Andrew Z. Szendrovits

Optimizing multi-stage production with constant lot size and varying numbers of batches

The model presented in this paper assumes that a uniform lot size is produced through a series of manufacturing stages, with a single set-up and without interruption at each stage. Transportation of partial lots, called batches, is allowed between stages after the whole batch is completed. The batch sizes must be equal at any particular stage, but the optimal number of equal-sized batches may differ across stages. Of course, the set-up costs, the inventory-holding costs and the transportation costs influence both the optimal batch-sizes at the various stages and the uniform lot size. An optimization method for this deterministic model is developed and is illustrated by an example.

Multi-stage production with variable lot sizes and transportation of partial lots

Abstract This paper describes a model for a multi-stage production/inventory system where lots may be of different sizes. In addition, either completed lots or partial lots, called batches, may be transported to succeeding stages. The model incorporates constraints on lot and batch-sizes and thus provides a rather comprehensive set of possibilities for organizing a production/inventory system. A heuristic solution procedure is developed and is shown to be ‘close to optimal’ by bounding.

Non-inteǵer optimal lot size ratios in two-staǵe production/inventory systems

It is widely believed that, when completed lots are transported through a multistage production system, lot sizes at a given stage must be integer multiples of subsequent lot sizes to achieve optimality. It is shown in this paper that even in a two-stage system non-integer lot size ratios could be optimal. Depending on the problem parameters, different inventory patterns represent optimal policies. This paper presents efficient optimization procedures for the various inventory patterns and gives examples of these optimization methods.

An inventory model for interrupted multi-stage production

The interruption of production on machines which are set up for a specific product incurs idle time costs but reduces inventory holding costs. This phenomenon is generally ignored in multi-stage inventory models. Interrupted production runs are economical when the additional costs generated by restarting the machines and by idle time are off-set by the reduced frequency of major set-up costs and by decreased inventory holding costs. Under these circumstances, the machine idle-time can be optimized for each stage. An appropriate production/inventory model for this situation and a suitable optimization method are developed; the method is illustrated by an example.

Optimizing total safety inventory for large transfer lines

Serial production lines are widely used in production systems. Balancing the capacities of a group of machines and connecting them by a common transfer mechanism constitutes a transfer line. Generally, the term transfer line represents a synchronized serial production line where the output from each production stage is equal to the output of the line. Because the stages are tightly linked together, loss of production due to breakdowns or defective items at any stage can temporarily stop the entire line. Consequently, transfer lines often have low efficiences. However, efficiency can be increased by adding safety inventories to decouple the stages. This paper presents a model and procedures for determining the safety inventories needed at each stage to assure that a prespecified transfer line efficiency is met and that the minimum amount of safety inventory is used. To reduce inventory carrying costs, larger inventories are arranged near the beginning of the line where the unit costs are lower than at the end of the line. Examples illustrate a solution procedure which is applicable to large transfer lines and can accommodate any theoretical or empirical probability distribution for breakdowns and production of defective items.

Economic packaging frequency of two items jointly manufactured in a multi-stage system

Abstract The objective of this paper is to show that the models suggested in the literature for optimizing the packaging frequency of jointly replenished items are invalid when the material to be packaged is processed in a multi-stage production/inventory system. Two basic models are presented for the case in which the internally manufactured material is packaged into two items of different size on the same packaging facility. Deterministic and constant demand and production rates, as well as fixed (set-up) costs and linear inventory unit holding costs, are assumed over an infinite time horizon. The ratio of the packaging frequency of the two items is restricted to be an integer and no back-logging of packaged items is allowed. A quite simple solution method and a computational example are given for each model.

Linear programming optimization of a network for an aluminum plant: A case study

Abstract With the dawn of economical and political reforms in Hungary in the mid-1980s the aluminum industry, among others, wanted to escape the trappings of centralized planning and direction. The managers were inexperienced and unadvised regarding the path of transformation to a market economy, as well as of the OR/MS techniques that would enable them to map the activities in their operations and provide the solutions needed to make good decisions. Managers joined outside researchers in exploring opportunities in major aluminum plants. This gave rise to the present study which brought an integrated systems approach to decision making. In this paper a logistics network is developed to model the activities of a medium-sized aluminum plant. For reasons of management requirements, a linear programming optimization appeared feasible to support decision making and to explore decision alternatives by postoptimality analysis.

A unified EPQ model for packaging two items jointly manufactured through several stages

Abstract The production/inventory model presented in this paper unifies two basic economic-packaging-quantity (EPQ) models and, depending on the problem parameters, will yield the same or a lower cost than either of these two models. The model assumes that the material is manufactured internally through several stages and is packaged into two different (sized) items. The material is manufactured jointly for the two items and, possibly, further manufacturing is undertaken separately for one of the items. In contrast with the packaging-frequency models found in the literature that are invalid whenever the material is not procured from outside but is internally processed in a multi-stage system, this model incorporates work-in-process inventory. An optimization procedure for solving the model is developed and a numerical example is given.

Least cost safety inventory for large transfer lines

The term transfer line represents a synchronized serial production line where the output from each production stage is equal to the output of the line. The efficiency of the line is the fraction of good units produced over an infinite time horizon. Loss of production due to breakdowns or defective items at any stage stops the entire line temporarily and this often results in low efficiency. The efficiency can be increased by adding safety inventories to decouple the stages. This paper presents a model and a simulation method for determining the safety inventories needed at each stage to ensure that a prespecified efficiency is met and that the carrying cost of the total safety inventory is minimized. The solution procedure is applicable to large transfer lines and can accommodate any theoretical or empirical probability distribution for breakdowns and production of defective items.