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One of the celebrated extensions of the economic order/production quantity (EOQ/EPQ) model is one that assumes a received shipment contains a fraction of imperfect (non-conforming) quality items, where these items, detected by 100% screening, are sold as a single batch at a discounted price. This paper revisits this model (Salameh and Jaber, 2000, Int. J. Prod. Econ. 64 (1), 59–64) and extends it by assuming that a shipment is coming from a distant supplier and, therefore, it is not feasible to replace the imperfect items with an additional order to the same supplier. To address this restriction, two models are presented. The first assumes that imperfect items are sent to a repair shop who charges a cost plus a markup margin, while the second model assumes that imperfect items are replaced by good ones from a local supplier at a higher cost. The inventory environment assumed in this paper is relevant in todays globalised supply chains, thus practical implications of the problem faced are discussed. Numerical results are also presented and discussed. The results show that there exists a threshold value of the unit purchase cost of an emergency-ordered item and a fraction of defectives to which it is decided to either buy or repair.

The paper considers two research issues that usually interact in practice, which are the ‘VMI with consignment’ inventory policy and the ‘Learning Curve’. Under a VMI with consignment agreement, the vendor is the one who manages the buyer's inventory, and he holds the property of the inventory until the withdrawal of the buyer: this practice also offers to the vendor the possibility of revising its production plans and shipments according to alternative policy also exploiting the opportunity offered by learning in production. The paper, which considers a two-level supply chain system with a single-vendor and a single-buyer at each level, investigates and compares different policies that the vendor may adopt to exploit the advantages offered by the VMI with consignment agreement when the vendor's production process is subject to learning effects. The main result of the study is to show how learning in production can give flexibility to the supply chain stake holders in assigning the size and the time of each shipment.

In recent years, companies have strengthened their supply agreements, and even the management of their inventories. To this aim, vendor-managed inventory (VMI) represents an interesting approach to stock monitoring and control, and it has been progressively considered and introduced in several companies. The research proposed investigates the way how a particular VMI policy, known as Consignment Stock (CS), may represent a successful strategy for both the buyer and the supplier. The most radical application of CS may lead to the suppression of the vendor inventory, as this actor uses the buyer's warehouse to stock its finished products. As a counterpart, the vendor will guarantee that the quantity stored in the buyer's warehouse will be kept between a maximum level and a minimum one, also supporting the additional costs eventually induced by stock-out conditions. The buyer will pick up from its store the quantity of material needed to meet its production plans and the material itself will be paid to the buyer according to the agreement signed. In previous studies, Braglia and Zavanella [2003. Modelling an industrial strategy for inventory management in supply chains: The ‘Consignment Stock’ case. International Journal of Production Research 41, 3793–3808] developed an analytical model of the CS policy, referring to a single-vendor and single-buyer situation. The same authors presented a comparison with the optimal solution available in the literature (in particular, with reference to Hill's model [1997. The single-vendor single-buyer integrated production-inventory model with a generalised policy. European Journal of Operational Research 97, 493–499]). The analytical results obtained allow the identification of the benefits and profitability that the CS approach determines in environments affected by uncertain demand. In order to understand the potential benefits of the CS policy, an analytical model is offered with reference to the interesting industrial case of a single-vendor and multiple-buyer productive situation, thus obtaining the optimal replenishment decisions for both the vendor and buyers in such a situation. The results show how the CS policy works better than the uncoordinated optimisation.

This paper originated from an industrial case study in the field of the aluminium supply chain. In particular, the most original aspects of the study are linked to the use of an alternative supply method for raw material (aluminium) in manufacturing. This method consists in the possibility of the company receiving the aluminium alloy from its supplier (refiner and remelter of secondary aluminium) in the liquid phase, as an alternative to the traditional supply of solid material. This practice has been possible by the use of special ladles, transportable by truck and moved within factories, thanks to specially equipped overhead bridge cranes. The supply of molten metal represents a substantial benefit for the whole supply chain, because of the energy savings implicit in the method itself (i.e. both energy and time can be saved when melting the metal at the company furnaces). Moreover, the study integrates the concerns about transport pollution, addressing the topics of a green supply chain problem and incorporating the environmental aspects in its analytical description. Therefore, the study proposes a model to evaluate the economic and environmental effects of the industrial practice described. The result of the model is the determination of the supply aluminium mix, i.e. molten and solid alloy, capable of balancing the economic benefits (highest scrap values, lowest total costs, etc.) as well as environmental requirements (least pollution).

The study originated from an industrial case study in the field of steel production, but it presents a larger interest, as many other manufacturing fields have similar concerns (e.g. foundries, food, textile and paper industries). A significant phase of steel manufacturing is the product cooling (likewise, drying in paper and textile production, or maturing in food production). This phase may be completed in different ways, but (1) it must be carried out in the finished product warehouse and (2) it must meet both production optimisation and customer needs. The latter requirement acquires a strategic relevance in JIT environments. The present study proposes a mathematical model to find the optimal production schedule of steel billets, based on the relevant parameters of the productive system (set-up and processing times, demand profile). In the industrial case examined, the negative impact of holding costs on cash flows is also linked to the space required by the cooling process, which depends on the production schedule adopted. In other words, the finished product storage can be considered a part of the manufacturing cycle and impacts on it. In the case of steel plants operating in JIT environments, the warehouse must be promptly emptied and carefully managed to exploit the available space. Thus, the effect of inventory costs is examined in a production–inventory system with finite capacity, where products are made to order and share the same manufacturing facility. The study is completed by an experimental analysis to investigate the effect of variations in the relevant parameters of the problem.

at least one shipment for each buyer will occur within the cycle T. Within the same cycle T, all the shipments to the same buyer following the first one (if any) have to be done immediately, thus completely fulfilling each buyer by consecutive deliveries per each cycle; as far as the delivery sequence is concerned, the first buyer gets the first delivery, followed by its second delivery and so on. Once completed the deliveries planned within the cycle for the first buyer, the second one is served and so on, up to the last buyer Y. Within the same cycle T, multiple equal-sized consecutive deliveries to the same buyer may occur, but the sequence assigned must be observed, i.e. the buyers are served according to the order initially set. Therefore, under the assumptions made, it should be underlined that the sequencing of the deliveries to the buyers is relevant to the cost function and to the deliveries organisation.