Fixed ordering cost

Consider the problem of managing the inventory of Xerox paper in a wmehouse. Although demands from retailers may fluctuate a bit in their demand, your aggregate demand for the item is fairly constant at 100,000 cases for the year. Due to your volume, your supplier has agreed to provide you an everyday low price of 55.00 a case. You calculate that it will cost about 4.00 per ctise per year to hold each case. Costs associated with each order and delivery charges by your supplier yield a fixed ordering cost of 75.00. 

Fixed-income assets, 757-859 Fixed-location storage systems, 1534, 1535 Fixed ordering costs, 2021 Fixtures ... 

In the above expression, 4,000 is the fixed ordering cost for one truckload, 200 is the demand for component 1 at Boston each day, and 0.4 is the holding cost per unit per day.)... 

In the second paper, Thomas considers a related problem but incorporates a general stochastic demand function and backlogging of excess demand. Specifically, Thomas considers a periodic review, finite horizon model with a fixed ordering cost and stochastic, price-dependent demand. The paper postulates a simple policy, referred to by Thomas as (5,5,p), which can be described as follows. The inventory strategy is an (5, S) policy If the inventory level at the beginning of period t is below the reorder point, st, an order is placed to raise the inventory level to the order-up-to level, St. Otherwise, no order is placed. Price depends on the initial inventory level at the beginning of the period. Thomas provides a counterexample which shows that when price is restricted to a discrete set this policy may fail to be optimal. Thomas goes on to say ... 

See Bernstein and Federgruen [15] in Section 4.3 for an example of pricing coordination with fixed ordering costs and multiple retailers. 

X. Chen and D. Simchi-Levi. Coordinating inventory control and pricing strategies with random demand and fixed ordering cost The finite horizon case. Working Paper, MIT, 2002a. 

Serial Supply Chain with Deterministic Demand and Fixed Ordering Costs... 

Consider a two-stage, serial supply chain where the annual demand at stage 2 is D = 10,000 units. Fixed ordering costs at stages 1 and 2 are Ai = 400/order and A2 = 50/order, and inventory holding costs are hi = 10/unit/year and Izj = 15/unit/year. 

Given the broad discussion in this chapter, one can see that computing inventory control parameters for even relatively simple multi-echelon systems— e.g., a two-stage, serial system with fixed ordering costs, or a three-stage, serial system without fixed cosfs— is a complex endeavor. Unfortunately, finding even approximately optimal solutions to more extensive systems is even more challenging, and beyond the scope of this book. While interested readers can consult the end-of-chapter references for extensions to the problems considered in this chapter, we believe that a few additional comments about multi-echelon inventory systems are warranted. 

Note that for TL shipments, the freight charge FC effectively serves as a fixed ordering cost. For each order placed, we must pay FCn to the carrier in order to transport the resulting shipment on a dedicated truck, and therefore the annual transportation cost is... 

Fixed ordering cost A ao per order Economic order otv EOQ S91.95 nils... 

Fixed ordering cost associated with supplier k Demand of product i for buyer j... 

Fixed ordering cost of supplier k Demand for product i for buyer j Lead time of supplier k to supply product i to buyer j Production capacity at supplier k for product i Maximum number of suppliers that can be selected Quantified VaR type risk for supplier k Quantified MtT type risk for supplier k Description... 

Total cost is the sum of annual purchase cost and fixed ordering cost. Where y, represents quantity of material ordered to ith supplier. 

Equation 9.1 assumes zero lead time. For the first period fj is either equal to 0 or equal to the inventory held in the system at the end of previous cycle. Similarly, at the end of the cycle, the ending inventory could be either equal to 0 or an amount decided by the buyer. In our formulation, the buyer has to trade-off among the fixed order cost (transaction cost), the inventory holding cost, and the benefits of product bundling. 

Cycle inventory exists in a supply chain because different stages exploit economies of scale to lower total cost. The costs considered include material cost, fixed ordering cost, and holding cost... 

This is significantly higher than the total cost of 97,980 that Best Buy incurred when ordering in lots of 980 units, as in Example 11-1. Thus, there are clear financial reasons that the store manager would be unwilling to reduce the lot size to 200. To make it feasible to reduce the lot size, the manager should work to reduce the fixed order cost S. If the fixed cost associated with each lot is reduced to 1,000 (from the current value of 4,000), the optimal lot size reduces to 490 (from the current value of 980). We illustrate the relationship between desired lot size and order cost in Example 11-2 (see worksheet Example 11-2). 

To reduce the optimal lot size by a factor of k, the fixed order cost S must be reduced by a factor of k. ... 

Because each model is ordered and delivered independently, a separate truck delivers each model. Thus, a fixed ordering cost of 5,000 ( 4,000 + 1,000) is incurred for each product delivery. The optimal ordering policies and resulting costs for the three products (when the three products are ordered independently) are evaluated using the E(XJ formula (Equation 11.5) and are shown in Table 11-1. 

LOTS ARE ORDERED AND DELIVERED JOINTLY FOR ALL THREE MODELS Given that all three models are included each time an order is placed, the combined fixed order cost per order is given by... 

If the manufacturer in Example 11-7 sold all bottles for 3, it would be optimal for DO to order in lots of 6,325 bottles. The quantity discount is an incentive for DO to order in larger lots of 10,000 bottles, raising both the cycle inventory and the flow time. The impact of the discount is further magnified if DO works hard to reduce its fixed ordering cost to 5 = 4 (from the current 100). Then, the optimal lot size in (he absence of a discount is 1,265 bottles. In the presence of the all unit quantity discount, the optimal lot size is still 10,000 bottles. In this case, the presence of quantity discounts leads to an eightfold increase in average inventory and flow time at DO. 

If // is the holding cost per unit per unit time, p the fixed shortage cost per unit per unit time, and S the fixed order cost per batch, Gallego suggests a batch size of Q, where... 

Gavimeni, S. 2002. Information flows in capacitated supply chains in fixed ordering costs. Management Science 48 (5) 644-651. 

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