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Principles of Inventory Management: When You Are Down to Four, Order More

John A. Muckstadt, Amar Sapra

Chapter 3

Power-of-Two Policies - all with Video Answers

Educators

Chapter Questions

Problem 1

Compute the optimal power-of-three reorder interval for a single-stage system.
Show that the cost of this policy is at most 15.47% more than the cost of the optimal
policy.

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Problem 2

Compute the optimal power-of-three reorder interval for a single-stage system.
Show that the cost of this policy is at most 15.47% more than the cost of the optimal
policy. Compute the optimal power-of-three reorder interval for a single-stage system.
Show that the cost of this policy is at most 15.47% more than the cost of the optimal
policy.

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03:28

Problem 3

Derive inequality (3.7).

James Kiss
James Kiss
Numerade Educator

Problem 4

Consider a five-stage serial system. Suppose the on-hand holding costs are as follows: $h_1=4.5, h_2=4.25, h_3=3, h_4=2$, and $h_5=0.5$ (in $\$$ per unit per year). Compute the echelon holding cost for each stage.

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Problem 5

For a four-stage serial system, compute the on-hand holding costs if the echelon holding costs are $h_1^{\prime}=1, h_2^{\prime}=1.25, h_3^{\prime}=0.4$, and $h_4^{\prime}=0.6$ (in $\$$ per unit per year).

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Problem 6

A regional retail chain receives shipments from manufacturers at its central warehouse and in turn sends the shipments to the retail stores. Consider a miniature version of this problem having three retail stores and a single item, ceiling lamps. The annual demand for ceiling lamps is 100 at store 1,80 at store 2 , and 110 at store 3 . The holding cost rate at each of the stores is .20 and the cost of a ceiling lamp at the time of entering a store is $\$ 15$ per unit. This cost includes the original purchasing cost and all the value added. The value can be added, for example, by transportation, testing, unpackaging, etc. The holding cost rate for the central warehouse is .15 and the cost of an item at the time it enters the warehouse is estimated to be $\$ 12$. The fixed cost to place an order is $\$ 100$ for the warehouse and $\$ 10$ for the retail stores. Assuming a base planning period of 2 weeks and a year consisting of 52 weeks, determine the optimal PO2 policy for each of the retail stores and the central warehouse.

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Problem 7

In a serial system, is it enough to constrain the reorder intervals such that $T_i \geq T_{i-1}$ to ensure nestedness?

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05:42

Problem 8

A deli orders three different types of patties (vegan, tuna, and beef) from a local manufacturer for use in sandwiches. The demand for vegan, tuna, and beef patties is 20 , 30 , and 125 per week, respectively. The order placement is rather easy; the store manager just goes to the manufacturer and collects as many patties as he wants. Each trip takes 30 minutes; assume the worth of the manager's time to be $\$ 30$ per hour. The store manager, being a conscientious person, ensures that the patties are safe for consumption. This takes 30 minutes per order of the vegan and tuna patties and 20 minutes per order of the beef patties. This task is performed by an hourly-wage employee who earns $\$ 7$ per hour. Taking the holding cost of these patties to be $\$ 0.80 /$ patty/year, determine the optimal PO2 replenishment policy. Assume a base planning period of a week.

Carson Merrill
Carson Merrill
Numerade Educator

Problem 9

Suppose the demands for each of the three products in the last problem were doubled. Compute the new optimal PO2 policy.

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Problem 10

Consider the system in Section 3.3.1. Suppose the demands in the regional warehouses are not identical, but are equal to $100,125,200,80,150$, and 225 , respectively. Assume the fixed cost and holding costs are as in the example. Determine the optimal PO 2 reorder intervals assuming the base planning period is 2 weeks.

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Problem 11

Source: http://bmrc.berkeley.edu/courseware/ICMfg92/text/fab-6) There are four major manufacturing stages in the production of an Integrated Chip (IC)
- Wafer Fabrication
- Wafer Probe
- Chip Assembly
- Chip Test

Consider an IC that is used in a mature product and whose demand for the next year is projected to be 100,000 units. The setup cost for the four processes is $\$ 500, \$ 260, \$ 425$, and $\$ 700$ per setup, respectively. The on-hand inventory holding cost at these stages is equal to $\$ 1, \$ 1.50, \$ 1.75$, and $\$ 2$, respectively. Assuming the production system to be a serial system, determine the optimal PO 2 policy. Assume a base planning period of a week.

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41:50

Problem 12

Let $f: \Re \rightarrow \Re$ be a convex function and let $x_1, x_2$, and $x_3$ be three points in its domain such that $x_1 \leq x_2 \leq x_3$. Show that $f\left(x_2\right) \leq \max \left\{f\left(x_1\right), f\left(x_3\right)\right\}$.

Oswaldo JimƩnez
Oswaldo JimƩnez
Numerade Educator

Problem 13

Show that the joint replenishment problem can be represented as a serial system problem.

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