A rolling horizon simulation approach for managing demand with lead time variability

This paper proposes a rolling horizon (RH) approach to deal with management problems under dynamic demand in planning horizons with variable lead times using system dynamics (SD) simulation. Thus, the nature of dynamic RH solutions entails no inconveniences to contemplate planning horizons with unpredictable demands. This is mainly because information is periodically updated and replanning is done in time. Therefore, inventory and logistic costs may be lower. For the first time, an RH is applied for demand management with variable lead times along with SD simulation models, which allowed the use of lot-sizing techniques to be evaluated (Wagner-Whitin and Silver-Meal). The basic scenario is based on a real-world example from an automotive single-level SC composed of a first-tier supplier and a car assembler that contemplates uncertain demands while planning the RH and 216 subscenarios by modifying constant and variable lead times, holding costs and order costs, combined with lot-sizing techniques. Twenty-eight more replications comprising 504 new subscenarios with variable lead times are generated to represent a relative variation coefficient of the initial demand. We conclude that our RH simulation approach, along with lot-sizing techniques, can generate more sustainable planning results in total costs, fill rates and bullwhip effect terms.     

Pricing and lot-sizing decisions in a two-echelon system with transportation costs

We consider a single-buyer single-supplier system. The market demand is sensitive to the selling price set by the buyer. Both the buyer and the supplier operate with unit product costs, inventory holding costs, and order placement costs. In addition, the buyer is responsible for the freight cost. We formulate a model for determining the optimal lot-sizing and pricing decisions. Existing models for the problem do not consider the transportation costs with price sensitive market demand, and determine the optimal decisions through an exhaustive search. We propose an approximate solution procedure, and report the computational results on the effectiveness of the proposed procedure.     

An integrated approach to inventory and flexible capacity management subject to fixed costs and non-stationary stochastic demand

In a manufacturing system with flexible capacity, inventory management can be coupled with capacity management in order to handle fluctuations in demand more effectively. Typical examples include the effective use of temporary workforce and overtime production. In this paper, we discuss an integrated model for inventory and flexible capacity management under non-stationary stochastic demand with the possibility of positive fixed costs, both for initiating production and for using contingent capacity. We analyze the characteristics of the optimal policies for the integrated problem. We also evaluate the value of utilizing flexible capacity under different settings, which enable us to develop managerial insights.     

Adapting lot-sizing techniques to stochastic demand through production scheduling policy

Production-inventory systems that experience significant demand variations from period to period often use deterministic lot-sizing techniques to schedule production runs. If demand is uncertain, safety stock is included to buffer against stockouts. In this paper we propose a 'dual-buffer' production scheduling policy and show that it has superior performance characteristics to the single buffer policies currently in use. The second buffer is a simple calculation based on prior work in stochastic inventory theory. Methodologically, data envelopment analysis (DEA) is used to analyze results. This represents an unusual use of DEA     

考虑运输能力约束的VMI补货发货动态批量研究

考虑由一个供应商和多个零售商构成的VMI供应链,在供应商运输能力有限、可采用外包策略的情况下,研究了动态需求环境下供应链补货及发货批量策略问题.分析得出供应商最优补货及发货期结构满足"零库存补货"性质,进而利用动态规划方法提出一个多项式算法优化补货及发货策略,其计算复杂度为O(T3),且通过平衡各种成本,可得每个发货周...     

Policy and cost approximations of two-echelon distribution systems with a procurement cost at the higher echelon

This paper investigates a two-echelon (warehouse-retailer) inventory system with stochastic demand and a pull system of inventory allocation. We assume that ordering costs are charged at the warehouse for procuring the item from a supplier. However, the internal costs of ordering the item from the warehouse by the retailers are considered negligible. For this problem, the lower echelon uses a single critical number, an order-up-to-level policy, whereas a (s, S) inventory system is followed at the upper echelon. We develop a cost model for this problem and provide a simple algorithm for estimating the optimal policy. Simulation is used to test the accuracy of the model.     

