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Supply Chain Transportation Coordination Book: Supply Chain Management, Chopra, Meindl, & Kalra, [6th Ed] Chapter 14: Transportation in a Supply Chain Chapter 10: Coordination in a Supply Chain Indranil Biswas Operations Management Group Office: Chintan, Room No. 211, Tel. 6663 Email: [email protected]

Supply Chain Transportation: Trade off through inventory aggregation Q 14-3: HighMed is a manufacturer of medical equipment based out of Madison, USA and directly sells her products to the doctors in USA. The company divides USA in 24 territories, each with its own sales team. The products sold fall into 2 categories: HighVal and LowVal Territory-wise demand and other details of the products are given below: HighVal: Weekly Demand μH = 2, σH = 5, weight = 0.1 lbs, cost = $200 LowVal: Weekly Demand μL = 20, σL = 5, weight = 0.04 lbs, cost = $30 Cycle Service Level = 0.997, Holding Cost = 25% of price Product inventories are maintained locally and replenished every 4 weeks (i.e. Reorder Interval, T = 4 weeks) by UPS. Details of UPS delivery are: Lead Time = 1 week, Per lb Cost = $(0.66 + 0.26x) where x is the number of lb shipped/ required to be shipped. In addition to the current arrangement, the management is also considering the following 2 options. Option A. Keep the current structure but replenish inventory once a week rather than once every four weeks by UPS. Option B. Eliminate inventories in the territories, aggregate all inventories in a finished-goods warehouse at Madison, and replenish the warehouse once a week by FedEx. Details of FedEx delivery are: Lead Time = overnight, Per lb Cost = $(5.53 + 0.53x). The factory requires 1 week lead time to replenish goods at Madison and after aggregation, average customer order for HighVal is 1 and that of LowVal is 10. What should HighMed do?

In this case we calculate reorder level (ROL) ROL = lead time demand + safety stock  ROL =D × L + sD × sqrt (L) In this case, the service level is calculated as: Service level = Pr (LT×D < ROL) = Pr (LT 0 𝑎𝑛𝑑 𝑥 > 0 ⇒ 𝑀𝐶 𝑥 < 𝐴𝐶(𝑥)

From the aforementioned inequality we can say that economies of scale exists in the cost structures of both UPS and FedEx. Evaluation of the current scenario Solving this problem requires application of the concepts discussed in (Fixed) Periodic Review Policy of Inventory. Part A: Calculation of Inventory Carrying Cost for HighMed Number of territories (n): 24. Territory-wise demand and subsequent calculations are as follows: HighVal: Weekly Demand μH = 2, σH = 5, 𝑤𝐻 = 0.1 lbs, 𝑝𝐻 = $200, ℎ𝐻 = 𝛼𝑝𝐻 = 0.25x$200 = $50 LowVal: Weekly Demand μL = 20, σL = 5, 𝑤𝐿 = 0.04 lbs, 𝑝𝐿 = $30, ℎ𝐿 = 𝛼𝑝𝐿 = 0.25x$30 = $7.5 Cycle Service Level (CSL) = 0.997, (Fixed) Reorder Interval T = 4 weeks, Lead Time, l = 1 week Average Lot Size(s): HighVal: QH =T x μH = 4x2= 8; LowVal: QL =T x μL = 4x20= 80 Safety Inventories: HighVal: ssH = 𝐹 −1 𝐶𝑆𝐿 × 𝑇 + 𝑙 × 𝜎𝐻 =NORMSINV(0.997)× 4 + 1 × 5 = 30.7 𝑎𝑝𝑝𝑟𝑜𝑥 LowVal: ssL = 𝐹 −1 𝐶𝑆𝐿 × 𝑇 + 𝑙 × 𝜎𝐿 =NORMSINV(0.997)× 4 + 1 × 5 = 30.7 (𝑎𝑝𝑝𝑟𝑜𝑥)

