A smoothing replenishment policy with endogenous lead times.

We consider a two echelon supply chain consisting of a single retailer and a single manufacturer. Inventory control policies at the retailer level often transmit customer demand variability to the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). When the manufacturer produces in a make-to-order fashion though, he prefers a smooth order pattern. But dampening the variability in orders inflates the retailer's safety stock due to the increased variance of the retailers inventory levels. We can turn this issue of conflicting objectives into a win-win situation for both supply chain echelons when we treat the lead time as an endogenous variable. A less variable order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer's safety stock. We show that by including endogenous lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels.Bullwhip effect; Demand; endogenous lead times; Fashion; Inventory; Inventory control; Markov processes; Order; Policy; Queueing; Research; Safety stock; Smoothing; Supply chain; Supply chain management; Time; Variability; Variance;

Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s, S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted

Periodic review base-stock replenishment policy with endogenous lead times.

In this paper, we consider a two stage supply chain where the retailer's inventory is controlled by the periodic review, base-stock level (R,S) replenishment policy and the replenishment lead times are endogenously generated by the manufacturer's production system with finite capacity. We extend the work of Benjaafar and Kim (2004) who study the effect of demand variability in a continuously reviewed base-stock policy with single unit demands. In our analysis, we allow for demand in batches of variable size, which is a common setting in supply chains. A procedure is developed using matrix analytic methods to provide an exact calculation of the lead time distribution, which enables the computation of the distribution of lead time demand and consequently the safety stock in an exact way instead of using approximations. Treating the lead time as an endogenous stochastic variable has a substantial impact on safety stock. We numerically show that the exogenous lead time assumption may dramatically degrade customer service.Production/inventory systems; Base-stock replenishment policy; endogenous lead times; Safety stock; Phase-type distribution; Matrix-analytical methods;

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

A lost sales inventory model with a compound poisson demand pattern.

Sales; Inventory; Model; Demand; University; Research;

Service and inventory models subject to a delay-limit

Abstract: This thesis is concerned with the mathematical analysis of situations where service must be provided to customers within a prespecified time after arrival, the delay-limit (e.g., due to a service contract). Customer arrivals are governed by a stochastic process, and customers can be served jointly to obtain economies of scale. In Part I a basic model is extensively analysed, using techniques from Markov decision theory and queueing theory. In Part II this model is extended to the context of the production of exchangeable items, leading to a general framework for inventory models with a delay-limit on backorders. Several models within this framework are then studied in detail, including lost-sales inventory models.

The impact of replenishment rules with endogenous lead times on supply chain performance..

In dit proefschrift beperken we ons tot een basis supply chain met één klant en één producent. We bestuderen verschillende bestelpolit ieken van de klant, en meten de impact van deze bestelregels op de produ ctie van de producent. We modelleren het productieproces als een wachtli jn- of queueing model. Uit de analyse van dit productiemodel vinden we de levertijden, die op hun beurt gebruikt worden in het voorra admodel van de klant. De methodologie die hiervoor gebruikt wordt, is tw eevoudig. Enerzijds maken we gebruik van statistische technieken om de v oorraad te beheren en bestellingen te plaatsen. Anderzijds maken we gebr uik van wachtlijntheorie en Markov ketens om de doorlooptijden te bepale n. Eerst onderzoeken we een eenvoudige "chase sales" bestelpolit iek: de klant plaatst elke periode een bestelling die gelijk is aan de c onsumentenvraag. We ontwikkelen een efficiënte procedure om de impact va n deze bestelregel op de doorlooptijden te berekenen op basis van

A MAP/PH/1 PRODUCTION INVENTORY MODEL

In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (,) policy. The production is switched on when the inventory level depletes to and the production remains on until the inventory level reaches to the maximum level . Once the inventory level becomes , the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory polic