Optimizing monitoring time in a continuous-review cyclic inventory system

This paper discusses a mathematical model for controlling amonitoring time by a sensing device in a continuous-review cyclicinventory system. The level of the inventory is monitored bythe sensor for a continuous period, whether the stock runs outor not. First, we consider the case where the lifetime of commoditiesis finite. It is shown that, under certain conditions, thereexists a finite and unique optimal monitoring time minimizingthe long-run average cost. Secondly, we discuss the case wherethe lifetime is infinite, with an appropriately modified restockingpolicy, and obtain an equation for the optimal monitoring timeunder milder conditions. Finally, some numerical examples arepresented, and sensitivity analyses for the optimal policiesare carried out.     

Optimizing a multi-stage production/inventory system by DC programming based approaches

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA (DC Algorithm)—an innovative approach in nonconvex programming framework. The mixed integer nonlinear problem is first reformulated as a DC program and then DCA is developed to solve the resulting problem. In order to globally solve the problem, we combine DCA with a Branch and Bound algorithm (BB-DCA). A convex minorant of the objective function is introduced. DCA is used to compute upper bounds while lower bounds are calculated from a convex relaxation problem. The numerical results compared with those of COUENNE (http://www.coin-or.org/download/binary/Couenne/), a solver for mixed integer nonconvex programming, show the rapidity and the ?-globality of DCA in almost cases, as well as the efficiency of the combined DCA-Branch and Bound algorithm. We also propose a simple heuristic algorithm which is proved by experimental results to be better than an existing heuristic in the literature for this problem.     

Stochastic inventory system with lead time flexibility: offered by a manufacturer/transporter

This paper studies lead time flexibility in a two-stage continuous review supply chain in which the retailer uses the (R, Q) inventory system: when his inventory position reaches R, the retailer places orders with size Q to the manufacturer, who uses a transportation provider to deliver them with different lead time options. According to the contract, the manufacturer is able to expedite or postpone the delivery if the retailer makes such a request. Hence, the retailer has the flexibility to modify the lead time by using the most up-to-date demand information. The optimal lead time policy is found to be a threshold-type policy. The sensitivity analysis also shows that R is much more sensitive to the change of lead time than Q, and thus, the paper is primarily focused on finding optimal R. We also provide a cost approximation which yields unimodal cost in R. Furthermore, we analyze the order crossing problem and derive an upper bound for the probability of order crossing. Finally, we conduct an extensive sensitivity analysis to illustrate the effects of lead time flexibility on supply chain performance and discuss the managerial insights.     

Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customer due dates

We consider a two-stage make-to-order manufacturing system with random demands, processing times, and distributed customer due dates. The work to each stage is released based on a planned lead time. A general approach to minimize total inventory holding and customer order tardiness cost is presented to find the optimal manufacturing capacities and planned lead times for each manufacturing stage. Expressions are derived for work-in process inventories, finished-goods-inventory and expected backorders under the assumption of a series of M/M/1 queuing systems and exponentially distributed customer required lead times. We prove that the distribution of customer required lead time has no influence on the optimal planned lead times whenever capacity is predefined but it influences the optimal capacity to invest into. For the simultaneous optimization of capacity and planned lead times we present a numerical study that shows that only marginal cost decreases can be gained by setting a planned lead time for the upstream stage and that a considerable cost penalty is incurred if capacity and planned lead time optimization are performed sequentially.     

Look-back policies for two-stage,pull-type production/inventory systems

We consider a two-stage, pull-type production/inventory system with a known service mechanism at the first stage. Set-ups and start-ups are involved in the operation of the second stage. We develop a production control policy for the second stage, within the class of (R, r) continuous-review policies, that minimizes the long run average total cost. We use a semi-Markov decision model to obtain an optimal policy for the operation of the second stage. The structure of the optimal policy suggests the use of a suboptimal look-back policy that delays the set-up at the second stage if the buffer lacks sufficient raw material. The performance of the system and the average total cost under the suboptimal policy can be obtained approximately using a decomposition algorithm. We show examples justifying the use of this suboptimal policy.This research is supported by the NSF Grant No. NSF-NCR-9110105, NSF Grant No. NSF-DDM-9014868 and by the North Atlantic Treaty Organization Grant No. NATO-CRG-900580.     

