Joanne Smith had just started her position in the logistics planning group at Retail Co. after graduating with her BSBA in Supply Chain Management. Retail Co. was a large retailer specializing in the distribution of hardware goods (e.g., lumber, lawnmowers, hand tools, etc.). One of their biggest challenges was determining the best transportation option to move finished goods from their suppliers manufacturing plants to Retail Co.s distribution centers. In particular, they continually faced decisions regarding whether to utilize direct truck transportation of complete intermodal moves whereby truck trailers would be filled at the suppliers facilities, drayed a short distance to a railroad yard, loaded on a train for the linehaul movement, and then drayed to Retail Co.s distribution centers. This was a problem they faced for the fastest moving items that they ordered in full truckload quantities. They also faced the separate challenge of determining whether to order some of the lower-demand items on a frequent basis and use more expensive LTL shipping versus ordering less frequently and shipping in TL quantities. Joanne had been told that there would be a project coming up that would require the examination of transportation modes, and she was excited to have the opportunity to work on such a project. The morning of her third week on the job she got to work and opened her email and noticed a message from Gary Wilcox (her boss) that asked for her to meet with him in her office at 9:30. When the time came, she left her cubicle and walked over to Garys office.

Joanne, began Gary as she walked in the door. Im not sure how much they told you, but we have been having some issues with two of our suppliers recently. Specifically, one supplier has been providing defective lawn mowers and another has been providing specialty flower pots that are receiving a lot of consumer complaints. As such, corporate is planning on switching to two new suppliers for each of these product lines. The challenge that we are having is that we need to determine the lowest cost option with regard to both transportation and inventory costs for these products. In one case (a new lawnmower supplier), we are going to need to make an analysis of intermodal rail versus trucking. In the other case (a new specialty flower plot supplier), we will need to determine whether we should go with LTL or TL shipping. Where would you start?

Well, lets start with the intermodal rail versus truck case began Joanne, taking out a pad of paper to start making some notes. The first thing we will need to determine is the freight rates for both direct truck transportation and for an intermodal option using rail. The intermodal option will be substantially lower so long as we are looking at a long distance line haul movement. The next factor we will need to consider is the pipeline cost of our inventory. By that, I mean the cost that we will incur while the inventory is in transit. One of the disadvantages of rail transportation is that we will not only have a longer lead time, but rail also tends to have a higher rate of damage, and thus would have a higher in-transit carrying cost. The third cost component is the cycle stock cost, which is calculated as the order quantity divided by two. Fourth, we need to consider the safety stock costs; safety stock will increase if we use the intermodal option because we will be looking at longer more variable lead times. Lastly, we will want to consider backorder costs stemming from not fulfilling all demand during a lead time.

Hold on one second, said Gary. What do you mean backorder costs? We currently operate using an S1 probability of no stockout policy where we plan on a 90 percent probability of no stockout service level.

Ah, we are going to need to change that then if we want to compare different transportation modes. I remember one of my professors explaining that a limitation of using probability of no stockout is that it does not work well when we are considering a different number of lead times in a given year[1]. Since rail is slower than truck, we are going to be managing fewer lead times in a given year. As such, we would be comparing apples and oranges if we tried to use a 90% probability of no stockout. However, if we would use, say, a 99% fill rate, then we would be able to make direct comparisons.

OK, that makes sense to me, said Gary. For the lawnmower setting, the order quantity is going to be fixed to a full 53-foot truckload or containerload quantity each time given that we sell a lot of lawnmowers. For both modes we will be ordering one truckload or container at a time. As such, it sounds like the biggest concern is to look at how much more transportation is going to be if we use the truckload option versus the additional cycle stock, pipeline inventory, and safety stock we will need to carry with using rail. Gary paused to write down a few notes. Now, lets talk about the other supplier and the LTL/TL decision. What are your thoughts?

In this case, we are looking at determining the order quantity that will minimize the sum total of transportation cost, cycle stock carrying cost, safety stock carrying cost, and backorder/lost sales cost. In this instance, our pipeline stock is going to be so similar across LTL and TL settings that I think we can remove it for simplicity. The challenge with solving this problem is that Im going to need to have information on freight rates for the specialty flower pots in order to determine what the transportation cost will be for each order quantity. Plus this will actually require me to solve for the order quantity, so Im going to need to rely on a spreadsheet optimization tool to take care of things. Joanne paused, thinking about the challenge that it would be to assemble such a tool. The key thing will be to incorporate the nonlinear nature of transportation cost as a function of shipment weight, which in turn will be a function of the order quantity.

Perfect, once I get all the information I need Ill get started working on the project.

