On Solving a Stochastic Programming Model for Perishable Inventory Control (original) (raw)
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Inventory control for a perishable product with non-stationary demand and service level constraints
We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a setup cost is incurred. Moreover, the producer has to deal with unit production cost, unit holding cost and unit cost of waste. The production plan for a finite time horizon specifies in which periods to produce and how much. We formulate this single item – single echelon production planning problem as a stochastic programming model with a chance constraint. We show that an approximate solution can be provided by a MILP model. The generated plan simultaneously specifies the periods to produce and the corresponding order-up-to levels. The order-up-to level for each period is corrected for the expected waste by explicitly considering for every period the expected age-distribution of the products in stock. The model assumes zero lead time and backlogging of shortages. The viability of the approach is illustrated by numerical experiments. Simulation shows that in 95.8% of the periods the service level requirements are met with an error tolerance of 1%.
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.
Stochastic Dynamic Programming for Three-Echelon Inventory System of Limited Shelf Life Products
MATEC Web of Conferences, 2016
Coordination of inventory decisions within the supply chain is one of the major determinants of its competitiveness in the global market. Products with limited shelf life impose additional challenges in managing the inventory across the supply chain because of the additional wastage costs incurred in case of being stored beyond product's useful life. This paper presents a stochastic dynamic programming model for inventory replenishment in a serial multi-echelon distribution supply chain. The model considers uncertain stationary discrete demand at the retailer and zero lead time. The objective is to minimize expected total costs across the supply chain echelons, while maintaining a preset service level. The results illustrate that a cost saving of around 17% is achievable due to coordinating inventory decisions across the supply chain.
The Supply Chain Design for Perishable Food with Stochastic Demand
It has been a challenging task to manage perishable food supply chains because of the perishable product's short lifetime, the possible spoilage of the product due to its deterioration nature, and the retail demand uncertainty. All of these factors can lead to a significant amount of shortage of food items and a substantial retail loss. The recent development of tracing and tracking technologies, which facilitate effective monitoring of the inventory level and product quality continuously, can greatly improve the performance of food supply chain and reduce spoilage waste. Motivated by this recent technological advancement, our research aims to investigate the joint decision of pricing strategy, shelf space allocation, and replenishment policy in a single-item food supply chain setting, where our goal is to maximize the retailer's total expected profit subject to stochastic retail demand. We prove the existence of optimality for the design of the perishable food supply chain. We then extend the single-item supply chain problem to a multi-item setting and propose an easy-to-implement searching algorithm to produce the optimal allocation of shelf space among these items for practical implementation. Finally, we provide numerical examples to demonstrate the effectiveness of our solution.
International Journal of Production Economics, 2014
We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a setup cost is incurred. Moreover, the producer has to deal with unit production cost, unit holding cost and unit cost of waste. The production plan for a finite time horizon specifies in which periods to produce and how much. We formulate this single item-single echelon production planning problem as a stochastic programming model with a chance constraint. We show that an approximate solution can be provided by an MILP model. The generated plan simultaneously specifies the periods to produce and the corresponding order-up-to levels. The order-up-to level for each period is corrected for the expected waste by explicitly considering for every period the expected age-distribution of the products in stock. The model assumes zero lead time and backlogging of shortages. The viability of the approach is illustrated by numerical experiments. Simulation shows that in 96.4% of the periods the service level requirements are met with an error tolerance of 1%.
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.
A Perishable Inventory Model with Unknown Time Horizon
2008
Traditionally, the time (planning) horizon over which the inventory for a particular item will be controlled is often assumed to be known (finite or infinite) and the total inventory cost is usually obtained by summing up the cost over the entire time horizon. However, in some inventory situations the period over which the inventory will be controlled are difficult to predict with certainty, as the inventory problems may not live up to or live beyond the assumed planning horizon, thereby affecting the optimality of the model. This paper presents a deterministic perishable inventory model for items with linear trend in demand and constant deterioration when time horizon is unknown, unspecified or unbounded. The heuristic model obtains replenishment policy by determining the ordering schedule to minimize the total cost per unit time over the duration of each schedule. A numerical example and sensitivity analysis are given to illustrate the model.
On a stochastic programming model for inventory planning
2004
This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a ...
A Two-Stage Production Planning Model for Perishable Products under Uncertainty
This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimized subject to a set of constraints such as warehouse space, labor working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilize the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilization of resources. Comparative analysis of solutions with and without postponement strategies is performed.
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.