Near-Optimal Modified Base Stock Policies for the Capacitated Inventory Problem with Stochastic Demand and Fixed Cost (original) (raw)
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Cost minimising order schedules for a capacitated inventory system
Annals of Operations Research, 2015
In this paper, we study an inventory system with multiple retailers under periodic review and stochastic demand. The demand is modelled as a discrete random variable. Linear holding and backorder costs as well as fixed order costs are assumed. Orders to replenish inventories can be placed at a manufacturer with a limited capacity according to a cyclic order schedule. A fixed portion of the total available capacity in a period is allocated to each retailer, who follows a modified base-stock policy to determine the order quantities. Thus, the order policy consists of four policy parameters for each retailer: the length of the review period, the first order point within a planning horizon, the individual capacity limit, and the modified base-stock level. We present an algorithm to compute the exact optimal policy parameters and two heuristics. In a numerical study, we compare the results of these approaches and derive insights into the performance of the heuristics. In addition, we introduce three different schedule types and identify the situations, in which they perform best.
Approximation Algorithms for Capacitated Stochastic Inventory Control Models
Operations Research, 2008
We develop the first algorithmic approach to compute provably good ordering policies for a multi-period, capacitated, stochastic inventory system facing stochastic non-stationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computational approach, we propose a novel scheme to account for backlogging costs in a capacitated, multi-period environment. Our cost-accounting scheme, called the forced marginal backlogging cost-accounting scheme, is significantly different from the period-by-period accounting approach to backlogging costs used in dynamic programming; it captures the long-term impact of a decision on system performance in the presence of capacity constrains. In the likely event that the per-unit order costs are large compared to the holding and backlogging costs, a transformation of cost parameters yields a significantly improved guarantee. We also introduce new semi-myopic policies based on our new cost-accounting scheme to derive bounds on the optimal base-stock levels. We show that these bounds can be used to effectively improve any policy. Finally, empirical evidence is presented that indicates that the typical performance of this approach is significantly stronger than these worst-case guarantees.
International Journal of Production Economics, 2007
We consider a model of single-item periodic-review inventory system with stochastic demand, linear ordering cost, where in each time period, the system must order either none or at least as much as a minimum order quantity (MOQ). Optimal inventory policies for such a system are typically too complicated to implement in practice. In fact, the ðs; SÞ type of policies are often utilized in the real world. We study the performance of a simple heuristic policy that is easily implementable because it is specified by only two parameters ðs; tÞ. We develop an algorithm to compute the optimal values for these parameters in the infinite time horizon under the average cost criterion. Through an extensive numerical study, we demonstrate that the best ðs; tÞ heuristic policy has performance close to that of the optimal policies when the coefficient of variation of the demand distribution is not very small. Furthermore, the best ðs; tÞ policy always outperforms the best feasible ðs; SÞ policies and on average the percentage differences are significant. Finally, we study the impact of MOQ on system performance. r
European Journal of Operational Research, 2006
This paper addresses the single-item, non-stationary stochastic demand inventory control problem under the nonstationary (R, S) policy. In non-stationary (R, S) policies two sets of control parameters-the review intervals, which are not necessarily equal, and the order-up-to-levels for replenishment periods-are fixed at the beginning of the planning horizon to minimize the expected total cost. It is assumed that the total cost is comprised of fixed ordering costs and proportional direct item, inventory holding and shortage costs. With the common assumption that the actual demand per period is a normally distributed random variable about some forecast value, a certainty equivalent mixed integer linear programming model is developed for computing policy parameters. The model is obtained by means of a piecewise linear approximation to the non-linear terms in the cost function. Numerical examples are provided. (S.A. Tarim). European Journal of Operational Research xxx (2005) xxx-xxx www.elsevier.com/locate/eor
Single item inventory control under periodic review and a minimum order quantity
International Journal of Production Economics, 2011
In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Q min. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Q min) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Q min) policy in practice.
Total-Cost Stochastic Inventory Control Problems
2016
This paper describes the structure of optimal policies for discounted periodic-review single-commodity total-cost inventory control problems with fixed ordering costs for finite and infinite horizons. There are known conditions in the literature for optimality of (st, St) policies for finite-horizon problems and the optimality of (s, S) policies for infinitehorizon problems. The results of this paper cover the situation, when such assumption may not hold. This paper describes a parameter, which, together with the value of the discount factor and the horizon length, defines the structure of an optimal policy. For the infinite horizon, depending on the values of this parameter and the discount factor, an optimal policy either is an (s, S) policy or never orders inventory. For a finite horizon, depending on the values of this parameter, the discount factor, and the horizon length, there are three possible structures of an optimal policy: (i) it is an (st, St) policy, (ii) it is an (st,...
New Policies for Stochastic Inventory Control Models: Theoretical and Computational Results
2000
Recently Levi, Pál, Roundy and Shmoys introduced a novel, Dual-Balancing policy for the classical singleitem, single-location inventory model with backlogged demands and dynamic forecasts of future demands that evolve as time advances. These models are usually computationally intractable due to the enormous size of the state space. The expected cost of the dual-balancing policy is guaranteed to be at most twice the optimal expected cost, but until now, no computational testing of the policy has been done. We propose two extended families of policies, based on cost-balancing techniques and myopic-like policies that generate lower and upper bounds on the optimal base-stock levels. We show that cost-balancing techniques combined together with these lower and upper bounds lead to improved policies. The expected cost of the new policies is also guaranteed to be at most twice the optimal expected cost. Nevertheless, empirically their performance is significantly better. Moreover, all of the new policies can be implemented efficiently in an on-line manner.
A Discrete Time Markov Chain Model for a Periodic Inventory System with One-Way Substitution
SSRN Electronic Journal, 2000
This paper studies the optimal design of an inventory system with "one-way substitution" , in which a high-quality (and hence, more expensive) item fulfills its own demand and simultaneously acts as backup safety stock for the (cheaper) low-quality item. Through the use of a discrete time Markov model we analyze the effect of one-way substitution in a periodic inventory system with an (R,s,S) or (R,S) order policy, assuming backorders, zero replenishment leadtime and correlated demand. In more detail, the optimal inventory control parameters (S and s) are determined in view of minimizing the expected total cost per period (i.e. sum of inventory holding costs, purchasing costs, backorder costs and adjustment costs). Numerical results show that the one-way substitution strategy can outperform both the "no pooling" (only product-specific stock is held, and demand can never be rerouted to stock of a different item) and "full pooling" strategies (implying that demand for a particular product type is always rerouted to the stock of the flexible product, and no product-specific stock is held)− provided the mix of dedicated and flexible inputs is chosen adequately − even when the cost premium for flexibility is significant.