Question

Hashimoto, Inc. is a Japanese Tier 2 automotive supplier that operates in several parts of the United States. It provides to the Big 3 U.S. automakers, as well as to some foreign automakers, various types of parts used in manufacturing the automobile. The company’s motto is: “Leaders in Reliability, Quality, and Efficiency in the Supply Chain”. It primarily uses several 3rd party logistics firms to meet its transportation needs when providing the OEMs with parts. Consistent with its motto, sometimes, this company has had to use premium shipments in order to eliminate or minimize OEM penalties for parts that are not supplied on time. One company that Hashimoto, Inc. relies heavily on during such times is Dusseldorf Speed Express, Inc. Dusseldorf Speed Express, Inc. is a German company operating in the U.S. and a few other countries. It provides shipping service that guarantees overnight delivery anywhere in the continental United States. The company has various operations centers, called hubs, at airports in major cities across the country. Packages are received at the hubs from other locations, and are shipped to intermediate hubs or to the final destinations. Ms. Sara Trondheim is the manager in charge of Dusseldorf’s Speed Express’ hub in Fresno, California. She is concerned about labor costs at the hub and therefore, she is interested in determining the most effective way to schedule workers. She could schedule workers in such a way as to minimize the number of workers needed, as a surrogate for minimizing labor costs or she could schedule the workers to directly minimize the labor costs. 23 The hub operates 7 days a week, and the number of packages it handles each day varies from one day to the next. Using historical data on the average number of packages received each day, Ms. Trondheim estimates the number of workers needed to handle the number of packages as: Day of Week Number of Workers Required Sunday Monday Tuesday Wednesday Thursday Friday Saturday 98 95 109 68 57 74 59 The package handlers working for Dusseldorf Speed Express, Inc. are unionized and are guaranteed a five-day work week with two-consecutive days off. The handlers work 8 hours per day and are paid $23.75 per hour as base wage (this includes benefits). Because most workers prefer to have Saturday or Sunday off, the union has negotiated bonuses of $45 per day for its members who work on these days. Ms. Trondheim needs to schedule the workers so that there is sufficient enough workers available each day. Consider the following shifts with the prescribed days off. Shift Days off 1 2 3 4 5 6 7 Sunday and Monday Monday and Tuesday Tuesday and Wednesday Wednesday and Thursday Thursday and Friday Friday and Saturday Saturday and Sunday

(a) Determine a schedule of workers that minimizes the total number of workers used per week as a surrogate measure for minimizing total weekly labor cost. How much will this cost the company in labor per week?  

(b) Determine a schedule of workers that directly minimizes the weekly labor cost. How much will this cost the company in labor per week?

(c) How much annual savings (loss) will Mr. Shi incur for using approach (b) instead of approach (a)? Indicate whether it is a savings or loss. There are 52 weeks in a year.

Answer 1

Let Xi be the number of workers starting their -day shift on the ith day of the week where i = 1,2,3,4,5,6,7. The schedule would look like as follows:

Part a) Let Z = X1+X2+X3+X4+X5+X6+X7. The objective is to minimize Z .

The model is given below:

Formulae for the above are:

And the solver Constraints are:

Cost of choosing this strategy is: $118,845

Part b)  The objective is to minimize total cost.

The model is given below:

Formulae are:

Solver constraints remain the same as in part a.

The total cost of choosing this strategy is: $118,215

Part c) Annual savings by choosing strategy b) over strategy a) = 52*(118845 - 118215) = $32,760