Supply Chain Transportation: Trade off through inventory aggregation Part A: Calculation of Inventory Carrying Cost for HighMed (contd.) Cycle Inventories: HighVal: CIH =QH /2 = 8/2 = 4; LowVal: CIL =QL /2 = 80/2 = 40 Total Inventories: HighVal: TIH = CIH + ssH = 4 + 30.7 = 34.7; LowVal: TIL = CIL + ssL = 40 + 30.7 = 70.7 Total Inventory Carrying Cost(s): HighVal: ICCH = hH x TIH = $50 x 34.7 = $1735; LowVal: ICCL = hL x TIL = $7.5 x 70.7 = $530.25 Therefore, across all 24 territories we have, Annual Inventory Holding Cost = ($1735 + $530.25) x 24 = $ 54,366 Part B: Calculation of Shipment Cost for HighMed Average Replenishment Orders: This value is equal to Average Lot Sizes. Therefore we have, HighVal: QH =T x μH = 4x2= 8; LowVal: QL =T x μL = 4x20= 80 Total weight of the shipment: QH x wH + QL x wL = (8 x 0.1 + 80 x 0.04) lbs = 4 lbs Shipping Cost per Replenishment Orders: $(0.66 + 0.26 x 4) = $ 1.70 As Reorder Interval, T = 4 weeks, therefore in 1 year Total Number of Shipments = 52/ 4 = 13 Such Shipment has to happen across all 24 territories. Thus, Annual Shipment Cost = $ 1.70 x 13 x 24 = $ 530.4 Therefore, Total Cost to HighMed due to current Replenishment & Transportation Policy: $ 54,366 + $ 530.4 = $ 54,896.4

Supply Chain Transportation: Trade off through inventory aggregation Evaluation of Option B Solving this problem requires application of the concepts discussed in (Fixed) Periodic Review Policy of Inventory and Inventory Pooling. Part A: Calculation of Inventory Carrying Cost for HighMed In this case, all the items are stocked centrally at Madison. Therefore, Number of territories (n): 1. Demand and subsequent calculations are required to be done on aggregate basis for the entire country. Other relevant information are: Cycle Service Level (CSL) = 0.997, (Fixed) Reorder Interval T = 1 week, Lead Time, l = 1 week HighVal: Weekly Countrywide Calculation: μH = 2x24 = 48, σH = 5x sqrt (24) = 24.49, 𝑤𝐻 = 0.1 lbs, 𝑝𝐻 = $200, ℎ𝐻 = 𝛼𝑝𝐻 = 0.25x$200 = $50 LowVal: Weekly Countrywide Calculation: μL = 20x24 = 480, σL = 5x sqrt (24) = 24.49, 𝑤𝐿 = 0.04 lbs, 𝑝𝐿 = $30, ℎ𝐿 = 𝛼𝑝𝐿 = 0.25x$30 = $7.5 Average Lot Size(s): HighVal: QH =T x μH = 1x48= 48; LowVal: QL =T x μL = 1x480= 480 Safety Inventories:

HighVal: ssH = 𝐹 −1 𝐶𝑆𝐿 × 𝑇 + 𝑙 × 𝜎𝐻 =NORMSINV(0.997)× 1 + 1 × 24.49 = 95.2 𝑎𝑝𝑝𝑟𝑜𝑥 LowVal: ssL = 𝐹 −1 𝐶𝑆𝐿 × 𝑇 + 𝑙 × 𝜎𝐿 =NORMSINV(0.997)× 1 + 1 × 24.49 = 95.2 (𝑎𝑝𝑝𝑟𝑜𝑥) Cycle Inventories: HighVal: CIH =QH /2 = 48/2 = 24; LowVal: CIL =QL /2 = 480/2 = 240 Total Inventories: HighVal: TIH = CIH + ssH = 24 + 95.2 = 119.2; LowVal: TIL = CIL + ssL = 240 + 95.2 = 335.2

