chapter 11

Managing Economies of Scale in a Supply Chain Cycle Inventory

• Aims at identifying ways to reduce cycle inventory in a supply chain without raising costs.
• Cycle inventory comes about because buying or producing in large lots allows exploitation of economies of scale

The Role of Cycle Inventory in a Supply Chain

• Lot or batch size refers to the quantity a supply chain stage produces or purchases at a given time.
• Cycle inventory is the average inventory in a supply chain resulting from production or purchases in larger lots than customer demand

Cycle Inventory at Jean-Mart Example

• With demand (D) at 100 pairs of jeans per day and lot sizes (Q) of 1,000 units, it takes 10 days to sell an entire lot.
• For a lot size of 1,000 units, the cycle inventory is Q/2, which equals 500 pairs of jeans.
• Average flow rate typically equals demand in any supply chain.
• Average flow time from cycle inventory equals cycle inventory divided by demand, or Q/2D.

Cycle Inventory Management

• Lower cycle inventory decreases vulnerability to demand changes.
• Lower inventory also lessens working capital needs and saves space.
• Cycle inventory is used to take advantage of economies of scale, reducing costs in a supply chain.
• Material cost (C) is the average price paid per unit purchased and is measured in dollars per unit; increasing lot sizes can decrease per-unit material costs.
• Fixed ordering cost (S) includes costs that don't vary with order size but are incurred each time an order is placed, measured in dollars per lot.
• Holding cost (H) is the cost of carrying one unit in inventory for a specified period (usually one year), and total holding cost increases with lot size.
• Total holding cost can be calculated as H = hC, where h is a fraction of the product's unit cost.

Considerations for Lot-Sizing Decisions

• Average price purchased per unit.
• Fixed ordering cost per lot.
• Holding cost incurred per unit per year.
• The role of cycle inventory is to enable stages in a supply cahin to purchase product in lot sizes

Economies of Scale to Exploit Fixed Costs

• Cycle inventory levels are set to minimize total cost, balancing order and holding costs.
• Estimating fixed order and holding costs is crucial in practice for cycle inventory.
• It's more efficient to quickly approximate costs than to spend excessive time seeking exact figures in cycle inventory models.
• Focus on incremental costs that vary with the lot-sizing decision, ignoring unchanged costs to streamline decision-making.

Components of Inventory Holding Cost

• Cost of Capital: Weighted-average cost of capital (WACC) is vital for products not quickly obsolete.
• Obsolescence Cost: Accounts for value decline of stored products.
• Handling Cost: Includes incremental receiving and storage expenses varying with quantity.
• Occupancy Cost: Reflects space cost changes due to inventory levels.
• Miscellaneous Costs: Covers theft, security, damage, tax, and insurance.

Components of the Cost of Ordering

• Buyer Time: Includes incremental time for placing orders, relevant only when the buyer is fully utilized.
• Transportation Costs: Fixed costs occur regardless of order size.
• Receiving Costs: Incurred regardless of order size.
• Other Costs: Costs unique to each situation should be considered.

Optimal Lot Sizing for a Single Product (Economic Order Quantity)

• Economic Order Quantity (EOQ) is the optimal lot size that minimizes total cost for a single product with steady demand.
• Demand is steady and shortages are not allowed with EOQ.
• Replenishment lead time is fixed while using EOQ
• Annual material, ordering, and holding costs must be considered.
• Total annual cost is the sum of material, ordering, and holding costs.
• Cycle inventory in the system is given by Q*/2, and flow time by Q*/(2D), with optimal lot size.

EOQ formula

• Q* = √(2DS/hC), helps figure the optimal level of ordering frequency.
• Total annual costs are relatively stable around the economic order quantity, so it can be advantageous to adjust to a more convenient lot size.
• If demand increases by a factor of k, the optimal lot size also increases by the factor of √k.
• To reduce the optimal lot size by a factor of k, fixed order must be reduced by k squared.

Production Lot Sizing

• Economic Production Quantity (EPQ) is determined when production occurs at a specified rate, accounting for inventory buildup when production is on and depletion when off.
• Production quantity is the EOQ multiplied by a correction factor that approaches 1 as production rate becomes much faster than demand.

Lot Sizing with Capacity Constraint

• The optimal order size is the minimum of the EOQ and the truck capacity (K).

Aggregating Multiple Products in a Single Order

• Reductions in fixed costs lead to lot size reduction
• Aggregating orders and deliveries across product families lowers fixed transportation costs, lowering overall cycle inventory.
• Other aggregation methods include single deliveries from multiple suppliers or single trucks delivering to multiple retailers.
• When fixed costs are considered it is important to consider recieving and loading costs.