Information and Data

A week later Joanne was sitting down in front of her computer organizing all of the materials that Gary had sent her. She had to admit, she was feeling a bit overwhelmed thinking about all of the moving parts and pieces of information she had been given. First the data on the lawnmowers:

50 lawnmowers fit within each 53 trailer or container. The companys projection was that it would sell 4000 lawnmowers over the next year. The standard deviation of forecast error for lawnmowers is 5 units per day. Assume there are 360 days in a year

Each lawnmower cost Retail Co. $125 per unit. They sold lawnmowers at an average price of $250 per unit.

The price to place an order is $25, excluding transportation cost. It takes the lawnmower supplier an average of 1 day to receive the order, process it, and load the truck trailer(s) or intermodal containers.

The companys annual inventory carrying cost for lawnmowers in stock is 25%.

The companys annual inventory carrying cost for lawnmowers in transit for the direct truckload move is 15% per year; it is 20% per year for the intermodal movement.

The estimated backorder cost per stockout is 40% of the lawnmowers retail value.

The target fill rate is 99%.

The average transit time for a full truckload direct shipment is 2 days with a standard deviation of 0.5 days.

The average transit time for a rail shipment, including the intermodal drayage moves, is 5 days with a standard deviation of 1.5 days.

Lead time demand is assumed to be approximately normally distributed.

Demand per day is assumed to be independent during a lead time.

Assume lead time and demand are uncorrelated

The distance from the lawnmower suppliers manufacturing plant to Retail Co.s distribution center is 800 miles by truck. Due to circuity, the distance is 875 miles for the intermodal shipment. The per mile cost for a full truckload shipment is $2.10 per mile. The all-inclusive cost for the intermodal movement is $1.75 per mile per container.

Joanne took a few minutes to try and process all of these pieces of information. She then took out her old lecture slides and looked at the following complete formula for estimated total annual logistics cost[2] (ETALC):

ETALC= [f(Q)*(1-d)*R*w/100]+[T *D *V* Y]+[Q/2 +(-LTD)* V * W]+[A* R/Q]+[ES * B* V *R/Q]

fQ = mathematical function representing freight rates in cost per 100 pounds

d = discount rate for freight

R = annual demand in units

w = weight of one unit of product

T = average transit time in days for a given transportation mode

D = average demand in units per day

V = value of the item in dollars

Y = carrying cost percentage for in-transit inventory for that transportation mode

Q = order quantity

= reorder point

LTD = expected lead time demand, calculated as average demand multiplied by average lead time

W = carrying cost percentage for inventory on hand

A = fixed administrative cost per order

ES = expected units short during a lead time

B = backorder percentage charge based on value for the item

OK, thought Joanne. Lets start to break this equation down. Consider the first term as it applies to this problem. fQ1-dRw100 represents the total transportation cost for a year. In the lawnmower case, I dont need to worry about any functions for pricing, discounts, or the weight of the shipment. All I need to concern myself with is [1] calculating the transportation cost for a single shipment and [2] multiplying it by the number of orders that will be placed in a given year. This is straightforward, as I just need to multiply the number of miles for a shipment by the $/mile of the shipment. The second term TDVY represents the cost of carrying pipeline stock for the given transportation mode. I need to be sure to change the value for average transit time and carrying cost for the two modes. The third term Q2+-LTDVW captures the carrying cost for cycle stock and safety stock. Now, the key thing Im going to need to do is calculate the amount of safety stock necessary to meet the 99% fill rate target, and the reorder point will equal the expected lead time demand plus safety stock. The fourth term ARQ represents the annual ordering cost. Lastly, the fifth term ESBVRQ represents the expected backordering costs. Since I will know the average lead time demand with both transportation modes and I know the fill rate, I can back into the units short (ES) by (1-FR) LTD. That will give me all the information I need to calculate all of the costs to make a decision regarding which strategy is preferred. The first step is going to be to calculate the order quantity under each transportation mode and the associated safety stock levels to determine the expected units short. I can then determine the number of orders a year to calculate transportation costs and ordering costs.

Question:

Gary wants you to conduct a sensitivity analysis to how a change in annual demand for flower pots will influence optimal order quantities, inventory turnover ratio, inventory cost per unit, transportation cost per unit, and total logistics costs per unit. To do this, vary the annual demand from 1000 units to 10,000 in sensible increments (e.g., 1000 units at a time) and resolve the optimization for different values of annual demand. For example, change the annual demand to 1000 units, solve for the optimal order quantity, and report the statistics that Gary requested. Then change annual demand to 2000 units and solve again, etc.

Use excel to solve the question