
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• 2000

본 연구에서는 정적시간하에서 다품종을 생산하는 다수의 공장과 수요지가 있을 때, 각 공장의 생산량과 각 수요지로의 수송단위의 수를 결정하는 문제에서 납기지연비용 및 수송비용을 최소화하는 수송량을 결정하는 새로운 수리 최적화모형을 제안한다. 이 모형에서는 기존과는 달리 제품수송단위별 비용을 적용하고, 또한 납기지연에 따른 벌칙비용을 고려함으로써 보다 실제적인 응용이 가능토록 하였다.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.2
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• pp.15-23
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• 1985

A multi-product multi=facility production planning model is in which known demands must be satisfied. The model considers concave production costs and piecewise concave inventory costs in the introduction of production capacity constraints. Backlogging of unsatisfied demand is permitted. The structure of optimal production schedules is characterized and then used to solve an illustrative numerical problem.

• Journal of the Korean Operations Research and Management Science Society
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• v.9 no.2
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• pp.15-22
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• 1984

A deterministic multiproduct, facility-in series multiperiod production planning model is analyzed, where each period demand for the product of a facility appear in a fixed proportion of that for the product of the immediately following facility. The model considers concave production and inventory costs, which can depend upon the production in different facilities. No backlogging is allowed. It is shown that the model is represented via a single source network, which facilitates development of efficient dynamic programming algorithms for computing the optimal production schedule.

• Journal of Korean Institute of Industrial Engineers
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• v.4 no.1
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• pp.49-55
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• 1978

This paper presents a new method, called a modified economic order quantity method, for determining the optimal inventory policy, which uses the rate of return as its decision criterion. Especially for the simplest possible inventory system with constant demand rate, no backlogging, no lead time, etc., the formula for the optimal order policy is derived. Also mentioned are the relative merits and shortcomings of this method compared to the conventional EOQ model.