Moueen K. Salameh

Economic production quantity model for items with imperfect quality

Abstract The assumptions necessary to justify the use of economic production quantity (EPQ/EOQ) models are rarely met. To provide mathematical models that more closely conform to actual inventories and respond to the factors that contribute to inventory costs, the models must be extended or altered. This paper hypothesizes a production/inventory situation where items, received or produced, are not of perfect quality. Items of imperfect quality; not necessarily defective; could be used in another production/inventory situation, that is, less restrictive process and acceptance control. The electronics industry gives good examples of such situations. This paper extends the traditional EPQ/EOQ model by accounting for imperfect quality items when using the EPQ/EOQ formulae. This paper also considers the issue that poor-quality items are sold as a single batch by the end of the 100% screening process. A mathematical model is developed and numerical examples are provided to illustrate the solution procedure.

Production lot sizing with the reworking of imperfect quality items produced

This paper studies the effect of imperfect quality items on the finite production model. When production stops, defective items are assumed to be reworked at a constant rate. The percentage of imperfect quality items is considered to be a random variable with a known probability density function. The demand for the initial perfect items and the perfect items being reworked is continuous during the cycle. The optimal operating policy that minimizes the total inventory cost per unit time for the finite production model under the effect of imperfect quality is derived where shortages are allowed and backordered.

CONTINUOUS REVIEW INVENTORY MODEL WITH DELAY IN PAYMENTS

Abstract In this paper, we examine the continuous review inventory model under permissible delays in payments. That is, a retailer has the option of either paying for the goods immediately upon the receipt of the order or delay the payment till the next replenishment order, where interest will be charged over the delay period. Expected demand will be assumed constant over time, and the order lead-time is considered random. The objective is to find the optimal ordering quantity and reorder level that will maximize the vendors total expected profit per unit time when payments are delayed.

Optimal just-in-time buffer inventory for regular preventive maintenance

Abstract Most manufacturing organizations, if not all, are trying to implement some of the ideas adopted by the just-in-time (JIT) philosophy, a philosophy that promises a continuous improvement in total productivity. Preventive maintenance, an essential element of the just-in-time structure, induced the idea of this paper. Performing regular preventive maintenance results in a shutdown of the production unit for a period of time to enhance the condition of the production unit to an acceptable level. During such interruption, a just-in-time buffer is needed so that normal operations will not be interrupted. The optimum just-in-time buffer level is determined by trading off the holding cost per unit per unit of time and the shortage cost per unit of time such that their sum is minimum.

Mathematical modelling of the effect of human learning in the finite production inventory model

Abstract It is a natural phenomenon that the performance of a person engaged in a repetitive task improves with time. In the manufacturing engineering literature, 1,2 this phenomenon is referred to as the learning curve, which is a decrease in the effort required for producing each unit in a repetitive manufacturing operation. Factors contributing to this improved performance include more effective use of tools and machines, increased familiarity with operation tasks and work environment, and enhanced management efficiency. Deterministic production inventory models found in the literature 3,4 have been formulated to show the effects of numerous variables or a combination of variables on model outputs. Variables considered include stock shortages, safety stock, and level of customer patience. More recently, a finite production inventory model was formulated taking into consideration the effect of machine unavailability on optimum production quantity. 5 Because the learning phenomenon is believed to have economic and decision-making implications in an inventory management system, 6 it is the objective of the study presented herein to investigate the effect of learning on both optimum production quantity and minimum total inventory system cost.

Effect of deteriorating items on the instantaneous replenishment model

The physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control. The traditional economic order quantity model (EOQ ) assumes that items stocked preserve their characteristics during their stay in inventory. The question is how reliable are the EOQ modelswhen items stocked deteriorate over time. This paper introduces a modified EOQ model in which it assumes that a percentage of the on-hand inventory is wasted due to deterioration. A mathematical model is developed and numerical examples provided to illustrate the solution procedure.

Optimal lot sizing under learning considerations: Shortages allowed and backordered

This paper treats the phenomenon of learning on the finite production model, with the consideration of shortages. The optimum operating inventory doctrine is obtained by trading off procurement cost per unit time, the inventory carrying cost unit per unit time, as well as the shortage cost per unit time, so that their sum will be a minimum.

Optimal lot sizing with regular maintenance interruptions

Abstract Most manufacturing organizations are trying to implement some, if not all, of the ideas adopted by the just-in-time (JIT) philosophy. A philosophy that promises a continuous improvement in total productivity, JIT became a synonym to the success of the Japanese in manufacturing and operations management. Preventive maintenance, an essential element of the JIT structure, induced the idea of studying the effect of scheduled regular interruptions on traditional square root formulas. Performing preventive maintenance results in the shutdown of the machine (or system) and hence interrupting the production cycle for a fixed time interval. Such a behavior requires resetting for a new subproduction run and adding a new element of maintenance and resetting cost to the total inventory system cost. This paper considers the lot-sizing problem with regular maintenance interruptions. The optimum production quantity is determined by trading off the procurement cost per unit of time, the inventory holding cost per unit of time, and the maintenance and resetting cost per unit of time such that their sum is a minimum.

Transshipment and safety stock under stochastic supply interruption in a production system

We consider a two-echelon system with one source supplying two locations with the same product. The random occurrence of interruptions at the source where downtime is also stochastic can result in stockouts at the two receiving locations. Our model studies the benefit of allowing each location to carry a safety stock where holding costs can be different at each location. The objective is to reduce overall cost at both locations. In some cases it is optimal to allow for a transshipment of inventory from the safety stock of one location to the other. We jointly solve for the optimal safety stock at each location and the optimal amount to be transshipped from a location to the other. We show that by conditioning on the transshipment direction the total cost becomes convex as a function of the safety stock levels at the receiving locations and the amount to be transshipped from a location to the other. Numerical examples are presented for different system cost parameters and probability distributions.

Reserve stock models: Deterioration and preventive replenishment

Reserve stocks are needed in a wide spectrum of industries from strategic oil reserves to tactical (machine buffer) reserves in manufacturing. One important aspect under-looked in research is the effect of deterioration, where a reserve stock, held for a long time, may be depleted gradually due to factors such as spoilage, evaporation, and leakage. We consider the common framework of a reserve stock that is utilized only when a supply interruption occurs. Supply outage occurs randomly and infrequently, and its duration is random. During the down time the reserve is depleted by demand, diverted from its main supply. We develop optimal stocking policies, for a reserve stock which deteriorates exponentially. These policies balance typical economic costs of ordering, holding, and shortage, as well as additional costs of deterioration and preventive measures. Our main results are showing that (i) deterioration significantly increases cost (up to 5%) and (ii) a preventive replenishment policy, with periodic restocking, can offset some of these additional costs. One side contribution is refining a classical reserve stock model (Hansmann, 1962).