Distribution-robust single-period inventory control problem with multiple unreliable suppliers

This paper presents a distribution-robust approach to the single-period inventory control problem with multiple unreliable suppliers and stochastic demand. Using the mean and covariance that are assumed to be the only known data, the proposed approach tries to find a solution that performs well independent of the specific distributions. The approach can provide a way to effectively hedge against risks coming not just from uncertainty itself but also from inaccurate estimation. Moreover, the resulting optimization model turns out to be computationally tractable and amenable to mathematical analysis. Using the model, we provide a complete characterization of the optimal sourcing strategies when there are two suppliers: a perfectly reliable supplier and an unreliable supplier. Various interesting issues relevant to sourcing problems, including the value of supplier diversification and yield quality improvement, also are addressed.     

Distribution planning for multi-echelon networks considering multiple sourcing and lateral transshipments

Nowadays, due to the increasing complexity of business environment, especially demand uncertainty, supply chain managers need to establish more-effective sourcing and distribution strategies to ensure high customer service and low stock costs. To overcome this challenge multi-echelon network structures and alternative distribution strategies such as lateral transshipments and multiple sourcing should be considered in inventory optimisation models. In this article, we propose a scenario-based modelling approach to solve a two-stage multi-echelon inventory optimisation problem with a non-stationary demand. The model is based on a distribution requirements planning (DRP) approach and minimises the expected total cost that is composed of the fixed allocation, inventory holding, procurement, transportation, and back-ordering costs. Alternative inventory optimisation models, including the lateral transshipment strategy and multiple sourcing, are thus built, and the corresponding stochastic programmes are solved using the sample average approximation method. Through a numerical investigation conducted with several generated instances and an empirical investigation based on the case of a major French retailer’s distribution network, we show the substantial benefit of lateral transshipments and multiple sourcing in reducing the expected total costs of the distribution network.     

Tactical capacity management under capacity flexibility

In many production systems a certain level of flexibility in the production capacity is either inherent or can be acquired. In that case, system costs may be decreased by managing the capacity and inventory in a joint fashion. In this paper we consider such a make-to-stock production environment with flexible capacity subject to periodic review under non-stationary stochastic demand, where we allow for positive fixed costs both for initiating production and for acquiring external capacity. Our focus is on tactical-level capacity management which refers to the determination of in-house production capacity while the operational-level integrated capacity and inventory management is executed in an optimal manner. We first develop a simple model to represent this relatively complicated problem. Then we elaborate on the characteristics of the general problem and provide the solution to some special cases. Finally, we develop several useful managerial insights as to the optimal capacity level, the effect of operating at a suboptimal capacity level and the value of utilizing flexible capacity.     

Supply chain network design with unreliable suppliers: a Lagrangian relaxation-based approach

This paper deals with the integrated facility location and supplier selection decisions for the design of supply chain network with reliable and unreliable suppliers. Two problems are addressed: (1) facility location/supplier selection; and (2) facility location/supplier reliability. We first consider the facility location and supplier selections problem where all the suppliers are reliable. The decisions concern the selection of suppliers, the location of distribution centres (DCs), the allocation of suppliers to DCs and the allocation of retailers to DCs. The objective is to minimise fixed DCs location costs, inventory and safety stock costs at the DCs and ordering costs and transportation costs across the network. The introduction of inventory costs and safety stock costs leads to a non-linear NP-hard optimisation problem. To solve this problem, a Lagrangian relaxation-based approach is developed. For the second problem, a two-period decision model is proposed in which selected suppliers are reliable in the first period and can fail in the second period. The corresponding facility location/supplier reliability problem is formulated as a non-linear stochastic programming problem. A Monte Carlo optimisation approach combining the sample average approximation scheme and the Lagrangian relaxation-based approach is proposed. Computational results are presented to evaluate the efficiency of the proposed approaches.     

Parallel machine,capacitated lot-sizing and scheduling for the pipe-insulation industry

We develop a solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon. The objective is to determine the product assignment, production quantities, and production sequence on each machine in order to meet demand and maximise the total production amount in a given planning horizon. We study this problem in the context of the manufacturing of pipe insulation, in which multiple features have to be considered simultaneously. The solution procedure combines mathematical programming and a post-processing sequencing heuristic. We also develop a procedure to determine safety stock levels and use Monte Carlo simulation to assess the risk associated with inventory shortages due to stochastic production rates. Computational tests are performed on both real and artificially-generated data.     