Lot Sizing with Multiple Products or Customers

• A portion of the fixed cost can be related to transporation/recieving
• Three approaches can be considered to organize lot-sizing decisions
• The cost is reduced when product managers orders jointly and not independently.
• The weakness of the second approach is that products with low needs is often aggregated with products with high needs, resulting in hgh order costs
• The third approach that produces best results involves jointly ordering but not containing every product; only a selected subset is delivered in each order. This approach results in lower costs as well as being more complex.

Lots are Ordered and Deliver Independently for each Product

• Involves each product being able to be delivered independently from another product.
• Results in independent ordering and is simple.
• Does not allow for the opportunities to aggregate orders.

Lots are Ordered and Deliver Joinlty for All Three Models

• Given that all three models are included each time an order is placed using this approach, the combined fixed order cost per order is given by S* = S + SL + SM + SH

Lots are Ordered and Delivered Jointly for a Selected Subset of the Products

• Being selective in aggregating orders into a single order.
• It is better to order the low-demand products less frequently than the high demand products, or it adds unnecessary cost.
• When product-specific order costs are small, complete aggregation, whereby every product is included in every order, is very effective.

Pricing Schedules

• Pricing that encourages buyers to make larger purchases
• Includes all unit quantity discounts and marginal unitquantity discounts
• Evaluation is done based on minimizing material, order, and holding costs

All Unit Quantity Discounts

• All pricing happens at a specified breakpoint
• General unit cost decreases as quantity increases

Steps to Evaluate the Economic Order Quantity for each price C

• Evaluate economic order quantity for each price Ci
• Select an order quantity per price
• Calculate annual cost of order
• Select a smaller, more cost effective price when considering all other factors

Quantity Discounts

• Involves both the marginal cost of a unit that decreases at a breapoint.
• Goal is to maximize profits or minimize material, order, and holding costs.
• Overall optimal lot size is obtained.

Why do Suppliers Offer Quantity Discounts

• Lot-size-based quantity discounts increases the level of cycle inventory through the entire supply chain, mainly when the buyer's fixed costs have been reduced
• Circumstances determine if such quantiy discounts will increase supply chain and supplier profits

Quantity Discounts to Increase Total Supply Chain Profits

• This happens when supply is coordinated and decisions retailers and suppliers make maximizes supply chain profits
• A big result of this independence is a lack of coordination because retailer profits may not maximize supply chain profits
• A supply chain can become more profitable if manufactures use appropriate quantity discounts to ensure profits even when acting independently

How to use discounts for Comodity Products

• Market provides product prices.
• Company goal needs to be decrease costs.
• Both the retailer and manufacturer have order costs.
• Only retailer has lot sizing decisions, but that lowers profits.

Impact of Locally Optimal Lot Sizes on a Supply Chain

• Supply chain cost decreases with total ordering sizes
• Retailer cost increases by ordering higher numbers of products, making it harder to lower their stock

Quantity Discounts for Suitable Lot-Size Based Discount

• The supply chain cost can increase if it is not managed correctly, even with discounts in place.
• By managing cost, you provide an incentive to keep quantity level consistent.

How to Market Quantity Discounts for Products

• Have the discounts appeal to the products, which will lead to increased retailer sales
• Two pricing schemes are suggested the manufacturer may use to achieve the coordinate solution and mazmize chain profits even though is acin a way
• Two part tariffs or volume based quantity discount

How to create a Two-Part Tariff

• By charging total profits as an up-front franshise fee
• This is referred to as a two part tariff because the manufacturer sets both the franshise free and wholesales price. Observe that the two part tariff is really volume based quantidy discoun where by the retailers pay by a smaller unit which results into purchase quantities each year for a larger amount

Short-Term Discounting: Trade Promotions

• Manufacturers strategically implement trade promotions by offering retailers a discounted price for a specified time period; which is often done for canned goods.
• The objectives of this is to influence the retailer's actions in a way that aligns with the manufacturer's goal; which is usually achieved through inducing retailers to use price discounts, displays, or advertisements to spur sales.
• It may be a result of trade for performance of the antire supply chain
• Is very reliant on a retailers reaction and response to the manufacturers trade promotion, the retailer has the folling options which include to passs through or customers buy in greater quantities.

Trade Promotion Example

• Some consumers are veryloyal
• Competitiors may do the samet
• Increase the discount price for the end user
• Give promotional discount for every product the scanner recives

Replenishment Policies to Improve Synchronization

• It happens in multi echelon system in order to descrease total cost by coordinateing orders
• Occurs when there is a lack of corrdination in lot sizing decisions
• It can ben synchronizing distribution can lower cycle inventory
• Cross docking is a way to synvronize and lower cost