• IE interfaces
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• v.13 no.2
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• pp.217-224
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• 2000

This paper analyzes the effects of setup cost reduction in a dynamic lot-sizing model for a single-facility multi-product problem. In the model, demands for each product are known, no backlogging is allowed, and a single resource is employed. Also, setup cost is defined as a function of capital expenditure to invest in setup cost reduction. Furthermore, in each production period the facility (or plant) produces many products, each representing a fixed part of the involved production activity (or input resource quantity). In this paper, the structure of the optimal solution is characterized and an efficient algorithm is proposed for simultaneously determining the optimal lot size with reduced setup cost and the optimal investment in setup cost reduction. Also, the proposed algorithm is illustrated by a numerical example with a linear and an exponential setup reduction functions.

• 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 Korean Institute of Industrial Engineers
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• v.41 no.3
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• pp.233-242
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• 2015

This paper analyzes a multi-product inbound lot-sizing and outbound dispatching problem with multi-vehicle types in a third-party logistics distribution center. The product must be delivered to the customers within the delivery time window and backlogging is not allowed. Replenishing orders are shipped by several types of vehicles with two types of the freight costs, i.e., uniform and decreasing, are considered. The objective of this study is to determine the lot-size and dispatching schedules to minimize the total cost with the sum of inbound and outbound transportation and inventory costs over the entire time horizon. In this study, we mathematically derive a mixed-integer programming model and propose a genetic algorithm (GA1) based on a local search heuristic algorithm to solve large-scale problems. In addition, we suggest a new genetic algorithm (GA2) with an adjusting algorithm to improve the performance of GA1. The basic mechanism of the GA2 is to provide an unidirectional partial move of products to available containers in the previous period. Finally, we analyze the results of GA1 and GA2 by evaluate the relative performance using the gap between the objective values of CPLEX and the each algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.61-64
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• 2000

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped immediately by containers in the period and the total freight cost is proportional to the number of each container type employed. Also, it is assumed that backlogging is not allowed. The objective of this study is to determine the lot-sizes and the shipping policy that minimizes the total costs, which consist of ordering costs, inventory holding costs, and freight costs. Because this problem is NP-hard, we propose a heuristic algorithm with an adjustment mechanism, based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.

• Industrial Engineering and Management Systems
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• v.7 no.3
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• pp.257-265
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• 2008

This paper deals with the joint decisions on pricing and ordering for a monopolistic retailer who sells perishable goods with a fixed lifetime or demand period. The newsvendor-typed problem is formulated as a two-period inventory system where the first period represents the inventory of fresh or new-arrival items and the second period represents the inventory of items that are older but still usable. Demand may be for either fresh items or for somewhat older items that exhibit physical decay or deterioration. The retailer is allowed to adjust the selling price of the deteriorated items in the second period, which stimulates demand and reduces excess season-end or stale inventory. This paper develops a stochastic dynamic programming model that solves the problem of preseason decisions on ordering-pricing and a within-season decision on markdown pricing. We also develop a fixed-price model as a benchmark against the dual-price dynamic model. To illustrate the effect of the dual-price policy on expected profit, we conduct a comparative study between the two models. Extension to a generalized multi-period model is also discussed.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.13-34
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• 1993

By operating on many part of a software system concurrently, the parallel processing computers may provide several orders of magnitude more computing power than traditional serial computers. If the Lagrangean approximation procedure is applied to a large scale manufacturing problem which is decomposable into many subproblems, the procedure is a perfect candidate for parallel processing. By distributing Lagrangean subproblems for given multiplier to multiple processors, concurrently running processors and modifying Lagrangean multipliers at the end of each iteration of a subgradient method,a parallel processing of a Lagrangean approximation procedure may provide a significant speedup. This purpose of this research is to investigate the potential of the parallelized Lagrangean approximation procedure (PLAP) for certain combinational optimization problems in manufacturing systems. The framework of a Plap is proposed for some combinatorial manufacturing problems which are decomposable into well-structured subproblems. The synchronous PLAP for the multistage dynamic lot-sizing problem is implemented on a parallel computer Alliant FX/4 and its computational experience is reported as a promising application of vector-concurrent computing.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.1
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• pp.157-165
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• 1998

This paper considers the single-product production and transportation problem with discrete time, dynamic demand and finite time horizon, an extension of classical dynamic lot-sizing model. In the model, multiple freight container types are allowed as the transportation mode and each order (product) placed in a period is shipped immediately by containers in the period. Moreover, each container has type-dependent carrying capacity restriction and at most one container type is allowed in each shipping period. The unit freight cost for each container type depends on the size of its carrying capacity. The total freight cost is proportional to the number of each container type employed. Such a freight cost is considered as another set-up cost. Also, it is assumed in the model that production and inventory cost functions are dynamically concave and backlogging is not allowed. The objective of this study is to determine the optimal production policy and the optimal transportation policy simultaneously that minimizes the total system cost (including production cost, inventory holding cost, and freight cost) to satisfy dynamic demands over a finite time horizon. In the analysis, the optimal solution properties are characterized, based on which a dynamic programming algorithm is derived. The solution algorithm is then illustrated with a numerical example.