Integrated workforce capacity and inventory management under labour supply uncertainty

In a manufacturing environment with volatile demand, inventory management can be coupled with dynamic capacity adjustments for handling the fluctuations more effectively. In this study, we consider the problem of integrated capacity and inventory management under non-stationary stochastic demand and capacity uncertainty. The capacity planning problem is investigated from the workforce planning perspective where the capacity can be temporarily increased by utilising contingent workers from an external labour supply agency. The contingent capacity received from the agency is subject to an uncertainty, but the supply of a certain number of workers can be guaranteed through contracts. There may also be uncertainty in the availability of the permanent and contracted workers due to factors such as absenteeism and fatigue. We formulate a dynamic programming model to make the optimal capacity decisions at a tactical level (permanent workforce size and contracted number of workers) as well as the operational level (number of workers to be requested from the external labour supply agency in each period), integrated with the optimal operational decision of how much to produce in each period. We analyse the characteristics of the optimal policies and we conduct an extensive numerical analysis that helps us provide several managerial insights.     

Random yield and coordination mechanisms of a supply chain with emergency backup sourcing

This paper considers a supply chain in which a buyer purchases finished items from a contracting supplier to satisfy a stochastic market demand, where the supplier’s production is subject to random yield. We assume that the buyer can make up the shortage by sourcing from an emergency backup supplier. We develop two Stackelberg game models, i.e. buyer-Stackelberg (BS) model and supplier-Stackelberg (SS) model, and find that the decentralised BS model results in a higher stocking factor of supplier’s input than the decentralised SS model. Compared with BS model, the buyer in SS model performs more explicit order plan, and we find that only when the actual yield of the supplier is insufficient, the buyer would use emergency backup sourcing to make up the shortage. When the manufacturing operation of the supplier is in the good state, the buyer only orders a certain amount and has some leftover. When the actual yield of the supplier is moderate, the buyer uses up every item produced from the supplier regardless of the yield rate. Comparing both channel structures, SS operation is a more effective way of controlling both inventory cost and backup sourcing cost, and it can be beneficial for each player as well as for the whole channel. Finally, we develop the coordination mechanism for each channel to investigate the issues of risk handling and risk sharing for uncertain demand and uncertain yield.     

A hierarchical approach for the capacitated lot-sizing and scheduling problem with a special structure of sequence-dependent setups

This research deals with the single machine multi-product capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times and setup costs. The CLSP determines the production quantities and the sequence to satisfy deterministic and dynamic demand during multiple periods. The objective is to minimise the total sum of the inventory holding costs and the sequence-dependent setup costs. We consider a special form of sequence-dependent setup times where the larger product we produce next, the more setup time we need. As a solution approach, we propose a two-level hierarchical method consisting of upper-level planning and the lower-level planning. In the upper-level planning, we solve the lot-sizing problem with estimated sequence-independent setup times utilising the characteristic of the special structure of setup times. Then we solve the scheduling problem in the lower-level planning. The proposed method is compared with the single-level optimal CLSP solution and an existing heuristic developed for the uniform structure of setup times.     

Assessing the benefits of labelling postponement in an export-focused winery

Supporting wine production operations in an increasingly global market has grown ever more challenging. Export-focused wineries supply many foreign clients, often requiring different labels for the same kind of wine. Order forecasts tend to be highly inaccurate, and wineries must be able to quickly react to changes, making lot-sizing an important consideration. One tool to reduce product misallocation is postponing product differentiation, where the natural decoupling point for premium wine is the labelling process. However, the double handling involved incurs additional costs and time penalties. We analyse the performance impact of postponing the labelling of bottled wines by developing a multi-stage mixed-integer stochastic programming model with full recourse for demand scenarios. The underlying data and policies are based on an unnamed Chilean export-focused winery. The model supports lot-sizing under several winery production policies. We experiment with different levels of capacity tightness, demand variability and demand correlation between wines, optimising for reducing order backlogs, inventory levels and line set-ups. While we find that some amount of postponement will always be recommended, the exact mix and degree depend on these external factors. Postponement has the most benefits when production capacity is moderately tight, demand variability is high and wines have negatively correlated demands.     