Supply Chain Transportation: Trade off through inventory aggregation Total Inventory Carrying Cost(s): HighVal: ICCH = hH x TIH = $50 x 119.2 = $5960 LowVal: ICCL = hL x TIL = $7.5 x 335.2 = $2514 Therefore, Annual Inventory Holding Cost = ($5960 + $2514) = $ 8,474 Part B: Calculation of Shipment Cost for HighMed Average Replenishment Orders: This value is equal to actual customer order. From the question we have, HighVal: ROH = 1; LowVal: ROL = 10 Total weight of the shipment: ROH x wH + ROL x wL = (1 x 0.1 + 10 x 0.04) lbs = 0.5 lbs Shipping Cost per Replenishment Orders: $(5.53 + 0.53 x 0.5) = $ 5.795 To meet weekly demands (2 and 20) number of shipments required in a week is = 2/1 = 2 As Reorder Interval, T = 1 week, and in 1 week number of required shipment is 2, therefore in 1 year Total Number of Shipments (for 1 location) = (52/ 1) x 2 = 52 x 2 = 104 Such 104 shipments are required across all 24 territories, hence Total Number of Shipments required for HighMed = 104 x 24 = 2496 Thus, Annual Shipment Cost = $ 5.795 x 2496 = $ 14,464.32 Therefore, Total Cost to HighMed due to current Replenishment & Transportation Policy: $ 8,474 + $ 14,464.32 = $ 22938.32

Supply Chain Transportation: Trade off through inventory aggregation

Number of stocking locations Reorder interval (weeks) HighVal Cycle inventory HighVal safety inventory HighVal inventory LowVal cycle inventory LowVal safety inventory LowVal inventory Annual inventory cost Shipment type Shipment size Highval LowVal Shipment weight (lbs) Number of shipments / year Annual transport cost Total Annual Cost

Current Scenario Option A Option B 24 24 1 4 1 1 96 24 24 737.3 466.3 95.2 833.3 490.3 119.2 960 240 240 737.3 466.3 95.2 1697.3 706.3 335.2 $ 54,395 $ 29,813 $ 8,473 Replenishment Replenishment Customer order 8 80 4 13 $ 530 $ 54,926

2 20 1 52 $ 1,148 $ 30,961

1 10 0.5 2496 $ 14,464 $ 22,938

Supply Chain Transportation: Trade off through inventory aggregation Extension Problem: If HighMed can convince the customers to order according to weekly average demand of one territory (i.e. ordering 2 HighVal instead of 1 and 20 LowVal instead of 10), how does it change your optimal cost calculation? Answer: Annual inventory cost remains unchanged. Therefore, Annual Inventory Holding Cost = ($5960 + $2514) = $ 8,474 Calculation of Shipment Cost for HighMed changes and it is given below: Average Replenishment Orders: This value is equal to weekly average demand from each territory. From the question we have, HighVal: ROH = 2; LowVal: ROL = 20 Total weight of the shipment: ROH x wH + ROL x wL = (2 x 0.1 + 20 x 0.04) lbs = 1.0 lbs Shipping Cost per Replenishment Orders: $(5.53 + 0.53 x 1) = $ 6.06 To meet weekly demands (2 and 20) number of shipments required in a week is = 1 As Reorder Interval, T = 1 week, and in 1 week number of required shipment is 1, therefore in 1 year Total Number of Shipments (for 1 location) = (52/ 1) x 1 = 52 x 1 = 52 Such 104 shipments are required across all 24 territories, hence Total Number of Shipments required for HighMed = 52 x 24 = 1248 Thus, Annual Shipment Cost = $ 6.06 x 1248 = $ 7,562.88 Therefore, Total Cost to HighMed due to current Replenishment & Transportation Policy: $ 8,474 + $ 7,562.88 = $ 16,036.88

Transportation in Supply Chain: Cross Docking Amazon’s China subsidiary has received United States approval to ship ocean freight for other companies. That could make it cheaper and easier for sellers on Amazon to move goods from Chinese factories to Amazon’s American warehouses. With this move Amazon China could start “cross-docking” goods in United States ports “for direct injection into Amazon’s courier network.” –NY Times Report (January 14, 2016)

Wal-Mart receives goods from its vendors at loading docks and its massive fleet of trucks take these to the warehouses, which are usually located in the range of 130 miles from the stores. For distribution purposes, Wal-Mart uses the technique of cross-docking to reduce or (in some cases) eliminate the intermediate storage costs. – (Too many articles have reported this news!)

Cross Docking – Points to remember Cross-docking refers to the direct transfer of goods from vendor end (incoming shipments) to warehouses (via outgoing vehicles) without any storage in between.

