Computing replenishment cycle policy parameters for a perishable item

In many industrial environments there is a significant class of problems for which the perishable nature of the inventory cannot be ignored in developing replenishment order plans. Food is the most salient example of a perishable inventory item. In this work, we consider the periodic-review, single-location, single-product production/inventory control problem under non-stationary stochastic demand and service level constraints. The product we consider can be held in stock for a limited amount of time after which it expires and it must be disposed of at a cost. In addition to wastage costs, our cost structure comprises fixed and unit variable ordering costs, and inventory holding costs. We propose an easy-to-implement replenishment cycle inventory control policy that yields at most 2N control parameters, where N is the number of periods in our planning horizon. We also show, on a simple numerical example, the improvement brought by this policy over two other simpler inventory control rules of common use

Inventory control for a non-stationary demand perishable product: comparing policies and solution methods

This paper summarizes our findings with respect to order policies for an inventory control problem for a perishable product with a maximum fixed shelf life in a periodic review system, where chance constraints play a role. A Stochastic Programming (SP) problem is presented which models a practical production planning problem over a finite horizon. Perishability, non-stationary demand, fixed ordering cost and a service level (chance) constraint make this problem complex. Inventory control handles this type of models with so-called order policies. We compare three different policies: a) production timing is fixed in advance combined with an order up-to level, b) production timing is fixed in advance and the production quantity takes the age distribution into account and c) the decision of the order quantity depends on the age-distribution of the items in stock. Several theoretical properties for the optimal solutions of the policies are presented. In this paper, four different solution approaches from earlier studies are used to derive parameter values for the order policies. For policy a), we use MILP approximations and alternatively the so-called Smoothed Monte Carlo method with sampled demand to optimize values. For policy b), we outline a sample based approach to determine the order quantities. The flexible policy c) is derived by SDP. All policies are compared on feasibility regarding the α-service level, computation time and ease of implementation to support management in the choice for an order policy.National project TIN2015-66680-C2-2-R, in part financed by the European Regional Development Fund (ERDF)

Efficient inventory control for imperfect quality items

In this paper, we present a general EOQ model for items that are subject to inspection for imperfect quality. Each lot that is delivered to the sorting facility undertakes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The generality of the model is viewed as important both from an academic and practitioner perspective. The mathematical formulation considers arbitrary functions of time that allow the decision maker to assess the consequences of a diverse range of strategies by employing a single inventory model. A rigorous methodology is utilised to show that the solution is a unique and global optimal and a general step-by-step solution procedure is presented for continuous intra-cycle periodic review applications. The value of the temperature history and flow time through the supply chain is also used to determine an efficient policy. Furthermore, coordination mechanisms that may affect the supplier and the retailer are explored to improve inventory control at both echelons. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings and lead to the generation of interesting managerial insights

A periodic inventory system of intermittent demand items with fixed lifetimes

Perishable items with a limited lifespan and intermittent/erratic consumption are found in a variety of industrial settings: dealing with such items is challenging for inventory managers. In this study, a periodic inventory control system is analysed, in which items are characterised by intermittent demand and known expiration dates. We propose a new inventory management method, considering both perishability and intermittency constraints. The new method is a modification of a method proposed in the literature, which uses a periodic order-up-to-level inventory policy and a compound Bernoulli demand. We derive the analytical expression of the fill rate and propose a computational procedure to calculate the optimal solution. A comparative numerical analysis is conducted to evaluate the performance of the proposed solution against the standard inventory control method, which does not take into account perishability. The proposed method leads to a bias that is only affected by demand size, in contrast to the standard method which is impacted by more severe biases driven by intermittence and periods before expiration

A NOVEL MODEL FOR THE CALCULATION OF SAFETY STOCK OF PERISHABLE PRODUCTS WITH A TOTAL WASTE CONSTRAINT

Perishable products cover a high percentage of all goods. The variability, long lead times, risk period, and high service level increase the safety stock level. An increase in safety stock will also increase the probability of perished products because of the increased probability of sales of less than stock during shelf life. This study proposes a model for calculating safety stocks of perishable products besides showing the effect of perishability on service level. The effects of long lead times, risk periods, high sales and lead-time variance, and short shelf life adversely affect perished products. The study investigates and proposes a novel model for calculating total expected waste and costs with a waste quantity constraint. A real-life example compares a proposed model with waste constraints and the traditional safety stock model based on costs and waste quantity. The case study shows the better results of the proposed models

Constrained Joint Replenishment Problem with Refrigerated Vehicles

We study a constrained joint replenishment problem with a multi-commodity refrigerated road transport in cold chain logistics. Each truck may have multiple temperature zones, since products in full truckload shipment may have different temperature requirements. In the proposed mathematical programming model, we want to minimize the expected total cost that includes the inventory cost and the transportation cost as well as the penalty cost if temperature violation occurs subject to the full truckload constraint. Under the deterministic demand, the cycle time of each product, the temperature of each zone in each truck and the allocation plan (the number of units of each product to be shipped in each zone in each truck) are obtained from the mixed-integer nonlinear optimization model. Under the stochastic demand, we assume that the inventory is controlled using a periodic review system, and the order-up-to level is chosen to maintain the desired cycle service level of each product. In the case study of one of the largest modern grocery retailers in Thailand, our model is applied to obtain the optimal replenishment policy. Currently, the company's fleet consists of single-temperature trucks. We estimate the monetary benefit obtained by switching from a single-temperature truck to a multi-temperature truck. We also estimate the cost reduction from reducing the lead time. Finally, our model can be used to quantify the trade-off between the service level and the inventory cost to help the company choose the appropriate service levels