Inventory performance under staggered deliveries and autocorrelated demand

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordProduction plans often span a whole week or month, even when independent production lots are completed every day and service performance is tallied daily. Such policies are said to use staggered deliveries, meaning that the production rate for multiple days are determined at a single point in time. Assuming autocorrelated demand, and linear inventory holding and backlog costs, we identify the optimal replenishment policy for order cycles of length P. With the addition of a once-per-cycle audit cost, we optimize the order cycle length P∗ via an inverse-function approach. In addition, we characterize periodic inventory costs, availability, and fill rate. As a consequence of staggering deliveries, the inventory level becomes cyclically heteroskedastic. This manifests itself as ripples in the expected cost and service levels. Nevertheless, the cost-optimal replenishment policy achieves a constant availability by using time-varying safety stocks; this is not the case with suboptimal constant safety stock policies, where the availability fluctuates over the cycle

Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning

This is the author accepted manuscript. the final version is available from Elsevier via the DOI in this recordCompanies tend to set their master production schedule weekly, even when producing and shipping on a daily basis—the term for this is staggered deliveries. This practice is common even when there is no marginal cost of setting a new schedule. We argue that the practice is sound for companies that use the ubiquitous order-up-to (OUT) policy to control production of products with a significant capacity cost. Under these conditions, the length of the order cycle (time between schedule updates) has a damping effect on production, while a unit (daily) order cycle can cause significant capacity costs. We call this the capacity cost trap. Developing an analytical model based on industrial evidence, we derive capacity and inventory costs under the staggered OUT policy, showing that for this policy there is an optimal order cycle possibly greater than unity. To improve on this solution, we consider three approaches to smoothing: either levelling within the cycle, deferring excess production or idling to future cycles via a proportional OUT policy, or increasing the length of the cycle. By deriving exact cost expressions we compare these approaches, finding that smoothing by employing the proportional OUT policy is sufficient to avoid the capacity cost trap.Norwegian Research CouncilBIA programm

Inventory performance under staggered deliveries and auto-correlated demand

Production plans often span a whole week or month, even when independent production lots are completed every day and service performance is tallied daily. Such policies are said to use staggered deliveries, meaning that the production rate for multiple days are determined at a single point in time. Assuming autocorrelated demand, and linear inventory holding and backlog costs, we identify the optimal replenishment policy for order cycles of length P. With the addition of a once-per-cycle audit cost, we optimize the order cycle length P* via an inverse-function approach. In addition, we characterize periodic inventory costs, availability, and fill rate. As a consequence of staggering deliveries, the inventory level becomes cyclically heteroskedastic. This manifests itself as ripples in the expected cost and service levels. Nevertheless, the cost-optimal replenishment policy achieves a constant availability by using time-varying safety stocks; this is not the case with suboptimal constant safety stock policies, where the availability fluctuates over the cycle

Staggered deliveries in production and inventory control

This thesis investigates production-inventory systems where replenishments are received every period (for example every day or shift), but where production plans are determined less frequently (weekly, fortnightly, or monthly). Such systems are said to use staggered deliveries. This practice is common in industry, but the theoretical knowledge is limited to a small set of inventory models, none of which include capacity costs. This thesis uses time series analysis to expand our understanding of staggered deliveries from the perspectives of inventory and production-inventory control. The contribution to inventory theory consists in the development of an optimal policy for autocorrelated demand and linear inventory costs, including exact expressions for costs, availability, and fill rate. In addition the thesis identifies a procedure for finding the optimal order cycle length, when a onceper- cycle audit cost is present. Notably, constant safety stocks are suboptimal, and cause both availability and fill rate to fluctuate over the cycle. Instead, the safety stocks should vary over time, causing the availability, but not the fill rate, to be constant. The contribution to production-inventory theory comes from two perspectives: First, an optimal policy is derived for quadratic inventory and capacity costs; second, four pragmatic policies are tested, each affording a different approach to production smoothing and the allocation of overtime work (once per cycle, or an equal amount of overtime every period). Assuming independent and identically distributed demand, these models reveal that all overtime or idling should be allocated to the first period of each cycle. Furthermore, it is shown that the order cycle length provides a crude production smoothing mechanism. Should a company with long reorder cycles decide to plan more often, the capacity costs may increase. Therefore, supply chains should implement a replenishment policy capable of production smoothing before the order cycle length is reduced. i

Integrated Supply Chain Network Design: Location, Transportation, Routing and Inventory Decisions

abstract: In this dissertation, an innovative framework for designing a multi-product integrated supply chain network is proposed. Multiple products are shipped from production facilities to retailers through a network of Distribution Centers (DCs). Each retailer has an independent, random demand for multiple products. The particular problem considered in this study also involves mixed-product transshipments between DCs with multiple truck size selection and routing delivery to retailers. Optimally solving such an integrated problem is in general not easy due to its combinatorial nature, especially when transshipments and routing are involved. In order to find out a good solution effectively, a two-phase solution methodology is derived: Phase I solves an integer programming model which includes all the constraints in the original model except that the routings are simplified to direct shipments by using estimated routing cost parameters. Then Phase II model solves the lower level inventory routing problem for each opened DC and its assigned retailers. The accuracy of the estimated routing cost and the effectiveness of the two-phase solution methodology are evaluated, the computational performance is found to be promising. The problem is able to be heuristically solved within a reasonable time frame for a broad range of problem sizes (one hour for the instance of 200 retailers). In addition, a model is generated for a similar network design problem considering direct shipment and consolidation within the same product set opportunities. A genetic algorithm and a specific problem heuristic are designed, tested and compared on several realistic scenarios.Dissertation/ThesisPh.D. Industrial Engineering 201

Mathematics in the Supply Chain

[no abstract available

Just-In-Time in high variety / low volume manufacturing environments.

Available from British Library Document Supply Centre-DSC:DXN049763 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Structure and Process of Channel Program Selections: Retailers Choice among Parity Trade Promotions

This research tried to explain the role of calculative commitment, loyalty commitment and power asymmetry on behavioral commitment in a business to business scenario. We specifically looked at the trade promotion scenario since retailers face more trade promotions than they can accept and extant research suggests that retailers always choose trade promotions that offer the greatest immediate benefit. This dissertation addressed the following managerial question, “How does a firm select a program (trade deal) when all its vendors offer the same short term economic incentives”. We proposed that other aspects of retailer’s relationship with its vendors determine / influence the program selection decision. First, incentives imbedded in channel relationships namely economic incentives (e.g., access to new products) and social incentives (e.g., affect toward vendor / salesperson) lead to a selection decision. Second, the power asymmetry the retailer has with the various vendors directly impacts decision making and also moderates the impact of the embedded economic / social incentives. We used commitment theory and an experimental design to test our model. We find that calculative commitment has the greatest impact on decision making followed by power asymmetry. We also find that loyalty commitment has the least impact. We also found that under high power asymmetry, calculative commitment has a bigger impact than loyalty commitment on behavioral commitment than under low power asymmetry when loyalty commitment has a bigger impact