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This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allow us to develop a solution algorithm based on the concept of atomic sub-problems. We present an optimal solution to an atomic sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the original problem. Computational tests and a comparison with a published algorithm confirm the efficiency of the solution algorithm developed here.

With today’s high cost of land acquisition observed in most countries, management can no longer afford large storage facilities to house their products. For this reason, one of the main concerns of inventory managers is to ensure that enough storage space is available upon the delivery of a product. They, therefore, have to determine the least cost ordering policy so as to meet demand and taking into account the space limitation. In this paper, we investigate the problem of a single item continuous review inventory problem in the presence of a space restriction when the demand is stochastic. Through a sensitivity analysis study, it is found that ordering cost, storage capacity, average demand per unit time, and holding cost rate are the most influential problem parameters on the expected inventory costs. It is also shown numerically that a simple solution based on economic order quantity is performing very well with an average and maximum cost penalty of 0.19% and 2.03%, respectively.

Firms often utilize and coordinate dynamic adjustment of price, non-price promotions such as advertisement and recruitment of excellent salespeople and proper inventory replenishment policies to satisfy customer demands and achieve maximal profit. This paper provides an analytical model for obtaining optimal decisions jointly on pricing, promotion and inventory control. Specifically, we study a single item, finite horizon, periodic review model in which the demand is influenced by price and promotion, and the objective is to maximize the total profit. We characterize the optimal policy and provide solution for coordinating promotion, pricing and inventory replenishment. We show that the optimal promotion policy is a threshold policy under some reasonable assumptions and once the promotion is determined the optimal inventory/pricing policy is a base-stock-list-price policy. Numerical study is also provided to demonstrate the contribution of our model.

We consider a single item inventory model which is observed periodically in a randomly changing environment. All model parameters are specified by the state of the environment which is assumed to be a time-homogeneous Markov chain. Yield is random due to the random capacity of the vendor, i.e., a given order is fully received if the order quantity is less than this capacity. Otherwise, the quantity received is equal to the available capacity. The problem is analyzed in single, multiple and infinite periods and it is shown that in all cases, the optimal policy is the well-known base-stock policy where the optimal order-up-to level depends on the state of the environment. The results are compared with the solutions of the certain yield model when there is infinite capacity. We show that the order-up-to levels are equal in the single period case. However, in multiple and infinite periods, we order the same or more if the yield is random.

We study a single item hybrid production system with manufacturing and remanufacturing. It is assumed that remanufacturing is profitable and that, on average, there are more demands than returns. We investigate using simulation, for a variety of cases with different demand, return, manufacturing, and remanufacturing characteristics, what the cost reduction associated with having a disposal option for returned items is. The results show that there is only a considerable cost reduction if an item is very slow-moving, the recovery rate is high, and remanufacturing is almost as expensive as manufacturing.

A production facility is used to produce more than a single item in order to maximize its utilization. This, however, introduces a well-known phenomenon of interference which gives rise to the class of economic lot scheduling problems. In solving this problem, researchers have always assumed that the production capacity is high enough to meet the demand of all items that are produced. In this paper, we relax the capacity constraint and analyze the lot scheduling problem under insufficient capacity. We specifically study the two-product problem using the common cycle approach, and then discuss a special extension that treats any number of products.

In this article we propose a single item, periodic review model that investigates the effects of changes in the demand process that occur after stockout realizations. We investigate a system where the demands in successive periods are deterministic but affected by the backorder realizations. In order to capture the effects of changes in the demand process we use a geometric type supply availability. We analytically derive the necessary components for obtaining profit related performance measures and provide computational analysis.

This study looks at the single-item discrete lot sizing problem with backorders. Most of the studies in the literature on lot sizing problems do not allow for backordering. This paper modifies some of the heuristic rules developed originally for the facility location problems and applies them to the lot sizing problem. The heuristic rules are tested and evaluated for their efficiency. The findings of this study illustrate that the heuristic rules provide solutions that are either optimal or very close to optimal.

Wagner and Whitin's inventory model is generalized to incorporate a limited production rate. The model is conspicuous amongst related models in the literature as Wagner and Whitin's original algorithm may be applied. The result requires restrictions on the cost coefficients that make conventional material requirements planning the model's natural field of application.