This practice can serve different goals: (i) Consolidation of shipments (Capacity utilization of vehicles) (ii) Shorter delivery lead time (iii) Reduction of total costs (Delivery + ICC) (iv) Usage of entire capacity of the truck ensures less emission Note: Cross-docking is probably not the best strategy in every case and in all circumstances. Two major factors influence the decision of cross docking and they are as follows: (1) Product Demand Rate: If there is an imbalance between the incoming load and the outgoing load, cross-docking will not work well. Hence, goods that are more suitable for cross-docking are the ones that have demand rates that are more or less stable (e.g. grocery and regularly consumed perishable food items). For these products, the warehousing and transportation requirements are much more predictable, and consequently the planning and implementation of crossdocking becomes easier.

Cross Docking – Points to remember (contd.) (2) Unit Stock-out Cost: As cross-docking minimizes the level of inventory at the warehouse, the probability of stock-out situations is higher. If the unit stock-out cost is low, the benefits of cross-docking can outweigh the increased stock-out cost, and so cross-docking can still be the preferred strategy.

Product Demand Rate

Unit Stock-out Costs

Stable & Constant High

Low

Unstable/ Fluctuating

Cross-docking can be implemented with proper systems & planning tools

Traditional Distribution preferred

Cross-docking preferred

Cross-docking can be implemented with proper systems & planning tools

It’s OSCAR Time! 

Supply Chain (Inventory) Coordination “The more inventory a company has, the less likely they will have what they need” – Taiichi Ohno All business entities are worried about their inventory levels. For most businesses, inventories represent a substantial portion of what the firm owns. Changes in inventory levels will result in significant changes in both gross as well as net profit levels. Changes in inventory levels tend to be indicative of broader business trends and therefore warrant close attention.

How does Wal-Mart continue to manage Every Day Low Price (EDLP)? Due to its large size, Wal-Mart enjoys strong negotiating power over her vendors. Wal-Mart offers long-term and high-volume purchase contracts to her vendors, and is therefore able to negotiate the best prices. Several vendors are entirely dependent on Wal-Mart for their business, which allows the retailer to squeeze the best possible agreement from them. Wal-Mart employs vendor-managed inventory (VMI) method, where her suppliers are responsible for managing their goods inside the retailer’s (WalMart) warehouses. As a result, inventory management becomes stronger and more vendor specific, which results in 100% order fulfillment. This strategies prevent the issues of inventory shortage or surplus, which helps in reducing the cost of goods and services. Her efficient supply chain has allowed Wal-Mart to become the price leader in the U.S. retail market. Forbes Report (September 9, 2014)

Case 1: Decentralized Supply Chain [No VMI Agreement between Supplier & Retailer] Supplier (Produces FG)

Supplier’s per unit production cost: s

w

Retailer (Sells FG)

Buyer’s per unit cost: c

Final Goods Market

Market Demand: q = a – p

Retail Price: p = a – q = p(q)

w: Supplier’s per unit selling price As in this model we are analyzing the effect of VMI on Supply Chain structure, therefore we are going to explicitly incorporate the associated inventory costs (i.e. Ordering Cost & Inventory Carrying Cost). Total Inventory Cost For this purpose, we assume the following: of the Supplier: AS : Setup Cost of the Supplier hS : Per unit Inventory Carrying Cost of the Supplier   q   QS      TC S QS    AS  hS  AB : Ordering Cost of the Retailer Q 2     S  h B : Per unit Inventory Carrying Cost of the Retailer Total Inventory Cost Q S : Economic Order Quantity of the Supplier of the Retailer: QB : Economic Order Quantity of the Retailer    

q Q     B hB  TC B QB    AB    QB   2  

Case 1: Decentralized Supply Chain [No VMI Agreement between Supplier & Retailer] (Contd.) Supplier (Produces FG)

w

Supplier’s per unit production cost: s

Retailer (Sells FG)

Final Goods Market

Retail Price: p = a – q = p(q)

Buyer’s per unit cost: c

We can obtain, EOQ of the Supplier: QS* 

Market Demand: q = a – p

2 AS q hS

  Q  

Optimal Total Inventory Cost: TCS QS*  2 AS hS q Similarly we obtain:

