La reforma del Estatuto de Cataluña y la sentencia del Tribunal

Researchers make different assumptions regarding policies on shortages when considering the product and market characteristics (Ghiami et al., 2013). An assumption that shortages are not allowed is critical when developing a blood bank model or optimising a distribution system for a group of pharmaceuticals as these products are related to health issues. Service level is normally adopted as an objective function. However, when there are similar products in the market and differences are negligible, it can be assumed that the shortages are lost. Sometimes customers wait for the orders if the products offered have a specific characteristic or outstanding quality. In the inventory control, different replenishment policy can be adopted under either periodic or continuous reviews.

Periodic (discrete) review

Under the periodic review policy, papers have considered the optimal control policy, the base stock policy that keeps a constant order-up-to-level for total items in system, other heuristics, and, when fixed ordering costs are present, the (s, S) and (R, S) policies, for instance.

Most of the research in replenishment policy for deteriorating inventory is dedicated to stock-level dependent policies including order-up-to S and (s, S)

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policies. Order-up-to policies are suggested as good approximations of optimal policies (Duan and Liao, 2013). With these operating policies, the facility replenishes its inventory according to its target order-up-to level. In an order-up- to without age consideration (s, S) policy, whenever the inventory level drops to s, an order for Q (=S-s) items is placed (Sivakumar, 2009). The order-up-to level can vary from day to day. However, these policies do not acknowledge the perishable nature of the product and are therefore generally suboptimal. Considering perishables with a fixed maximum shelf life, Haijema (2013) proposed a new class of stock-level dependent policy, the (s, S, q, Q) policy, which is a periodic review (s, S) policy with the order quantity restricted by a minimum (q) and maximum (Q). This simple policy is preferred for practical use given that only the total stock level is required as an input. This approach is developed in avoidance of the computational complexities by using some statistics from the optimal ordering policy computed by formulating and solving the underlying Markov decision problem as a benchmark.

For the management of inventory when products have reached end of life status, it can be considered that the deteriorated units are not repaired or replaced during the planning horizon (Wang, 2002, Balkhi and Benkherouf, 2004, Hsu et al., 2007, He et al., 2010, Cheng et al., 2011). However, due to new information technologies such as RFID, it is now economically feasible to track the age of the products. This leads to the development of inventory replenishment policies with age consideration.

The replenishment policy where an order size must be adjusted upwards to account for the deteriorated items has received attention by many researchers (Gürler and Özkaya, 2003, Zhou and Yang, 2003, Broekmeulen and van Donselaar, 2009, Rossi et al., 2010b, Rossi, 2013, Pauls-Worm et al., 2014). In this policy, the order quantity will be the difference between the current inventory level/position and the order-up-to-level, after disposing of the outdated items. Broekmeulen and van Donselaar (2009) named this method the EWA. This policy works similarly to the base order-up-to policy except that the inventory position (including outstanding orders in addition to the physical inventory) is corrected for the estimated amount of outdating and an order is placed if this revised inventory position drops below the target order-up-to level. With the known inventory state at the current period, the possible number of

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outdated items is determined. In the non-stationary (Rn, Sn) policy considered by Pauls-Worm et al. (2010, 2014), Rossi et al. (2010b) and Rossi (2013), the order-up-to level Sn for each period is corrected for the expected waste by explicitly considering for every period the expected age-distribution of the products in stock. Pauls-Worm et al. (2010, 2014) addressed this policy as a “waste-compensating” replenishment cycle policy.

Duan and Liao (2013) proposed an age-based replenishment policy called the old inventory ratio policy (OIR). This policy operates under the base order-up-to policy that takes an old inventory ratio (the proportion of “old” items to the total items on hand) into account. The definition of an old item is defined as an item with residual lifetime of a certain number of days that could also vary subject to optimisation with respect to the length of its lifetime. If the ratio exceeds a certain threshold level, an additional replenishment with the size of the total number of “old” items is triggered to account for the possible outdating.

Continuous review

Under continuous review policy, papers have considered the base stock policy, the (s, S) policy or the (r, Q) policy when batch sizes are fixed and the (Q, r, T) policy that orders when inventory is depleted below r or when items exceed T units of age, for instance.

A more realistic base stock policy with variable ordering quantity and arbitrary replenishment times has been considered in a continuous review perishable system (Kalpakam and Shanthi, 2001). At every demand period, an order for items is placed to restore the inventory position back to the maximum stock level S. There is no order initiated by deteriorated items for practical and economical purposes such that the continuous monitoring of items can be avoided.

Tekin et al. (2001) considered the modified lot-size (Q, r, T) replenishment control policy that involves both the inventory level and the remaining shelf life of the items in stock. A replenishment order of size Q is placed either when the inventory drops to r, or when T units of time have elapsed since the last instance at which the inventory level hit Q, whichever occurs first. Concerning the specified aging process, T corresponds directly to an age threshold for

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reorder, whereas, r is an inventory level threshold for reorder in the classical sense.

The perishable inventory is controlled with an (r, Q) review system in the inventory model proposed by Kouki et al. (2013). At each unit of time the inventory position is monitored. If it falls to or below the replenishment level r, an order of size Q is placed. The expected outdating quantity associated with an order is calculated following the replenishment policy. It is assumed that items arrive fresh in stock and there is no decrease in the value of products during their fixed usable lifetime. Additionally, the benefit of using time temperature integrator technology (TTI) on inventory management is investigated in this research. The TTI makes it possible to monitor product freshness and provides information on the products’ remaining shelf lives. The probability of products having a certain lifetime, which affects the expected outdated quantity, is integrated into the model.