NOTE: Exercises below may link to supporting files in a GitHub repository. If you follow such links and (at the GitHub website) right-click a file and choose “Save link as…”, it will appear to download a desired file but may in fact fail. A failure will be discovered when trying to open the downloaded file, usually in MATLAB, and learning that it is not in fact a MATLAB script, function, or SimEvents simulation model.
A remedy is to, at the GitHub website, back up to the project root (e.g. Courseware or Software), choose “Download ZIP” for the entire project, and find the desired file within the project's ZIP. Our apologies for the inconvenience.
A store sells basketballs at a fairly steady rate of 320/yr. The balls are purchased from a supplier for $4/unit. The store estimates that it costs $40 in paperwork and labor to place an order for basketballs, and unit holding costs are computed using a 20% annual interest rate.
BIG PICTURE: (1) practices the cost computation, (2) introduces the EOQ formula, and (3) provides an analytical versus simulation comparison in which results are expected to be quite similar. (4) uses simulation to sweep over Q and visualize the cost components; it would be ideal if we maintained two versions of the SimWrapper - one with run length randomization and one without - but unfortunately we did not build in that flexibility. With no randomness, sawtooth cost curves are expected following from the timing of the last reorder relative to the simulation stop, and to smooth out the curves a random run-length strategy is employed. Randomness in the demand arrival process can also have the same smoothing effect.
A store sells basketballs at a fairly steady rate of 320/yr. The balls are purchased from a supplier for $4/unit. The store estimates that it costs $40 in paperwork and labor to place an order for basketballs, and unit holding costs are computed using a 20% annual interest rate.
BIG PICTURE: This is expected to be a straightforward exercise which explores variations on the plain-vanilla EOQ model. (1) concerns parameter sensitivity, (2) restricts the range of choices for Q, (2) compares EOQ with a commonly-implemented reordering policy (powers of two means that order interval choices are {1, 2, 4, 8, …} weeks), and (3) introduces the common scenario of quantity discounts.
For the football game this Saturday, the Booster Club sees a great opportunity to sell commemorative t- shirts. Shirts can be purchased for $7 each, and the club thinks they can sell for $20 before the game but only $5 after the game.
1. If the demand is normally distributed with a mean of 2500 and a standard deviation of 500, how many shirts should the club purchase?
2. Open the MATLAB script DEMO_Newsvendor_SweepOrderSizeQ_VisualizeExpProfit.m (which controls the function NewsvendorMonteCarloSimulation.m). Configure the model (in the script’s top section, not the simulation function) with the given parameters for purchase cost and sales price, normally-distributed demand with a mean of 2500, and demand variability and salvage price for each row in the table below. Find the empirical Q* (note that you may have to adjust the search range and also the number of replications), add it to the table, and explain any trends in the results.
SCV of Demand | Salvage Value | Q* | E[Profit] | Pr[Profit < 0] |
---|---|---|---|---|
0.1 | 5 | |||
0.5 | 5 | |||
1.0 | 5 | |||
1.5 | 5 | |||
2.0 | 5 | |||
0.5 | 6 | |||
0.5 | 4 | |||
0.5 | 2 | |||
0.5 | 0 |
3. Using the original cost parameters and the demand parameters from (1), use the MATLAB script DEMO_Newsvendor_SweepOrderSizeQ_ VisualizeExpProfit.m to perform a Monte Carlo simulation. For any Q which yields 98% or more of the expected profit at Q*, which value would you choose and why? What factors would change your answer?
BIG PICTURE: (1) is plug-and-chug, and (2) examines Q* trends as various parameter values change. (3)'s purpose is that if Newsvendor concerns a one-time decision, then maximizing expected profit may not be the best decision rule, and reducing risk may also be important. If the decision is recurring and periodic losses are tolerable, however, then more risk may be welcomed in a bid to capture larger-than-expected demand. An example of results:
SCV of Demand | Salvage Value | Q* | E[Profit] | Pr[Profit < 0] |
---|---|---|---|---|
0.1 | 5 | 3465 | 29000 | 0.01 |
0.5 | 5 | 4630 | 27800 | 0.14 |
1.0 | 5 | 5220 | 27600 | 0.24 |
1.5 | 5 | 5900 | 28000 | 0.29 |
2.0 | 5 | 6350 | 28600 | 0.32 |
0.5 | 6 | 5205 | 30000 | 0.11 |
0.5 | 4 | 3910 | 26000 | 0.16 |
0.5 | 2 | 3565 | 23000 | 0.20 |
0.5 | 0 | 3185 | 20500 | 0.22 |
[This assignment is based on Hopp & Spearman chapter 2, problem 11 (ed. 2), which begins with the sentence “Slaq Computer Company manufactures notebook computers.”]
A company is a value-added reseller of consumer technology products. Such products have short market lifetime, so supply contracts for a production run are negotiated one-time and up-front. Demand for a particular product is estimated as normally-distributed with a mean of 10,000 units and standard deviation of 2500 units. The net revenue from a sale is $500, and the main critical part costs $200 with no salvage value.
BIG PICTURE: This should be a straightforward exercise to investigate the Newsvendor model. Simulation is used to explore risk-related performance measures and demand distribution sensitivity. An expected result is that more demand variability decreases expected profit, increases the probability of losing money, and increases Q* (depending on demand's distribution!). The final question also provides practice interpreting empirical CDF plots.
A certain dealership sells pickup trucks, and the average demand is 15 per month. When a truck is sold then a new one is ordered, which takes about ½ month to arrive. The average price of the trucks purchased is $20,000 and the average selling price is $23,000. The dealership figures that it costs about 5% a year to hold trucks in inventory, because in addition to the usual carrying cost they must keep washing them. If a customer wants a truck and none are in stock, trucks can be backordered, but persuading the customer to wait for delivery requires offering a rebate such that the average cost of a backorder is approximately $1500 per year.
BIG PICTURE: (1) through (5) are plug-and-chug using Base Stock analytical approximations. (6) and (7) concern the tradeoff between cost and fill rate, and an expected result is that for the given backorder cost (which is only 1.5 times the inventory holding cost), the fill rate at R* will be unacceptably low, a higher fill rate will be chosen despite the higher cost, and therefore reducing the backorder cost should bring no benefit.
An automotive service department stocks repair parts. For example, part X is known to regularly fail, and about 100 customers need replacements per year. The cost of the part is $250, and it takes about six weeks to get a replenishment order. The service department estimates that it costs about $10 dollars to place and receive an order for the part (regardless of quantity), and that the per-unit inventory cost is about 15 percent per year. The service department also estimates that a backorder costs around $120 per year in lost customer satisfaction, because customers do not leaving their cars in the shop overnight.
BIG PICTURE: (1), (2), (3), and (5) are plug-and-chug using Qr analytical approximations, and using a spreadsheet may help with the computations. An expected result is that analytical and simulation results will generally agree, but may diverge somewhat if the cost surface is relatively flat around the optimum. If true, then one might take advantage of the flat region to increase R or Q and hence the fill rate.