QB* 

2 AB q hB

TCB

* B

2 AB hB q

If the Supplier orders according to her EOQ then her profit level is given by:

 S  w  s q  TCS QS*   w  s q  2 AS hS q

If the Retailer also orders according to her EOQ then her profit level is given by:

 B  pq  (w  c)q  TCB QB*   pq  (w  c)q  2 AB hB q

Total Profit of the Supply Chain is:  S   B  pq   s  cq 

 2A h q  S

S

2 AB hB q



Case 2: Decentralized Supply Chain [VMI Agreement between Supplier & Retailer] Supplier (Produces WIP)

Supplier’s per unit production cost: s

w

Buyer (Produces FG)

Final Goods Market

Buyer’s per unit production cost: c

Market Demand: q = a – p

Retail Price: p = a – q = p(q)

1. The Retailer enters into VMI agreement with the supplier. Therefore the supplier maintains inventory at the Retailer’s end. 2. All the inventory related costs (of the retailer) are carried by the supplier. 3. As the incurred cost level increases, the supplier charges the buyer by a different per unit wholesale price level

wVMI : Supplier’s per unit wholesale price under VMI agreement Therefore, assuming supplier & retailer order according to their EOQ, we can calculate their profit level(s) as follows:

 S VMI  wVMI  sq  2 AS  AB hS  hB q  B VMI  pq   wVMI  c q

Observe: 1. The Retailer’s profit level does not incorporate inventory cost at all 2. The supplier is carrying the entire inventory cost, as well as the associated risk 3. Such an agreement can be enforced if and only if Retailer holds high bargaining power

Comparison between VMI & Non-VMI Supply Chains Now, we compare the overall supply chain profits of VMI and non-VMI supply chain. In order to get into comparable terms we assume that the supplier follows the EOQ of the * Retailer, i.e. (Q B )

 S VMI   B VMI    S   B   





2 AB hB q  TCS QS  QB*  2 AS  AB hS  hB q

   q   hS  *     2 AB hB q   AS  *    QB    2 AS  AB hS  hB q    Q B   2     A  h  AB hB q  AS hS       2 AB hB q 1  S 1  S  2  AB hB  AB  hB   1   AS  2  hS 1    1   2 AB hB q 1   2 AB   hB 

Thus algebraic simplification yields:

  

1 2

2

  0  

 S VMI   B VMI    S   B 

Observe: We have arrived at this conclusion without optimizing either supplier’s profit or retailer’s profit

Example Problem A supply chain consists of a supplier and a retailer. The details about ordering costs and holding costs of these firms, marginal costs of production, annual demand, wholesale prices are as follows: AS  45; AB  3; hS  8; hB  1; q  60,000; p  50; s  10; c  5; w  15, wVMI  20 Assume that, without VMI agreement, the supplier follows retailer’s EOQ decision. Calculate, the increase in profit level by implementing VMI Comment whether the aforementioned wholesale price (with VMI) is a correct price point. If we implement VMI, the supply chain profit increases by: 2

 A h  1 2 AB hB q  1  S  1  S  = 300 2 AB hB  

Without VMI Supplier’s profit: (15 – 10)x60,000 – [45x(60,000/600)+(8/2)x600] = 2,93,100 (as EOQ of retailer = 600) Retailer’s profit: {50 – (15+5)}x60,000 – sqrt. (2x3x1x60,000) = 17,99,400 With VMI Supplier’s profit: (20 – 10)x60,000 – sqrt. [2x(45+3)x(8+1)x60,000] = 5,92,800 (!!!) Retailer’s profit: {50 – (20+5)}x60,000 = 15,00,000 (!!!) Now calculate using w(VMI) = 15.005 Supplier’s profit: 2,93,100 Retailer’s profit: 17,99,700 (retailer captures that extra 300!)

Points to remember about VMI 1. VMI will reduce the total inventory-related cost of the whole system (Retailer and Supplier together). 2. VMI will increase the supplier’s inventory-related costs. 3. In the short-term, the buyer’s profit level will always be increased after VMI. The supplier’s profit could be decreased. Supplier’s profit level can increase only if she can enforce a suitable contractual agreement. 4. The purchase quantity of the Retailer with VMI agreement is higher than that without VMI agreement.