Analysis of two commodity Markovian inventory system with lead time

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity is fixed asS ⁱ (i = 1,2). The net inventory level at timet for the i-th commodity is denoted byI ⁱ(t),i = 1,2. If the total net inventory levelI(t) =I ¹(t) +I ²(t) drops to a prefixed level s[ leqslant tfrac(S₁ - 2)2ortfrac(S₂ - 2)2]s[ leqslant tfrac{{(S_1 - 2)}}{2}ortfrac{{(S_2 - 2)}}{2}] , an order will be placed for (S ⁱ −s) units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.     

Determining the Pareto set in a bicriteria two-echelon inventory/distribution system

This article concerns two-echelon inventory/distribution system, consisting of a warehouse and a retailer. We assume that the demand is deterministic and stockouts are not permitted. Two criteria are considered: to minimize the annual inventory cost and the annual total number of damaged items by improper shipment handling. The problem consists of determining the non-dominated inventory policies in such a way that the trade-off between both criteria is achieved. We present the characterization of the non-dominated optimal solution set and we use this result to correct the solution method previously proposed by other authors for a problem with identical cost structure. An efficient algorithm to calculate the non-dominated solution set is introduced. Computational results on several randomly generated problems are reported.     

Optimal configuration of a decentralized, market-driven production/inventory system

Pull systems are inherently easier to implement on the shop-floor; however, they are quite difficult to plan and design for optimal operation, leaving little guidelines to system designers and practitioners. In this paper we use an effective and relatively fast numerical method to understand the optimal configuration of a multi-stage, multi-product, decentralized, market-driven production/inventory system that minimizes average inventory holding subject to a service level constraint through selection of various production and procurement control parameters. We have also conducted a number of numerical experiments to understand how the control policies respond to changes in the system parameters, such as the number of stages, system workload, demand arrival rates of products, and inventory holding costs.     

Optimal production run time for two-stage production system with imperfect processes and allowable shortages

This paper considers a two-stage production system with imperfect processes. Shortages are allowed, and the unsatisfied demand is completely backlogged. In addition, the capital investment in process quality improvement is adopted. Under these assumptions, we first formulate the proposed problem as a cost minimization model where the production run time and process quality are decision variables. Then we develop the criterion for judging whether the optimal solution not only exists but also is unique. If the criterion is not satisfied, the production system should not be opened. An algorithm for the computations of the optimal solutions is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.     

Impacts of inventory shortage policies on transportation requirements in two-stage distribution systems

This paper investigates the impacts inventory shortage policies have on transportation costs in base-stock distribution systems under uncertain demand. The model proposed demonstrates how backlogging arrangements can serve to decrease the variability of transportation capacity requirements, and hence the magnitude of transportation costs, when compared with policies that expedite demand shortages. The model shows how inventory policy decisions directly impact expected transportation costs and provides a new method for setting stock levels that jointly minimizes inventory and transportation costs. The model and solution method provide insights into the relationship between inventory decisions and transportation costs and can serve to support delivery policy negotiations between a supplier and customer that must choose between expediting and backlogging demand shortages.     

Stochastic decomposition in production inventory with service time

We study an (s, S) production inventory system where the processing of inventory requires a positive random amount of time. As a consequence a queue of demands is formed. Demand process is assumed to be Poisson, duration of each service and time required to add an item to the inventory when the production is on, are independent, non-identically distributed exponential random variables. We assume that no customer joins the queue when the inventory level is zero. This assumption leads to an explicit product form solution for the steady state probability vector, using a simple approach. This is despite the fact that there is a strong correlation between the lead-time (the time required to add an item into the inventory) and the number of customers waiting in the system. The technique is: combine the steady state vector of the classical M/M/1 queue and the steady state vector of a production inventory system where the service is instantaneous and no backlogs are allowed. Using a similar technique, the expected length of a production cycle is also obtained explicitly. The optimal values of S and the production switching on level s have been studied for a cost function involving the steady state system performance measures. Since we have obtained explicit expressions for the performance measures, analytic expressions have been derived for calculating the optimal values of S and s.     

Some stochastic inventory models with deterministic variable lead time

In this paper we determine optimal reduction in the procurement lead time duration for some stochastic inventory models, jointly with the optimal ordering decisions. The models are developed with complete and partial information about the lead time demand distribution. The stochastic models analyzed in this paper are the classical continuous and periodic review models with a mixture of backorders and lost sales and the base stock model. For each of these models, we provide sufficient conditions for the uniqueness of the optimal operating policy. We also develop algorithms for solving these models and provide illustrative numerical examples.     