Replenishment planning in discrete-time, capacitated, non-stationary, stochastic inventory systems

In this paper, we examine a single-product, discrete-time, non-stationary, inventory replenishment problem with both supply and demand uncertainty, capacity limits on replenishment quantities, and service level requirements. A scenario-based stochastic program for the static, finite-horizon problem is presented to determine replenishment orders over the horizon. We propose a heuristic that is based on the first two moments of the random variables and a normal approximation, whose solution is compared with the optimal from a simulation-based optimization method. Computational experiments show that the heuristic performs very well (within 0.25% of optimal, on average) even when the uncertainty is non-normal or when there are periods without any supply. We also present insights obtained from sensitivity analyses on the effects of supply parameters, shortage penalty costs, capacity limits, and demand variance. A rolling-horizon implementation is illustrated.     

Dynamic capacitated lot sizing with random demand and dynamic safety stocks

We present a stochastic version of the single-level, multi-product dynamic lot-sizing problem subject to a capacity constraint. A production schedule has to be determined for random demand so that expected costs are minimized and a constraint based on a new backlog-oriented δ-service-level measure is met. This leads to a non-linear model that is approximated by two different linear models. In the first approximation, a scenario approach based on the random samples is used. In the second approximation model, the expected values of physical inventory and backlog as functions of the cumulated production are approximated by piecewise linear functions. Both models can be solved to determine efficient, robust and stable production schedules in the presence of uncertain and dynamic demand. They lead to dynamic safety stocks that are endogenously coordinated with the production quantities. A numerical analysis based on a set of (artificial) problem instances is used to evaluate the relative performance of the two different approximation approaches. We furthermore show under which conditions precise demand forecasts are particularly useful from a production–scheduling perspective.     

The supplier–buyer integrated production-inventory model with random yield

This paper revisits the traditional supplier–buyer integrated production-inventory model which deals with the problem of a manufacturer (supplier) supplying a product to a retailer (buyer) serving the consumer market with constant stationary demand. The product is manufactured in batches at a finite rate. The supplier's production batch is depleted by the buyer's replenishment orders at periodic intervals. The buyer's inventory is then consumed by the market demand at a fixed rate. The problem is the simultaneous computation of the manufacturer's production lot-size and the buyer's replenishment order quantity, i.e. the integrated production-inventory policy parameters. The key characteristic considered in this paper is that the manufacturing process is imperfect, and, hence, there are defective items in each production lot. As a result, each replenishment order shipped to the buyer includes defective products and the non-defective percentage in each such shipment is random. Considering the case where the supplier replenishes the buyer via equal-sized shipments, we develop an analytical expression of the total expected cost for the supplier–buyer system under consideration, with and without a considerable inspection time. We first examine the case where the inspection time is negligible, and then we present a generalisation to consider the inspection time explicitly. Our goal is to model the impact of random yield on the system performance. Our findings are useful for computing the integrated production-inventory policy parameters while considering the supply uncertainty due to an imperfect manufacturing process. Through numerical examples, we quantify the impact of supply with random yield on the system performance and illustrate its relationship with the demand and production rate.     

The value of VMI beyond information sharing under time-varying stochastic demand

This study aims to determine the incremental value vendor-managed inventory (VMI) provides beyond that of independent decision-making with full information sharing (IS) under time-varying stochastic demand with service-level constraints. For this purpose, we apply mixed integer linear programming formulations to examine benefits for a supplier, a retailer and the system as a whole. To highlight the benefits of VMI vs. IS, a comprehensive numerical study is carried out considering a large number of business settings under both static and rolling horizons.     

Purchasing Policy of New Containers Considering the Random Returns of Previously Issued Containers

A number of organizations sell products in containers that can be reused. The time from issue to return of an individual container is usually not known with certainty and there is a chance that the container is never returned (because of loss or irrepairable damage). Consequently, even under a level demand pattern new containers must be acquired from time to time. In this paper a purchasing policy of these new containers is determined for a finite time horizon so as to minimize the total purchasing and expected carrying costs under a prescribed service level. The associated stochastic model is reduced to a deterministic, dynamic lot-sizing problem with possible occurrence of negative net demand (demand minus return). A transformation into the usual nonnegative demand case allows us to apply well-known deterministic lot-sizing procedures to obtain the solution.