How to copy the Wal-Mart model?

Although Wal-Mart’s methodologies are well known to other logistics providers, just a handful of retailers have achieved them. Copying the model is not easy because of the high initial costs, huge inventory levels involved, and assurance of high sales. Simply, no other chain can attain this scale. Rank

Store

1 2 3 4 5

Wal-Mart Kroger Costco Target The Home Depot

2013 U.S. Sales Sales Growth (000) (’13 vs. ’12) $334,302,000 $93,598,000 $74,740,000 $71,279,000 $69,951,000

1.7% 1.6% 5.2% – 0.9% 6.6%

Data Source(s): Forbes, IBT

How is this relevant in Indian Retail scenario? Marico's organizational goal of ‘constant innovation’ led it to focus on the introduction of a large number of newer brands in its supply chain. The company also anticipated that each of these new products might not get adequate attention from dealers because of (initial) smaller volumes and uncertain demand.

Marico solved this problem by introducing Vendor Managed Inventory (VMI) system whose primary objective was to provide greater support to newer brands at the dealer end and not solely reduce inventory. Attempts to replicate this across several sectors like retail, electronics components, textiles and automobile manufacturing in India have taken place over the last 10 years with Marico Industries Limited, Shoppers Stop, Future Group, Nokia India, Maruti Udyog Limited, Mahindra & Mahindra

Indian Railway Budget 2016

Mission PACE (Procurement and Consumption Efficiency): This mission aims to improve procurement and consumption practices of Indian Railways to improve the quality of goods and services. It will introduce a culture of optimum usage by adopting practices such as Vendor Managed Inventory, new procedures for identification and disposal of scrap, etc. Adoption of new procurement and consumption practices will lead to an estimated saving of more than Rs 1,500 Crore in 2016-17.

Numerical Problem from Supply Chain Coordination Question: A retailer faces market demand: q = 100 – 2p, where p is the retail price of the product. The marginal production cost of the retailer is $1/unit. The retailer procures the product from a supplier. The supplier has a marginal production cost: $3/ unit and she sells the product to the retailer at a price point: $5/ unit. (i) Calculate the optimal retail price. (ii) Calculate the profits made by the retailer and the supplier. (iii) Comment whether the wholesale price is optimal.

Answer (i): The retailer’s profit function is: R  p  1  5100  2 p   2 p  650  p  The optimal retail price set by the retailer is calculated from the first order condition as follows:  R  250  p    p  6  0  2 p  56  p*  28 p Answer (ii): The retailer’s profit:  R  28  6 100  2  28  22  44  968

The supplier’s profit:  S  w  s q  w  s 100  2 p   5  3100  2  28  2  44  88

Answer (iii): The wholesale price ($5/ unit) is not optimal as the optimal wholesale price should be: 1 1 100  2  3  1  1  104  26 w  a  bs  c   2b 22 4 Under optimality the order quantity should be: 1 1 1 q*  a  bs  c   100  2  3  1   92  23 4 4 4 * a  q 100  23 p*    38.5 b 2

Numerical Problem from Supply Chain Coordination (contd.) At p = 38.5 and q = 23, the profits of retailer and supplier are as follows: 1 a  bs  c 2  1 100  2  3  12  264.5 R  16b 16  2 1 1 100  2  3  12  529  S  a  bs  c 2  8b 82 Cross verification of the result:  S  w  s q  26  3  23  529  R  p  w  c q  38.5  26  1 23  264.5 Observation: Though the given wholesale price is not optimal from the point of view of the supplier, it helped the overall supply chain to gather more profit compared to the optimal case, as seen.  DC   S   R  529  264.5  793.5

Previously computed total profit was:  DC   S   R  88  968  1056 The centralized profit in this case is: 1 1 100  2  3  12  1058  C  a  bs  c 2  4b 42 Observation(s): (a) If we observe the given problem statement, we can see that, w ≈ s. (b) It made the supply chain behave (almost) like a centralized supply chain. (c) As a result the overall supply chain profit increased even compared to an optimal decentralized supply chain. (d) However, the profit of the supplier was heavily reduced and that of the retailer increased compared to an optimal decentralized supply chain.