A bi-objective coordination setup problem in a two-stage production system

This paper addresses a problem arising in the coordination between two consecutive departments of a production system, where parts are processed in batches, and each batch is characterized by two distinct attributes. Due to the lack of interstage buffering between the two stages, these departments have to follow the same batch sequence. In the first department, a setup occurs every time the first attribute of a new batch is different from the one of the previous batch. In the downstream department, there is a setup when the second attribute changes in two consecutive batches. The problem consists in finding a batch sequence optimizing the number of setups paid by each department. This case results in a particular bi-objective combinatorial optimization problem. We present a geometrical characterization for the feasible solution set of the problem, and we propose three effective heuristics, as shown by an extensive experimental campaign. The proposed approach can be also used to solve a class of single-objective problems, in which setup costs in the two departments are general increasing functions of the number of setups.     

Demand selection decisions for a multi-echelon inventory distribution system

In this paper, we study an integrated demand selection and multi-echelon inventory control problem that generalizes the classical deterministic single distribution centre (DC) multi-retailer model by incorporating demand selection decisions. In addition to the ordering and holding cost components, a concave operating cost of the DC and a capacity on the total market demand served are also considered. For given revenue and cost parameters, the problem is to determine which sets of demand to fulfill and which multi-echelon inventory control policy to implement so as to maximize the net profit. We show that the problem can be formulated as a nonlinear discrete optimization model. We analyse the structural properties of the model and, based on these, outline an approach to solve the model efficiently. We also present some interesting managerial insights obtained from the numerical experiments.     

Inventory competition in a dual-channel supply chain with delivery lead time consideration

Aimed at the inventory competition of perishable products in a dual-channel supply chain with consideration of the delivery lead time in the online direct channel, we extend the Newsvendor model considering stock-out-based consumer switching behavior to include the delivery lead time. We examine the retailer's optimal order quantity decision in the retail channel and the manufacturer's optimal inventory level decision in the online direct channel, explore the manufacturer's optimal delivery lead time decision in the online direct channel, discuss the impact of the product price and consumer switching behavior on the optimal decisions of supply chain members, and compare the optimal decisions between decentralized and centralized scenarios. The results show that, compared with the centralized scenario, at least one of the supply chain members will overstock in the decentralized scenario and that consumers in the online direct channel enjoy a shorter delivery lead time and hence better service in the decentralized scenario. Finally, we present numerical examples to analyze the impact of relevant parameters on the supply chain members’ profits and the supply chain efficiency.     

Waiting time analysis of a two-stage queueing system with priorities

A two-stage queueing system with two types of customers and non-preemptive priorities is analyzed. There is no waiting space between stages and so the blocking phenomenon is observed. The arrivals follow a Poisson distribution for the high priority customers and a gamma distribution for the low priority customers, while all service times are arbitrarily distributed. We derive expressions for the Laplace transform of the waiting time density of a low priority customer both in the transient and the steady state.     

An optimal ordering and issuing policy for a two-stage inventory system for perishable products

This paper considers the problem of ordering and issuing policies arising in controlling finite-life-time fresh-meat-carcass inventories in supermarkets. A supermarket orders a product, which constitutes a set of sub-products of fixed proportion, from a vendor at the beginning of each time cycle. After it is received from the vendor, the product is stored in the cool-room, before being issued to the display shelves. The sub-products then satisfy random customer demand. After passing the life-time, sub-products are salvaged. In this system, the sub-products are issued to the display shelves according to theorder-up-to level policies at the beginning of every period. The decisions to be taken to solve this problem are the product-ordering quantity from the outside vendor and the order-up-to issuing quantities for each sub-product. The objective function to be maximized is the expected profit per unit time, consisting of revenue from sales and salvage, and the cost of ordering, processing (or issuing), inventory holding, emergency issuing, and shortage. In this paper we first develop a mathematical model describing actual operations and then simplify the sub-product runout period so that optimal ordering and issuing policies are easily established. We then carry out extensive numerical experiments for a case of two sub-products in order to ascertain the properties and the behavior of the optimal solutions.     

Capacitated dynamic lot-sizing problem with delivery/production time windows

In this paper we generalize the classical dynamic lot-sizing problem by considering production capacity constraints as well as delivery and/or production time windows. Utilizing an untraditional decomposition principle, we develop a polynomial-time algorithm for computing an optimal solution for the problem under the assumption of non-speculative costs. The proposed solution methodology is based on a dynamic programming algorithm that runs in O(nT⁴) time, where n is the number of demands and T is the length of the planning horizon.