An exact analysis on age-based control policies for perishable inventories (original) (raw)
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A Discrete-Time Model for Common Lifetime Inventory Systems
Mathematics of Operations Research, 2005
We consider a discrete-time s S inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventorylevel process. We obtain a closed-form expected cost function. Numerical results demonstrate some properties of optimal ordering policies and cost functions. When compared with the results for the constant lifetime model, the variance of the lifetime significantly affects the system behavior. Thus, the formalism that we create here adds a new dimension to the research in perishable inventory control under uncertainty in lifetime.
Analysis of the (Q,r) Inventory Model for Perishables with Positive Leal Times and Lost Sales
Operations Research, 2008
We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q r) policy, where r < Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q r) policy with respect to a time-based benchmark policy and find that the (Q r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.
2018
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 orderup-to level, b) production timing is fixed in advance and the production quantity takes the agedistribution 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.
Analysis of the (s, S) policy for perishables with a random shelf life
IIE Transactions, 2008
A continuous review perishable inventory system operating under the (s, S) policy is considered. Assuming a random shelf life with a general distribution, renewal arrivals and a negligible replenishment lead time, exact expressions for the expected cost rate function for unit and batch demands are derived. For unit demands, it is shown that the average cost rate function is quasi-convex in (s, S). Numerical findings indicate that the loss incurred by ignoring the randomness of the shelf life can be drastic. It is observed that the shape of the shelf life distribution has a significant impact on the costs and a precise estimation of shelf life distribution may result in substantial savings. Based on the presented analytical results, a new heuristic for positive lead times is proposed. Extensive numerical studies show that the proposed heuristic performs better than an existing one suggested for fixed shelf lives in most of the cases studied.
European Journal of Operational Research, 2016
We study the inventory management decisions of a retailer selling a single perishable good in a determin-istic setting. We take into account consumers' assessment of quality over the lifetime of the products, and assume that the demand rate is a linearly decreasing function of the age of the products. We analytically obtain the optimal cycle length of the retailer. Using our model, we obtain traditional non-perishable Economic Order Quantity (EOQ)-like lower and upper bounds on the cycle length and the profit, and show that they lead to near-optimal results for our typical examples, which are grocery items. We show that a perishable good acts similarly to a non-perishable good with unit holding cost equal to the ratio of contribution margin to lifetime. We also approximate the contribution margin the perishable good needs to have to maintain profitability parity with non-perishable goods.
Optimal replenishment policy with variable deterioration for fixed lifetime products
Scientia Iranica
Although numerous researchers have developed di erent inventory models for deteriorating items, very few of them have taken the maximum lifetime of a deteriorating item into consideration. This paper illustrates a mathematical model to obtain an optimal replenishment policy for deteriorating items with maximum lifetime, ramp-type demand, and shortages. Both holding cost and deterioration function are linear functions of time, which are treated as constants in most of the deteriorating inventory models. A simple solution procedure is provided to obtain the optimal solutions. Numerical examples along with graphical representations are provided to illustrate the model. Sensitivity analysis of the optimal solution with respect to key parameters of the model has been carried out and the implications are discussed.
A Lost Sales (r,Q) Inventory Control Model for Perishables with Fixed Lifetime and Lead Time
International Journal of Production Economics, 2015
We consider a perishable inventory system that operates under stochastic demand, constant lifetime and a constant lead time. The system employs a continuous review ðr; Q Þ inventory control policy where unfilled demands are lost. We investigate the properties of the cost function and present an approximation procedure to find the parameters r and Q that minimize the total cost. We then conduct a numerical analysis to examine the performance of the proposed model and study the sensitivity to changes in the system parameters. We demonstrate the suitability of the proposed approximations compared to optimal ðr; Q Þ parameters obtained by simulation and show that our proposal outperforms another approximation procedure from the literature, in particular for increasing ordering cost and demand variability. The proposed model contributes to the literature by providing a simple and efficient algorithm to compute the best (r, Q) parameters that minimize the total cost. Besides, it can be used in automated store ordering systems.
Markov models of inventory management systems with positive service time applications
Izvestiâ Akademii nauk SSSR. Tehničeskaâ kibernetika, 2018
Markov models of perishable inventory systems where some customers are withdrawn after completion of the service without buying the stock are studied. It is assumed that the service time and filling supply orders are positive random variables. The inventory replenishment size is a variable and depends on the current inventory level. Exact and approximate methods for calculating the joint distribution of the inventory level and the number of orders in the system are developed. Formulas for calculating the main characteristics of the studied systems are proposed and the problem of their optimization is solved. The high level of accuracy of the proposed formulas is confirmed by the numerical experiments.
Modelling, Identification and Control, 2017
This paper we propose a continuous review inventory system for perishable inventory with lost sales. We consider a single demand types and a single unit for placing and depleting the demand. The demand, lead time and life time is random variables according to an exponentially distributed. We develop the inventory system as a Markov process with impatient customer. We formulate the model as a M/M/∞ queuing model given a (r, S) and (r, K) policies. The state of system is a number of on-hand inventories and obtains the limited steady state probability at state n. The limited steady state probability approach is based on a basic rule of the rate of transition out equal to the rate of transition into the state. Numerical results indicate that the model provides no difference of the limited steady state probability comparing to the results of the augmented generator matrix. Furthermore, the results show that the (r, S) policy provides more efficiency than the (r, K) policy as (K > r) on the probability of lost sale (P0) whereas the (r, S) policy provides a larger on-hand inventory than the (r, K) policy as (K > r).